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THE RATE OF INTEREST 




THE MACMILLAN COMPANY 

NEW YORK • BOSTON • CHICAGO 
ATLANTA • SAN FKANCISCO 

MACMILLAN & CO., Limitbd 

LONDON ■ BOMBAY • CALCUTTA 
MELBOURNE 

THE MACMILLAN CO. OF CANADA. Ltd. 

TORONTO 



'i 

1 



THE RATE OF INTEREST 



ITS NATURE, DETERMINATION AND 

RELATION TO ECONOMIC 

PHENOMENA 



BY 

IRVING FISHER, Ph.D. 

PR0FK880K OF POLITICAL ECONOMY, YALE UNIVERSITY 



N(tD gorft 
THE MACMILLAN COMPANY 

1907 

All rights reserved 



COPTBIOHT, 1907, 

By the MACMILLAN COMPANY. 
Set up and printed. Publiihcd October, 1907. 



J. 8. Cuihlnif Co. — Berwick & Smith Co. 
Norwood, Mmi., U.S.A. 



I I 



TO 

QTiie iUtmorg 

or 

JOHN RAE 

WHO LAID THE FOUNDATIONS 

UPON WHICH 

I HAVE ENDEAVORED 

TO BUILD 



PREFACE 



The problem of interest has engaged the attention of 
writers for two thousand years, and of economists since 
economics began. And yet, with the exception of what 
has been accomplished by Rae, Bohm-Bawerk, Landry, 
and some others, very little progress has been made toward 
a satisfactory solution. Even these writers can scarcely 
claim to have established a definitive theory of interest. 
While the value of their work is g-eat, it is chiefly 
negative. They have cleared the way to a true theory 
by removing the confusions and fallacies which have 
beset the subject, and have pointed out that the rate 
of interest is not a phenomenon restricted to money 
markets, but is omnipresent in economic relations. 

The theory of interest here presented is largely based 
upon the theories of the three writers above mentioned, 
and may therefore be called, in deference to Bohm-Bawerk, 
an "agio theory." But it differs from former versions 
of that theory by the introduction explicitly of an income 
concept. This concept, which I have developed at length 
in The Nature of Capital and Income, is found to play p 
central role in the theory of interest. The difficult problem 
is not whether the rate of interest i» an agio, or premium, for 
of this th'^re can be no question, but upon what does that 
agio depend and in what manner? Does it depend, for 
instance, on the volume of money, the amount of capital, 
the productivity of capital, the " superior productivity of 
roundabout processes," the labor of the capitalist, the 
helplessness of the laborer, or upon some other condition ? 



Vll 



VUl 



PREFACE 



^. The solution here offered is that the rate of interest de- 
/pends on the character of the income-stream, - its size 
j composition, probability, and above all, its distribution 

lu Ume. It might be called a theory of prospective provi- 

ston of income. 

As in The Nature of Capital and Income, mathematics 
liave here been relegated to appendices. These appendices 
are not, however, mere translations into mathematical 
language of the theory verbally expressed in tho text. 
Mathematics can properly claim no place in economic 
discussions except as they add something not expressible 
or at any rate only imperfectly expressible, in ordinary 
laiigUB ,'e. 

Parts of Chapters V and XIV with their appendices 
have appeared in somewhat different forms in Apprecia- 
tion and Interest. My thanks are due to the American 
Economic Association for permission to use portion of 
this monograph unaltered. Since it appeared a decade 
ago, the view expressed in it, to the effect that apprecia- 
tion of money should, and to some extent does, lower the 
rate of interest expressed in money, has gained con- 
siderable currency, though it is still unfamiliar to most 
persons. It has been thought wise to present again the 
statistical evidence in its favor, and to bring the statis- 
tics down to date. 

In the preparation of this book I have received impor- 
tant aul from many persons. For general criticism I am 
indebted to my wife, to my colleagues, I'rofesscrs II. C 
Lraery and J. V. Norton, and to my f,.i,„d Richard M. 
Hurd, I'resident of the Mortgage- IJon.l Company of New 
York City. My thanks are also due to Finance Minister 
ohm-Huwerk for his kindness in reading and criticising 
the chapter devoted to his theory of interest; to Professor 
Clive Day for facts and references on tiie history of inter- 
est rates; to Dr. Lester W. Zart.nan fur a large part of 



■■'V 



PREFACE 



IX 



the Htatistical compatation and for many helpful criti- 
cisms ; to two of my students, Mr. Harry G. Brown and 
Mr. J. H. Parmelee, for valuable aid in proof-reading, 
including many keen and fruitful suggestions ; and to 
my brother, Herbert W. Fisher, for a most searching 
and valuable criticism of the mode of expression and 
exposition. 

IRVING FISHER. 
New Havbn, July, 1907. 









CONTENTS 



FIRST SUMMA-RY 



cnAmKS 
I-IV 



PART I. CRITICISM OF PREVIOUS THEORIES 
PART II. FIRST APPROXIMATION .... V-VII 
PART m. SECOND AND THIRD APPROXIMATIONS Vm-XI 
PART IV. CONCLUSIONS XII-XVIl 



xn 



CONTENTS 



SECOND SUMMARY 



cu.^.^^^'' '• ^«"^CISM OF PREVIOUS THEORIES 
I. Crude Thbobws 
II. Prodcctivitt Theories 

III. Cost Theories . . . ' ' 

IV. Bohm-Bawebk's Theory . . ' ' 



VI. 
VII. 



PART II. FIRST APPROXIMATION 
V. Appreciation awp Interest 

TlMB-PRBFERENCB 

First Approximation (Riom Income) 



PAoa 
3 

10 

29 

63 



77 
87 
117 



PART m. SECOND AND THIRD APPROXIMATIONS 

Vm. S-ond Approximation (F«xiBi.B Income) . ,,, 

lA. Classes of Options ... • • 137 

X. Invention * ' • • • • 178 

XI. Thiri, Approximation (Uncertain Income) .' [ l^^ 

PART IV. CONCLUSIONS 
XII. Roi-B OF Interest IN Economic Theort . 



XIII. Application to Actual Conditions. 

XIV. Inductive Verification (Monetart) ." 
XV. Inductive V.bification (Economic) 

xvS" s:::r """'"'-:' ^':^-" ^-- 

Olossart . . 
APPENDir*^ 
INDEX . 



225 

236 

267 

289 

317 

327 

337 

345 

429 



n 



ANALYTICAL TABLE OF CONTENTS 

CIIAl'TER I 
Ckcue Theories 

PAOS 

§ 1. Introduction ^ 

§ 2. Early theories * 

§ 3. " Supply and demand " theory 8 

§ 4. " Use of money " theory 7 

CHAPTER II 



Prodcctivitt Theories 

§ 1. Distinction between explicit and implicit interest . 

§ 2. Target's productivity theory based on land . 

§ 3. Common form of productivity theory 

§ 4. True sequtnce: capital-goods, income-services, income-value 

capital-value 

§ 6. To increase productivity 1*111 not increase interest . 

$ 6. Case of ten replaceable machines examined 

§ 7. The same when the rate of interest is zero 

§ 8. Reproductivity theory of Del Mar and Henry Georpe 

§ 0. Example of growing timber 

§ 10. Conclusions 



10 
11 
12 

14 
15 
16 
20 
22 
23 
28 



CHAPTER III 



Cost Theobibs 

) 1. Cost theories overlook the fact that cost is usually discounted 

return 29 

S 2. Case when rate of return on cost exceeds rate of interest 31 

{ 3. Roscher's flsliing net, where sacrifice and return are both 

measured in flsh 33 

§4. Theory chat capiul " saves labor " 35 

§ 5. Case where sacritice and return are both measured subjectively 36 

xiii 



xiv 



§6. 

§7. 
§8. 
§0. 

§ 10. 
§11. 

§ 12. 
§13. 



§1 
5 2, 

§3. 

§4. 



§5. 
§6. 



ANALYTICAL TABLE OF CONTENTS 
"t^S"''^'''' ''-^' — ^ ^^ clal. that value ex- 

Abstinence theory. ''La^ o IttL?- nTa^'"^'' ^''P'^' 
cause not discounted "'»'"«§ not a true cost, be- 

income ^'^''P^'^' '^^P'^l-value isequal to its expected 

CHAPTER IV 

Boiim-Bawehk's Tiieorv 

• ^'''**'"«">' of Bohm-Bawerk's ac^in .ho 
Criticism of Bohm-Bawprk.« ^ ^^""^ °^ '"t^'^st • . 
period . *''"'' ^ ''*""=^P' °f an average production 

Error nlade" iXirZ! ^'"^ °*'^«^ ^-tor^'Ibsent ! i 

"ot to go on intS Jy ' '"'^'^ '""^^^^ «' Productivity 

Final criticisms ..""'••• 



PASI 

38 
40 
42 

43 
45 

48 
60 
61 



63 

65 



68 



61 
63 

68 
71 



CHAPTER V 
Appreciatiok and Interest 

"• "I'nX'::,'-" '*"» "^ .PP-i....n « a.p„o;„,„„ 



77 
78 

80 

81 

82 



'i 



ANALYTICAL TABLE OF CONTENTS 



XV 



CHAPTER VI 



Time-preference 



PAOB 

87 



§ 1. " Tim --preference " is a particular species of "desirability " . 
§ 2. Tills preference applies to all goods, but in the last analysis 

only to final income 89 

§ 3. The rate of interest enters into all prices except the price of 

final services 00 

§ 4. Time-preference depends on income 92 

§ 5. Time-preference depends on size of income .... 94 

§ 6. Time-preference depends on time-shape of income ... 95 

§ 7. Time-preference depends on composition of income . . 98 

§ 8. Time-preference depends on probability of income ... 99 
§ 9. The character of the dependence of time-preference on income 

varies with five human characteristics 102 

§ 10. Summaiy 109 

§ 11. Shortcomings of statement that interest depends on abundance 

of capital 109 

$ 12. Schedule of relation between time-preference and income . 113 



CHAPTER VII 

First Approximation to the Theory of Interest 
(assuming In<.-ome Rigid) 

§ 1. Introductory 117 

§ 2. Equalization of individual rates of preference, by borrowing 

and lending 118 

§ 3. Diagrammatic illustration 120 

§ 4. P'(iualization of preference rates by buying and selling . 126 
§ 5. Futility of socialistic suppression of interest .... 127 
§ 6. Equalization of preference rates means maximizing " desira- 
bility " 129 

§ 7. Formulation of the first approximation to the theory of 

interest 130 



CHAITER VIII 

Second Approximation to the Theory of Interest 
(assuming Income Flexible) 

§ 1. Introductory I37 

§ 2. Choice of optional income-streams depends on maximum 

present value I39 

§ 3. Any resulting inconvenience in time-shape of income may he 

offset by borrowing or lending 141 

§ 4. A change in the rate of Interest produces a change in choice . 146 



XVI 



ANALYTICAL TABLE OF CONTENTS 



§5, 



§7. 
§8. 
§0. 

§10. 

§11. 
§12. 
§13. 
§ 14. 

§15. 

§16. 



■ri,e .Lira mctkod wT., '^^ ■»»"»Met.rn,lnrn. condition 

si«, .„ „„.. ,„„,, ^, z^tj:^:::xZ': 



PAOI 



147 

149 
160 
152 

160 



169 
1«1 
103 
164 

167 

171 



176 



§1. 

§2. 

§3. 

§4. 

§6. 

§6. 

§7. 

§8. 

§9. 

S 10. 



CHAPTER IX 

Classes of Options 
Three groups of options . 
Options as to time of using capiul .■ '. " 
The effect of the slowness of Nature on interest 
The effect of the productivity of Nature oSres, 
Case of perishable goods . . '-'leresi 

Case of renewable gooils . ' ' ' 

Case of repairs and betterment 
Case of optional methods of production ." ' 
Ca^e of optional employments of labor . ' 
Selection of option varies with rate of interest 



178 

180 

186 

186 

187 

188 

190 

191 

193 

196 



§1 
§2, 

§3. 

§4. 

§6. 



CHAPTER X 
Invention 

Effect of invention nn '^ ""^ ^"'"'"^ "'"«'"« • 109 

profiu . ". °" "''^'''' «'^' '^gi^ered by insidcn,' 

Inventions raise interest only iemp^^rarlK- " ' ' ' ^^ 
Conditions which facilitate invention . ! " " ' ^""^ 



ANALYTICAL TABLE OF CONTENTS 



XVll 



CHAPTER XI 

Third Approximation to tiie Theokt of Interest 
(assuming Income Uncertain) 

PAOI 

§ 1. Possibilities of borrowing and lending limited by necessity of 

giving security 207 

§ 2. One^cgoaeiiuence is divergences in rates of preference, inter- 
est, and return on sacrifice 210 

§3. Another consequence of risk is variation in duration of loans 211 

§ 4. Ano ther consequence of risk is divergence between expected 

and realized return 212 

§ 5. Effect of risk on rate of interest on riskless loans . . . 213 

§ 6. Differentiation of risky and safe investments and investors, 

bonds and stocks 216 

§ 7. Effect of the introduction of element of risk upon the interest- 
determining conditions 217 

iS 8. Summary 220 

CHAPTER XII 
RdLE or Interest in Economic Theort 



§1. 
§2. 

§3. 
§4. 
§6 
§6. 



The interest rate plays a rflle in determining the prices of 

capital 225 

The interest rate plays a rOle in determining the prices of 

general services 226 

The interest rate plays a rdle in determining wages in particular 228 
The problem of distribution usually misconceived . . . 229 
The interest rate plays a rdle in distribution .... 231 
Inequality in distribution of capital due to opportunity to ex- 
change income 234 



CHAPTER XIII 



Application to Actual Conditions 



in 



§ 1. Application of the theory of interest to personal loans . 

$ 2. Application of the theory of interest to public loans 

§ 3. Application of the theory of interest to business loans 

general 

§ 4. Application of the theory of interest to short-term loans 
S 6. Application of the theory of interest to long-term loans , 
S 6. Business loans not "productive" except as they enable mer- 
chants to choose " productive " options 
{ 7. Classification of loans 



236 
238 

240 
242 
244 

246 

252 



i •! 



XVIU 



ANALYTICAL TABLE OF CONTENTS 



« ,n t ,^ ^*'*"'' '*«'°" maturity . 
SIO. Ezphcit and Implicit interest. Risk 



§1. 
§2. 

§3. 
§4. 
§6. 
§6. 

§7. 

§8. 

§». 
§10. 

§11. 

§12. 
§13. 



CHAPTER XIV 
IsDucTivB Verification (Monetary) 

^^r.itMSt.r^ZinrjT^';:^^^^^^'^ contracts in 
?X:ltTdir.rp:f ':" 'r^ T ^-eding eWdence 

^ France, and tL UnTd Tuts '"'''''"* ''^ ««™y' 
^TndTJr .P'^~ and interest .. India. Japan! 

^l:^: '"^.'"^ :^°^« -* '""^ 'adjust iu;,f to- monetary 

Errors due to misUking lligh or low r<.»J- • " ' ' • 
absolutely high or low ^^ '" """^^ '<>' ^tes 

When long periods of time are tairon ♦i, ' , . ' 
appreciation and intere'tis mo2 dell^^ "'^''^ ^«»-- 

r^^^LTadiT ^'~— . the rate Of interesi 
^icat^ to theoiy Of ..credit cydes"- ; ; ; ; 



rAOB 

263 
254 
266 



257 

268 
261 
266 
270 

273 

276 

277 

280 

282 



284 
285 
287 



§1 
§2. 

§3. 
§4. 
§6. 

§6. 
§7. 

§8. 

§»■ 



CHAPTER XV 

iNDt-cTiVK Verification (Economic) 
Similar significance of low inter«.t i«„^- 

and durability of instmmeSu ' °'""^' '"'cumulation, 
Where foresight, self-control, and' reeard fnr «.". • " 

present, interest tends to be low ^'^"^^ *"« 

Ssre^n' f "" ""*' ''"'*' «P'anation; may enter " ' 

and U^ aTq^JS' '^"^ '"' P*^''^"'^ P"''^ natural 

Where Incomes are low, interest tends to' be hU " " " 
Where incomes are low in the food elemir/nte'st te^ds to 



280 

290 
294 
296 

297 
200 

301 

802 

304 



ANALYTICAL TABLE OF CONTENTS 



ZIX 



I 


J 10. 


f 


$11. 




§12. 




$13. 




$14. 



PAOl 

Ditto, caae of particular parts of United States . . .306 

Ditto, case of other countries 309 

Ditto, case of misfortune and invention 311 

Ditto, case of rliytlimic changes in income .... 314 
Summary 316 



SI- 

$2. 
$3. 

§4 

$5. 



CHAPTER XVI 

InDCCTIVK RkFUTATIOK of '♦ MoyBT-THEORT " 

Statistical refutation of money-theory necessary for business 

man 

Table giving rate of interest in relation to price-level 

Table giving rate of interest in relation to money per capita . 

Relation of bank reserves to rate of interest explained 



317 
318 
320 
322 



Case of panics 324 



CHAPTER XVII 

SnXMABT 

$ 1. Appieciation and interest 

$ 2. Enumeration of interest-determining conditions 

$ 3. Possible future changes in range of choice 

$ 4. Possible future changes in character of man 

$ 5. The element of fashion as a factor in determining interest 

§ 6. Conclusion 



327 
328 
329 
331 
332 
334 



GLOSSARY 
Definitions of Technical Terms Used 



337 



! 1 



APPENDICES 



Appendix to Chapter II. Productivity Theories 

§ 1 (to Ch. II, § 6). Mathematical proof that the rate of net in- 
come from reconstituted capital is equal to the rate of inter- 
est employed in valuing the elements of which it is composed 

§ 2 (to Ch. II, § 7). Discussion of the ca.se of zero interest as ap- 
plied to the valuation of reconstituted capital 



347 



349 



AppE»-nix TO Chapter IV. Bohm-Bawerk's Theory 

§ 1 (to Ch. IV. 2). Nature of various means, — arithmetical, geo- 
metrical, harmonical, etc 351 

§ 2 (to Ch. IV, § 2). Case illustrating futility of measuring average 

production period 362 

§ 3 (to Ch. IV, § 3). Showing how periods of production which 

are relatively long but unproductive are eliminated . . 353 

§ 4 (to Ch. IV, § 4). Mathematical refutation of Bolim-Bawerk's 
claim as to ground of preference for present over future in- 
vestment of labor 364 



Appendix to Chapter V. Appreciation and Interest 



51 

§2 

§3 

§4 
§6 

§6 



$7 

§8 
§9 



(toCh. V, §2). History of theory of ap;)reciation and interest 36fl 
(to Ch. V, § 3). Formula connecting the rates of interest in 

two diverging standards 368 

(to Ch. V, § 4). Formulae, when rates of interest and of appre- 
ciation are reckoned oftener than yearly .... 360 
(toCh. V, §6). Case of partial payments .... 361 
(to Ch. V, § 6). Formulae for cases of compound interest and 

partial payments 363 

(to Ch. V, § 6). Case of separate payments of interest and 
principal in one of the two standards and equivalent pay- 
ments in the other 366 

(toCh. V, §5). Case of separate payments of interest and 

principal in both utanHards Rm 

(to Ch. V, § 5). Case of perpetual annuity .... 367 
(to Ch. V, § 6). Case in which the rate of appreciation changes 

each year 369 

xxi 



1 t 

i I 



11 



xxn 



ANALYTICAL TABLE OF CONTENTS 



§1. 

$2. 
§3. 

§4. 
§5. 
§6. 



§7. 



First Approximatios 



ArPB.„., ,o CH.Pr.H VIL ..„„ ^pprox.«„,o. 

of interest "P''°" determination of rate 

The condition that rates nt,Z c " ^**'" ^ ^^^ • 
rate of interest i,^Svae?S'tf'""!r, f'*" ^'^'^ "»« 
desirability" shall 2 a Ixlum''^ *'""'^"°" ^^^^ "'°^' 

ity curve and a straSt Z .k T""'^ °^ *° iso-desirabil- 
to the rate ;? inte^T '' "°^ '' ''''•'='' corresponds 

Extension from two to three or more years ' " " ' 
Ceometncal solution of the rate of interest .' ." ; ; 

Appk..., ,o Chaptkh Vin. S.eo.„ Appro„«.,.o, 
* ^a'daTd'"" ''' ''^ '"' approximation repeated and re- 

'" s:.riS''^^sxti:rT"'''^''-'''-^^^^^ ■ 

of choice '^P'"'""'*"''" '" t^o dimensions of the range 

"'z:::t:7^ °^ ^"^ ^-™'-'- of cice fo; 

Exte„Mi..„ to three and more dimensions 

.:rpr„t vXr"" '^:'™''"''^ •-•"''- '"^t of maxi: 

§ 8. Summary . , _ ''•■.. 



PAOE 

374 
376 

377 
380 
383 



386 



§8. 

§9. 
§ 10. 



387 

300 
3!)2 
394 



§2. 
5 3. 

I 4. 

J 7, 



306 
307 

402 

406 
407 
408 

411 
412 



Of thi'n,^;iroxtX'°' ""''"'"^ '""''•--'-I '--en^ 

Appendix to Ciuptkh Xtv a. 

" *IV. Statistical Data 

INDEX . . 



410 



418 
421 
426 
420 



J 



PART 

Chapter I. 
Chapter II. 
Chapter III. 
Chapter IV. 



I. Criticism 

Crude Theories 
Productivity Theories 
Cost Theories 
Bohm-Bawkrk's Theory 



THE RATE OF INTEREST 



CHAPTER I 

CRUDE THEORIES 
§1 

If the theory to be presenter! in this book is correct, the 
rate of interest m any community is an index of the 
preference, in that community, for dollar of present 
over a dollar of future income. The ^k of justifying 
this theory will be facilitated by a brief preliminary review 
of rival theories. A complete history of theories of interest 
has been made unnecessary by Bohm-Bawerk's admirable 
Capital and Interest.^ For the san e reason, it is not neces- 
sary to combat many of the special theories advanced by 
individual writers. The theories which are here selected 
for criticism are for the most part those which have the 
greatest currency, either in economic literature or in the 
unexpressed but none the less firmly rooted ideas of busi- 
ness or professional men. Experience shows that nearly 
every student of economic science has almost unconsciously 
acquired a number of crude and usually false ideas on this 
important subject. Such, for instance, is the i<lea that 
interest is the price paid for the "use of money"; or that 
it represents the "productivity" of capital or the "fecun- 
dity" of plants and animals; or that it represents .some 

' English translation by Smart, (Macmillan) 1890. See also Recent 
Litfrature on InUr^M, English translation by Sct-tt &. Fcilbogrc, (Mac- 



millan) 1903. 



8 






4 THE RATE OF INTEREST [Chap. I 

"cost" to the producer, such as the cost of the capitalist's 
personal exertion in controlling capital, or the "cost of 
waiting ; or that it constitutes a species of legalized plun- 
der perpetrated by the employer on the employed. Be- 
fore the correct theory of interest can be securely implanted 
m any mind, these ideas must first be eradicated To 
accomplish this is the object of the present and of the 
next three chapters.' 

§2 
An objection, formerly common, to the practice of taking 
interest was that interest is " unnatural." The word em- 
ployed among the Greeks to signify interest or usury was 
To*o9, offspring"; and Aristotle declaimed against *»>e 
taking of interest, on the ground that money could not 
have offspring," -a curious instance of the influence of 
terminology on thought. 

Interest-taking between Jews was forbidden by the 
Mosaic laws, an.l similarly, in Rome, interest-taking be- 
tween Romans was prohibited. Many biblical texts show 
the hostile attitude of the writers, both m the Old and New 
restaments, toward the practice, and the Church Fathers 
through the Middle Ages for over a thousand years waged 
a ceaseless but fruitless war against interest-taking. St 
Thomas Aquinas stated that interest was an attempt to 
extort a price for the use of things which had already been 
used up, as for instance, grain and wine.' He also declared 
that interest constituted a payment for time, and that time 
wa^^a free gift of the Creator to which aU have a natural 

omJ^Z "^"^^r" '"!. "''" ""•"* P*'* ""^y ^^ "aJd to be a brief cpit- 
cT;j«t /n^r"^ ^'-^'•-«-. - B«.u„-Bawerk', exhauXe 

^^•vo^hv n'h' "n '"''''."'* ^^^ ^"'^^'"^'^'^y "^ interest In very nearly re- 
r„wf.t'X:^r?h:p.tin""^''" '' the.odern..Se"tiL'; 

by th^c-Tnll'T^ ''r' """''" °"" "^ *•>« objection, made to !and-r.nt 
bj the »mgl.. ux ad vorau.8 ; namely, that .poce is a free gift of nature. 



M 



Sec. 2] 



CRUDE THEORIES 



The unpopularity of interest-taking increased until the 
thirteenth centiu-y; but the practice persisted, and as 
business operations increased in importance, certain exemp- 
tions and exceptions from its general prohibition were 
secured. Pawnshops, banks, and money-lenders were 
specially licensed, and permission was granted for buying 
annuities, an 1 taking land on mortgage for money loaned. 
One of the subterfuges by which the allowance of interest 
was excused suggests the true idea of interest as an index 
of the relative preference for present over future goods. 
It was conceited that, whereas a loan should be nominally 
without interest, yet when the debtor delayed payment, he 
should be fined for his delay (mora), and the creditor should 
receive compensation in the form of " inter esse." Through 
this loophole it became common to make an understanding 
in advance, by which the payment of a loan should be " de- 
layed" year after year, and with every such postponement 
a "fine" should become payable. 

Some of the Protestant reformers, while not denying that 
iiiterest-taking was WTong, admitted that it was impossi- 
ble to suppress it, and that it should therefore be tolerated. 
This toleration was in the same spirit as that in which 
many reformers to-day defend the licensing of vicious 
institutions, such as saloons, racetracks, lotteries, and 
houses of prostitution. 

In the sixteenth century interest -taking began to find 
some definite champions. Calvin attempted to di.scrimi- 
nate between interest-taking which was right and interest- 
taking which was \\Tong. Among the wTong kinds he 
classed the taking of interest from the poor and from those 
in urgent need, and the taking of interest in excess of a 
legal maximum. 

In order to defend interest, its chain{)ion8 began to con- 
struct theories to account for the phenomenon. Most of 
these early theories were little more than a shifting of the 
problem. It was seen that capital efirned income whether 
it was lent or not. The income which a lender obtains 



6 



THE RATE OF INTEREST 



[Chap. I 

through a loan contract may be called ex^it interest; but 
It was dear that the borrower was enabled to pay this 
interest because the capital which he borrowed earned it 
for h,m. The income which capital thus earns may be 
called tmj^ rrUerest. The earliest -.ttempt to construct 
a theory of interest merely explained explicit interest in 
terms of imphcit mterest. Salmasius and Locke, both in 
the seventeenth centm-y, attempted thus to explain in- 
terest. They tried to justify the taking of interest in a 
loan on the gromid that an equivalent to that interest was 
obtamed by the borrower from the capital he borrowed, 
an( might have been obtained by the lender of the capita 
had he retained it. If, they said, a man lends $lboo, 
he IS entitled to mterest upon it because, had he used 

of ?t ^X.'I "f ^L^r°"^^^ ^"^^ '""''^ P'-^fit^ by means 
of t. But beyond the bare statement that unlent capital 
yields income, these theories did not go. The real prob- 
lem- why capital yields income to the user" -was left 
untouched. "oo leii 



§3 

The theories just described are for the most part obsolete 
to-day; yet we have a number of other theories almost 
equally crude. If a modern business man is asked what 
determines the rate of interest, he may usually be expected 
to answer, the supply and demand of loanable money " 
But supply and demand" is a phrase which has been too 
often forced mto service to cover up difficult problems 
Even economists have been prone to employ it to describe 
economic causation which thoy could not unravel. It was 
once Witt. ly remarked of the early ^Titer. on economic 
problems, "Catch a parrot an<l teach him to say 'supX 
and demand,' and you have an excellent economis?.^ 
Z'7^^ ^u^'\ ':'"*;„^"terest, and rofits were thought to 
be fully "expla.ne.1" by this glib phra^. It i. tru. that 
every ratio of exchange is due to the resultant of causes 



-I 



Sec. 4] 



CRUDE THEORIES 



operating on the buyer and seller, and we may classify 
these as "demand" and "supply." But this fact does not 
relieve us of the necessity of examining specifically the two 
sets of causes, including utility in its effect on demand, and 
cost in its effect on supply. Consequently, when we say 
that the rate of interest is due to the supply and demand 
of "capital" or of "money" or of "loans," we are very far 
from having an adequate explanation. It is true that 
when merchants seek to discount bills a.t a bank in large 
niunbers and for large amounts, the rate of interest will 
tend to be high, and that when merchants do not apply in 
large numbers and for large amoimts, the rate of interest 
will tend to be low. But we must inquire for what purposes 
and from what causes merchants thus apply to a bank for 
the discount of loans, and why it is that some apply to the 
bank for loans and others supply the bank with the funds 
to be loaned. The real problem is : What causes make thej 
demand for loans, and what causes make the supply ? This 
question is not answered by the summary " supply and de- 
mand" theory. The explanation is not simply that those 
who have much capital supply the loans and those who 
have little capital demand them. In fact, the contrary is 
quite often the case. The depositors in savings banks arej 
the lenders, and they are usually poor, whereas those to' 
whom the savings bank in turn lends the fumls are rela- 
tively rich. 



§4 

There is another phrase often employed by business 
men to explain the rate of interest or, at all events, its 
existence. It is often said that interest is the price paid 
for the "use of money." As an explanation th's is almost 
as superficial as "supply and demand " ; for it is clear that 
the "use" of money is to facilitate exchange, and that, ex- 
cept in rare instances (as when a bank borrows a chest of 
gold to reinforce its cash reserve), the money borrowed 



8 



THE RATE OP INTEREST 



[Chap. I 



r 



does not remain long in the hands nf f>,» u 
interest is a payment for nlT :* • *^® borrower. If 

of the borroCrne^brif ti?^^^^^ 1°V^^ "^' ^'^^ 
money is expended Fnr.v °^^^''^ *^^ ^^^^o^^d 

- .; of the^ate ^^^J^^IT^X f^J ^^^^^"^"°1 
* cause. sought m anymonetaryf 

that the Quantitv nf ^„ • • ? ^^'^ Pe-^istent belief 
-d low when ttr:yVZl^^^:iT'y '^ ^'"^' 

wUl al» equally increas^ aTSniTd "r^^ '^'' " 
piano dealer who borrows smnnnT J .^°' .'"^On^!. a 
to Lis stock in tradT^ piTo'i:^^^'"' "" ""^ "if 

dU Lreim- T ^™s,*rZra^roi 
would douuTtrL'Tf ittrtdtn °' ^;T"'^ 

50 pianos -costing now^ . • • ° '^'"' '" °'"»'" 
he would have ^o ^Z ,Z.1ZJT^, ^*^ " 

belief.' ^'" ''^^^^•"g' 1«"J support to thi.^ 

rnerof'to^rrtL'r ^'^^^7^--' -^ng business 
the mte of inCt if I'oh ""'f ?' '' '"^"^^^ ''^''-^^^ 
interest i.s high when /h '^ ^^'* ^^^^ ^'^^ ^' « of 

ally redu;cd by brindnr ' T ^'"" ''^^^'- ^^" ^^« "^^teri- 
J uiccd by brmgmg to that center a sujmly of actual 



Sec. 4] 



CRUDE THEORIES 



money to relieve the "stringency." This is true, and it is 
not denied that money plays a part in determining the 
rate of interest. But the part which it plays is chiefly 
ias a puppet of other and mightier factors. The fimda- 
Imental causes at work in a "money" market are not mone- 
tary at all, but economic. The economic causes operated 
through money and seldom show themselves save imder a| 
money disguise; but, generally speaking, money is only 
their instrument, not an independent factor. If money is 
plentiful for loan purposes, it is because its owners decide 
to apply it for these rather than for other purposes, 
and not because money in general is plentiful. The owners 
of money determine the purpose to which it shall be applied. 
To understand the real causes at work in the loan market, 
we must go back of the money itself and learn the reasons 
[for bringing it into that market instead of spending it in 
[other markets, —the meat, fish, fruit, or grocery markets, 
for instance. The abimdance or scarcity of money for 
loan purposes is merely a sign or symptom of those more 
fundamental causes operating upon the rate of interest. 

A full consideration of the manner in which money in loan 
centers is related to the rate of interest must, however, be 
deferred to Chapters V, XIV, and XVI. In the present 
chapter we are content merely to point out thai the theories 
of which it treats are crude and superficial. They contain 
a modicum of truth, but they do not reach the root causes 
of interest. It is true that explicit interest is dependent 
upon implicit interest; but this being so, the question 
still remains, Wliat determines implicit interest? Again, 
it is true that the rate of intereb,. like every other ratio of 
exchange, depends on "supply and demand"; but the 
question is. What constitutes the supply and demand? 
And again, it is true that interest varies with loanable funds ; 
but what causes the variation of those funds? To answer 
these ulterior questions, more careful and elaborate theories 
have been constructed. These will be considered in the 
three following chapters. 



■■f 



CHAPTER II 

PRODUCTIVITY THEORIES 
§1 

In the previous chapter it was shown that the problem 

Pirsons the rate of interest" means simply the exolirit 
rate of mterest in a loan contract. When a nrr Infl^ . 

exphcit but implicit. It is implied by the prLe of Z 

those pre.„t values wiU 'he the pric'on' b nh" """ " 

rate rftateS "^'"'' ■?"!" ""'' "'"^ "PO'ted returns a 
in stlfar^,, ™™f "l'^ "■> ™P"ri' ™tc of interest 

10 



Sec. 2] 



PRODUCTIVITY THEORIES 



11 



employment of a rate of interest.' In the same way all 
instruments of wealth, such as land, imply a rate of interest. 
This is recognized when land is sold on the basis of a num- 
ber of "years' purchase." In like manner, machinery, 
dwellings, furniture, and, in fact, all articles of wealth, 
as was shown in The Nature of Capital and Income, are 
valued by discounting expected income ; and all discounting 
of income can be calculated only by means of a "rate of 
interest." There is thus an "implicit rate of interest" in' 
the value of every capital-good. It is, to be sure, often 
difficult to work out this rate definitely, on accomit of the 
elusiv.; element of chance; but it has an existence in u 
capital. From this it is clear that the extent and impor- 
tance of the interest problem cannot be grasped until 
implicit interest is recognized; and, as a matter of history, 
it was only after implicit interest was in some degree thus 
recognized that any theory of interest worthy of the name 
was evolvetl. 



§2 

The first writer who attempted to explain natural or 
implicit interest, as distinct from contractual or explicit 
interest, appeals to have been Turgot. His « xplanation 
consisted simply in shif ling the onus of the pro. lem on to 
land. He explained that interest must be obtai lable from 
the use of capital in general, because it is obtainable from 
the use of land in particular. He reasoned that, were it 
not likewise obtainable from other capital, every one would 
invest in lantl. A man with $1000 worth of other goods 
would, if he received no increase, prefer to sell these goods 
and buy $1000 worth of land, from which he could obtain 
say $50 a year. Land, he explained, evidently yields 
interest because it yieMs a perpetual series of crops, the 
land being bought for so many "yer -s' purchase" of those 
crops. This number of years' puichase, ho saiil, was de- 
' See The Nature of Capital and Income, Chap. XVI. 



12 



THE RATE OF INTEREST 



[Chap. II 
of th?n . '^ "Y ^ '""^^''^^^ ^« ^ Pa'-ticular species 



§3 

This idea few share .o-<lav vo, . , -„ 

seems more obvious than ^h«f t^" ^ f ^* ^'"''^ ''^^* 
will yield 5 pi cent Sn^^ .".'^ ^'""^ ^^P'^^^ 

seems self-evident tlf .'^^'^^^ '' productive, it 

tive land Z T " '^vestment of $m in produe- 

552F- -^'--^^^ 

faC'o ais^rr^-f, s::ie:-r;s'. J! 

• See r*. A'a/«re o/ Capital ar,d Income, Chap. XI. 



Sec. 3] 



PRODUCTIVITY THEORIES 



13 



productivity of a factory — the ratio of its output to the 
size of the plant - and its value-return — the ratio of the 
value of the output to the value of the factory.' 

It is evident thai if an orchard of ten acres yields 100 
barrels of apples a year, the physical-productivity, ten 
barrels per acre, does not of itself give any clew to what rate 
of return on its value the orchard yields. To obtain the 
value-return, we must reduce both income and capital to 
a common standard of value. If the net annual crop of 
apples is worth $1000 and the orchard is worth $20,000, 
the ratio of the former to the latter, or 5 per cent., is a 
rate of value-return ; and if this rate is maintained without 
depreciation of the value of the orchard, this rate of value- 
return is also the rate of interest. 

It seems at first sight very easy to pass from quantities 
to values, — to translate the ten acres of orchartl and the 
100 barrels of apples into dollars. But this apparently 
simple step begs the whole question. The importar*; fact, 
and the one lost sight of in the productivity theory, is that 
the value of the orchard depends upon the value of its crops ; 
and in this dependence lurks implicitly the rate of interest/ 
itself. The statement that "''nrUal produces income" is 
true only in the physical sense ; it is not true in the value 
sense. That is to say, capital-value does not produce in-/ 
come-value. On the contrary, income-value produces 
capital-value. It is not because the orchard is worth 
$20,000 that the annual crop will be worth $1000, but it is 
because the annual crop is worth $1000 that the orchard 
will be worth $20,000. The $20,000 is the discounted value 
of the expected income of $1000 per annum; and in the 
process of discounting, a rate of interest of 5 per cent, is 
implied. In general, it is not because a man has $100 
worth of property that he will get $5 a year, but it is because 

'Certain theories, which Bohm-Bawerk calls "indir^-ct pr-duc- 
tivity theories," have taken account in some degree of the ,< inc- 
tion between the relation of quantity and value of income tc quan- 
tity and value of capital, and have attempted to bridge the chasms 
between them, but, as B5hm-Bawerk has shown, without success. 



ii 






14 THE RATE OF INTEREST [Chap. II 

he will get that $5 a year that his property is worth Sinn 
n short, when capital and Income 'are' n^ealldt S' 

ru Zf thr"*'°" '^ ''^ "^"" °^ ^h^^ -hich holds 
ime « hen they are measured in qmntity. The orchard 



^he 



§4 



C^tlX 't^ ^',tr '-™-»'» P^luce, pre«„t 
«f •. . . . ^^'^ ^" "e observec in the sfnrJv 

quantity of ca|,ital, or capital-wealth (2) nimmiiv J 

roILr r"--™"^. ») value of iiinT"" valu 
»^oa|^Tl,«„r,le|^s shown in the following JohemeT- 



Pbebent 
Capital 



FuTt'RE 

Income 



Quantities . n -^ i . 

Capital-wealth. 

Values . . ri t 1 . 

l-apital-value - 



• Income-services 

I 
Income-value 



n e": ""'.[r Z'th""" ""' "'"'"^ involve XTattrf 



Sec. 5] 



PRODUCTIVITY THEORIES 



15 



discoimting. This final process introduces the element of 
interest. It is clearly with this last process that we are 
concerne ! in the study of interest. 

V pciialox that, when we come to the value of capital, 
it ie iiu'omr' wliic' produces capital, and not the reverse, 
jis, t .^), iho stum 'ing-block of the productivity theorists.! 
It is cLiT. ;'f c'.'urse, in any ordinary investment, that 
the selling value of a stock or bond is dependent on its 
expected income. And yet busmess men, although they 
are constantly employing this discount process in every 
specific case, usually cherish the illusion that they do so 
because their money could be "productively invested" 
elsewhere. They fail to observe that the principle of 
discounting the future is universal, anil applies to any 
investment whatsoever, and that in such a discount- 
process there is necessarily mvolved a rate of interest.' 
Consequently, any attempt to deduce the rate of interest 
from the ratio of the income from capital to the value of 
that capital is a pelitio principii. 



§5 

The futility of the ordinary productivity theory may be 
further illustrated by observing the effect of a change of 
productivity. If an orchard could in some way be made 
to yield double its original crop, the productivity of that 
capital in the physical sense would be doubled, but its yield 
in the sense of the rate of mterest would not necessarily be 
affected at all, certainly not doubled. For the orchard 
whose yield of apples should increase from $1000 worth to 
$2000 worth would itself correspondingly increase in value 
from, say, $20,000 to something like $40,000, and the ratio 
of the income to the capital-value would remain about as 
before, namely, 5 per cent. To raise the rate of interest 
by raising the productivity of capital is, therefore, like 
trying to raise one's self by one's boot-straps. 



.A 



16 



THE RATE OF INTEREST 



[Chap. II 

tivity to be universal Tr u ''^^''easmg produc- 

of interesl- v^f if tu^ j • . ^'^"^^ '**"iy attect the rate 

the simple direct rat ^supp„^^Mee7 ' ""' *" '" 



I- 

1^ 



special an( niproved form nf fj,^ , ■! ^' ^'^^ * 

ordinary P-luoSy Z„ ^''^^^ S '^oZ , '?"'' 
an unspecife,! sometliing callef it, "?' 7 f ,?™,'"™« 

or servioo. This arpor.ia f^ specincaiiy as a use 

theory of services but n - .K T' .'"'^"^ ^'^^ a correct 



I 



Sec. 6] 



PRODUCTIVITY THEORIES 



17 



interest itself in order to 'mow the value of the machine. 
Suppose that the rate of ixiterest, on the basis of which 
the machine is valued, is 5 per cent. Then the value of 
the machine, when new, would be $772, this being the dis- 
counted value, at 5 per cent., of the income above speci- 
fied. Tliis capital-value is, of course, derived from the 
expected income, and not vice versa. If, for any reason, 
the services of the machine are doubled in quantity, and 
the price of these services remains unchanged, their value 
will rise and become $200 a year for eacli of the ten years. 
But the effect will not be to double tne rate of interest ; it 
will rather be to ilouble the cajjital-value of the machine, 
and instead of being worth $772, which is the discounted 
value, at 5 per cent., of $100 a year for ten years, it will 
now be worth $1544, which is the discounted value, at 5 per 
cent., of $200 a year for ten years. 

Actually, of course, the doubling of the income-services 
performed by the machine will lower the price of tho^e .ser- 
vices and affect the manufacture of the r -hine which 
performs them. \Mien the effects are complete, ..le resultant 
income-value of the servi( js of the machine may rise above, 
fall short of, or remain stationary at $200 a year, according 
to the extent of the fall in the price of the 'Services. As a 
consequence of such a changed income-value, the capital- 
value of the machine may also change in either direction, or 
remain stationary. The capital-value follows the rate' of 
interest, not the rever.se. Whatever the effect on the rate of 
interest involved in these events, it is not the simple one, 
imagined by the use theorists, of a ri.se or fall proportionate 
to a ri.se or fall in incomp-.services, or even to a rise or fall 
of income-value. 

The objections which have been urged to the produc- 
tivity and use theories apply with st:!' greater force in cases 
where the depreciation of capital is offset so as to "stand- 
ardize"* the income. It is sorr-times said that interest 
is the income which capital yields U^vond what is neces- 
' See TAf Nature of Capital and Income, Chap. XIV. 






18 



THE RATE OF INTEREST 



[Chap. II 



sary to replace the capital. But in tl . ost of replacement 
which maintains the capital there lurks again the very 
rate of interest to be explained. 

Let us examine the case of a factory plant of ten machines, 
each like the one just described. Suppose that those ten 
machines are evenly distributed through the years, as to 
wear —that, for instance, the life of each machine is ten 
years and that, accordingly, the cost of renewal is the cost 
of one machine annually. Let us imagine a man buying 
these ten machines for $4556. Knowing that the cost of 
each machine is $772 and its annual use is $100, he will 
calculate that he is "making 5 per cent, on his capital," 
because he will receive 10 x $100 or $1000 a year in service 
from his machines, and will spend each year for replace- 
ment $772. This leaves a net income of $228, which, 
divided by the capital invested, $4556, makes just 5 per 
cent. If asked why the rate of interest is 5 per cent., this 
owner is likely to answer, because outfits like his yield 
5 per cent, on their cost, over and above the cost of replace- 
ment. A little reflection, however, will show that th e rate 
of intercsLia implicitly assumed in his calculation. Not 
only the $4556 of capital, but even the $228 of income, are 
calculated on the assumption of a rate of interest of 5 
per cent. 

Tliat this is true of the capital, $4556, is evident by re- 
peating, with reference to the entire ten machines, the 
calculations alroady explained for one. Each ma chine i^ 
valued by discounting its future annual services o f $100 fo r 
Us lifotijiie. One of the machines i.s new and ha.s a life 
of^Jen years; consequently, it is worth, as already seen, 
$772, this being the discounted value of ten aimual instal- 
ments of SUM) each, on the assumption of a 5 per cent, 
interest rate as the basis for the calculation. Tlie life of the 
next machine is only nine years, making, by a similar reck- 
oning, a present value of $71 1 ; the life of the third machine, 
eight years, Jiiaking its value $646, and so on. Thus the 
total fur the ten machines is $772 + $711 + $640 4- $57S 



i 



Sec. 6] 



PRODUCTIVITY THEORIES 



19 



+ $508 + $433 + $355 + $272 + $186 + $95, or $4556. It 
is clear that this item and each of the ten sums of which it 
is composed are calculated only by the aid of a rate of interest. 
So much for the capital; now let us turn to the net in- 
come of $228. The gross income is $100 per machine for 
ten machines, or $1000, and fro: ■ this is deducted the cost 
of replenishing one machine, 'xliis cost is $772, leaving 
$228 as net income. But this^ qst of replacement, $772, is 
the capkal-value of a machine, and is obtained by means 
of a rate of interest,^ namely, S per eeat. The reason, then, 
that the $4556 yields $228, or 5 per cent., is not because of 
the productivity of the maclunes, but because 5 per cent, 
is assumed in the calculati«.>n both of the $4556 and of the 
$228. The 5 per cent, emerges at the end only because it| 
\was put in at the beginning.* 

Were the productivity the source of the rate of interest, 
we should expect a double productivity to double the rate 
of interest. But the reasoning used in the case of the or- 
chard shows that not only will the value of the use of the 
machinery be doubled, but the cost of each new machine 
may be doubleil, so as to leave the rate of interest at 
5 per cent. 

As stated above, the doubling in productivity would 
naturally result in lowering the price of the services pro- 
duced, so that the value of the doubled quantity of .ser- 
vices might be less than double the value of the original 
quantity of services. Consequently, the value of the now 
machines and the cost of replacing an old machine i)y 
ft new one might not lie double what they were before. 
But they certainly would not be unaffected. 

The process of adjusting supply and price reconciles 
what has been said with the old cost-of-production theory 
of value. The reader may have felt that we have treateil 
the value of the machines and the cost of replacement as 
though they had no relation whatever to the cost of pro- 
ducing the machines. One cannot deny that the classieai 
* For a mathematical formulation, sec Appendix to Chap. II, } 1. 



20 



THE RATE OF INTEREST 



[Chap. II 



economists were partly right in ascribing value to cost of 

jproduction. But cost of production affects the value of 

^■""— h la capital good only indirectly by affecting the scarcity of 

jits products or uses. The value of its products or uses 

depends on its marginal utility. The marginal utility is 

dependent on the scarcity, and this scarcity depends, in 

turn, partly on cost of production, so far as this cost 

of production has any independent existence.* 



§7 

Extreme cases are always instructive, even when they are 
impossible of realization. As an extreme case, let us im- 
agine a community in which the rate of interest is zero. 
In this case we can scarcely fail to observe the wide dif- 
ference between physical-productivity and value-return; 
for we shall find that the disappearance of interest does 
not carry with it the disappearance of physical-produc- 
tivity, though it does bring about the cessation of value- 
return. Consider a plant of ten machines, of which the 
annual use is worth, as before, $100. The value of a new 
machine to last ten years will now be, not $772 as before, 
but $1000, this being the capital-value of ten annual in- 
stalments of $100 each, reckoned at full value, or, if we 
prefer to say so, each discounted at zero per cent. Simi- 
larly, the value of a machine one year old, having nine more 
years of life, would be, not $711 as before, but $900; of 
one two years old, $800, and so on, making a total value, not 
of $4556, but $1000 + $900 4- $800 + $700 + $600 -I- $500 
+ $400 + $300 + $200 + $100, or $5500. This is the capi- 
tal-value of the plant. We next seek the net annual income 
from the t^n machines. Strange as it may stHjm, this 
net income, if the plant is exactly kept up, would be zero ; 
for the gross annual income from the ten machines is 
10 X $100, or $1000, and the deduction for the cost of a new 

' See The Nature of Capital and Income, p. 173. 






Sic. 7] 



PRODUCTIVITY THEORIES 



21 



machine is, as we have seen, also $1000. Consequently 
the net income is zero, and the value-return, being , 

oOUU 

is also zero. Yet the case supposed does not imply any 
reduction in physical-productivity; the machines produce 
the same amoimt of work as when the rate of interest was 
supposed to be 5 per cent. 

It may be asked how it is possible that the plant, if it 
yields no income, could have any value. We have found it 
worth $5500 and yet it yields no net income. The answer 
is that the annihilation of net income which we have wit- 
nessed takes place only so long as the up-keep of the plant 
is maintained. At any time that the owner of the plant, 
sees ^.t to do so, he may draw income from the plant tot 
any amount up to $5500, but no more. If, for instance, he 
decides at the end of ten years to withdraw from manu- 
factm-ing, he may discontinue his annual renewals and ob- 
tain in the first year thereafter his $100 income from each 
of the ten machines, or $1000 in all, without any deduc- 
tion for up-keep. During the next year, as one machine 
will have been worn out and imreplaced, he will obtain 
the income from only nine machines, or $900, and likewise, 
in the years succeeding this, he will obtain $700, $600, etc., 
until the last machine is worn cat and no capital remains. 
The total of this income is evidently $5500. 

In other words the owner of the machines, as long as 
he keeps up his capital, obtains no net income, but he 
has the possibility at any time of obtaining a total net 
income of $5500 simply by letting his plant run down. 
The possibility of obtaining this return keeps the value of 
the capital at $5500 as long as it is kept up. His capital is 
like a fixed treasure and remains $5500.* The process of 
keeping up the capital is virtually to keep the $5500 in 
cold storage, so to speak. 



' For a mathematical treatment of this peculiar case, see Appendix 
to Chap. II, I 2. 



22 



THE RATE OF INTEREST 



[Chap. II 



If it be asked what motive could ever prompt any one 
to keep up his capital when, as long as he does so, all 
income is foregone, the answer is that, under our assump- 
tion of zero interest, there would be no preference for the 
immediate over the remote income of $5500. The owner 
of the plant would just as willingly wait a hundred years 
for his $5500 as to receive it now. In actual fact, men are 
not thus willing to wait, and therein lies the unreality of 
our assumption that interest is zero. In otu- supposititious 
case the element of time-preference was abstracted with 
the element of interest. But this imaginary case shows 
that absence of interest is quite compatible with the pres- 
ence of physical-productivity, and that, therefore, whatever 
element is responsible for the existence of interest in the 
actual world, that element cannot be physical-productivity. 



I 

r. 



§8 

It was with a view to meeting some of the difficulties 
which have just been pomted out in the productivity theo- 
ries, that Alexander Del Mar and Henry George suggested 
their theory of interest,' basing it on the productivity of 
those particular kinds of capital which reproduce them- 
selves. They state that, were all capital inanimate, the 
phenomena of interest would not exist, because inanimate 
capital is incapable of increasing; but that the organic 
forms of capital are capable, without labor, of reproducing 
and increasing with time. Money, as Aristotle said, is 
barren, and coal and iron cannot breed. Were all capital 
of this non-increasing kind, it would, said Henry George, 
not yield interest. But a flock of sheep, herd of cattle, or 
group of Belgian hares will, from its own natural powers 
of breeding, increase and multiply ; it will, as it were, ac- 

* Del Mar, Science of Money, (Macmillan) 1896, p. 144. Henry 
George, Progress and Poverty. For a general criticism of this theory, 
Bee Dwight M. Lowry, "The Basis of Interest," American Academy 
of Political and Social Science, March, 1892, pp. 53-76. 



Sec. 9] 



PRODUCTIVITY THEORIES 



23 



cumulate at compound interest. In liKe manner a forest 
will grow, and crops will spring up. Tliese seeui to show a 
rate of interest in Nature herself. Mr. George contends 
that a man who puts $1000 into a savings bank can tle- 
mand that it receive interest, for the reason that he might 
invest it in a flock of sheep and let it accumulate naturally. 
According to this theory, interest exists because plants and 
animals grow, because the seed becomes the crop, the sap- 
ling becomes a tree, the egg a chick, and the chick a hen. 
The conclusion is drawn that, in the last analysis, the rate 
of interest consists in the "average rate of growth of ani- 
mals and plants." 

We niay remark at the outset that this theory, like the 
land-yicliling theory of Turgot, is one-sided and partial, 
inasmuch as it makes the rate of interest from all capital 
depenil on the rate of interest from one particular form of 
capital ; and it does not seem likely, a priori, that any theory 
of interest can be true which does not apply alike to all 
forms of capital which yield interest. But, aside from 
this preliminary objection, a specific examination of his 
theory will show that Henry George has not escaped the 
j fatal error of assuming a rate of interest in order to prove 
I it. We propose to make a thorough reexamination of this 
theory, not because it has attracted any special attention 
or been accepted by others than its author or authors, but 
because it puts the productivity theory on its strongest 
grounds — stronger grounds than its opponents have 
usually acknowledged or understood — and more esp)ecially 
because, in a dormant state, it seems to exist in the minds 
of a great many persons. 



§9 



Ix'f us imagine a forest growing at a certain rate, such, for 
instance, that an acre of spruce cuutaiuing 100 cords of wood 
suitable for making wood pulp will, if let alone, in five 



24 



THE RATE OF INTEREST 



[Chap. II 



years amount to 200 cords. Here is an increase of 100 
per cent, in five years, which is at the rate of about 15 
per cent, per annum. Does this 15 per cent, represent a 
natural rate of interest? Would 100 cords of this year's 
timber exchange for 115 cords of next year's timber? If 
80, we certainly have a simp.j physical basis for the rate 
of interest quite independent of the psychological element. 
But a little consideration will show that there is an error 
in the reasoning. If the supply of wood pulp is decreas- 
ing as years go on, while the demand is steadily increasing 
(and these conditions correspond to the facts as they are 
to-day), it may well be that 100 cords of this year's timber 
would exchange for a relatively small amount of next year's 
timber, say 105 cords, in spite of the fact that it grows 
at 15 per cent, per annum instead of 5 per cent. That this 
rate of exchange of present wood for future wood is quite 
compa'ib^e with a much greater rate of growth will be- 
come apparent as soon as we consider that growing timber 
is not the same thing as cut wood. It is clear that to 
cut young timber which is growing very fast is like killing 
the goose that lays the golden egg, and to reckon the value 
of the growing timber as only equivalent to the wood 
contained in it is like reckoning a live goose equivalent 
to a dead one. The value, in cut wood of 100 cords of 
rapidly growing timber will be consitler{;bly greater than 100 
cords of cut wood. If, for instance, the possessor of the 
growing timber has the option, besides that of cutting it, 
of allowing it to stand for five years and then obtaining a 
stumpage of 200 cords, he will allow it to stand, for these 
200 cords due five years hence are worth, in present esti- 
mation, discounted at 5 per cent., 157 cords. Thus his present 
100 cords of standing timber is equivalent to 157 cords of 
present cut wood. The value of a tree at any time iai 
therefore not necessarily the physical amount of wood! 
then in it ; it may be the discounted value of the future wood ' 
which the tree will produce if left to grow. It will actually 
be whichever of the two happens to be the greater. For, 



Sec. 9] 



PRODUCTIVITY THEORIES 



25 



m 



■1 



of various optional employments of his capital, the investor 
selects the one which offers the maximum present value.* 
Were it true that the value of a tree in wood were always 
simply the physical amount of wood it contains, it would 
be a matter of indifference whether a tree were cut at 
the sapling stage or any other, whereas we know that 
part of the art of lumbering consists in selecting the right 
age for cutting. 
The case may be illustrated by Figure 1. Let AB repre- 




sent the number of cords of wood on an acre of growing 
trees, A'B* the amount of wood which may be expected 
at the end of five years, A^B" what may be expected in 
ten years, and so on for successive years until the forest 
reaches its maximum growth, MN, at the end of AM 

' See The Nature of Capital and Income, pp. 221-222. 



26 



THE RATE OF INTEREST 



[Chap. II 



I ' 



years. The percentage-slope* of the curve BN at any 
point, therefore, represents the rate of growth of the 
forest. The value at present of the forest in terms of cords 
of wood will be represented, not by the height AB, but in 
a different manner, as follows: If from B' the discount 
curve * B'C be drawn, the ordinates of which will represent 
the discountetl values of A'B' at any times, AC will repre- 
sent the present value of A'B', the wood if cut in five years. 
Similarly, AC" will represent the present value of A''B'', 
the wood if cut in ten years. Draw in like manner a num- 
ber of discount curves until one is found, tT, which is tan- 
gent to the curve BN. At will then be the correct value 
of the young forest, and D will represent the time at which 
it should be cut. Clearly, At is quite different from AB, 
the amoimt of wood at the present time, and also from 
DT, the amount of wooil at the time of cutting. At is the 
maximum present value out of all possible choices. If 
the forest is for some reason to be cut at once, its value 
will be only AB; if it is to e cut at A', its present value 
will be AC; if at A", its present value will be AC; if at 
D, its value will be At. At is the maximum, for if the for- 
est were cut at any other point on either side of T the dis- 
count curve passing through that point would evidently 
pass below tT. 

At the time A, then, the wood in the forest is only AB, 
but, assuming proper foresting, the value of the forest in 
terms of wood is At; the rate of growth of the forest is 
the percentage-slope of BN at B, but the rate of interest 
is the percentage-slope (the same at all points) of tT. At 
the point of tangency alone, namely, T, are the rate of 
growth and rate of interest identical, and to that extent 
there is truth in the thesis that the rate of interest is tht- 
rate of growth. This element of truth in the organic 

' By percentage-slope is meant the ratio of the slope to the ordi- 
nat«. See The Nature of Capital and Income, Appendi. tu Chaj; 
XII, J 2. 

' See The Nature of Capital and Income, Chap. XIII. 



Sec. 9] 



PRODUCTIVITY THEORIES 



27 






productivity theory will be more fully discussed when 
we come to develop our own theory of the rate of in- 
terest. But that this element of truth is insufficient to 
afford a determination of the rate^ of interest is evident 
when we consider that the point at which the forest is to 
be cut itself depends, among other causes, upon the rate of 
interest. If the interest rate risf's, the discount curves em- 
ployed become steeper and the point of tangency T moves 
toward the left ; that is, the forest will be cut earlier. This 
is undoubtedly one reason for the fact that forests in the 
United States have hitherto been cut early ; the owner 
have not felt that they could afford to "lose the interest" 
in waiting. In Europe, on the other hand, where interest' 
rates have been low, forestry culture, though often involv- 
ing fifty years' waitmg, has been profitable. It would 
not be correct, of course, to ascribe the difference in forest 
policy wholly to a difference in the rate of interest, for 
the European policy has also been more enlightened than 
the American. 

Not only does the most favorable time for cutting depend 
upon the rate of interest, but the rate of interest itself 
depends upon the future distribution of the times of cut- 
ting of many forests. If all the forests of a country are 
young, there will be a relative scarcity of present wood and 
a consequent enhancement of the rate of interest (in terms 
of wood) which will make for early cuttmg. In the United 
State- at the present time the reverse is the case. There 
^ a present abundant supply of spruce for wood pulp, 
Hir a single edition of a large metropolitan Sunday news- 
taper will use up two acres of spruce. We have, therefore, 
3 (SHitempiate a growing scarcity of wood, and probably 
=ai ^f same time an increasing demand for it. The effect 
is u enhance the value relatively of future wood, that is, 
to tower the rate of interest in wood. This shifts the point 
d sangency T toward the right and introduces a ten- 
deacy to postpone cutting, as is manifested by speculation 
m. ^ruce forests. 






^'H— 5WCJ/! 



28 



THE RATE OF INTEREST 



[Chap. II 



10 



t . 



It I 



From what has been said it is clear that although interest 
enters into the processe, ct /lature, it is not because of their 
physical expansion, but because they require time. It is 
not because the seed grows into crops or the egg into a 
chick that there is interest, but because the crops or the 
chick are unavailable until a future time. The type of 
interest is a "time-lock" like those used on the doors of 
some banks. Nature holds many treasures in her store- 
house, but she will not unlock them all at once. 

The conclusion, therefore, from our study of the various 
forms of the productivity theory is that physical-pro- 
ductivity, of itself, has no such direct relation to the rate 
of interest as is usually ascribed to it ; and in the theories 
which we have examined, the rate of interest is always 
surreptitiously introduced. It is, however, quite true that 
the productivity of capital does affect the rate of interest; 
for it aflfects the relative valuation of present and future 
goods by affecting the relative endowment of the present 
and the future. It is quite true, in particular, that the 
rapidity of growth of the organic world will affect the rate 
of interest by redistributing income between different points 
of time and by opening up a series of choices to the owner 
a: to the time of cutting his forests or of reaping the 
rewards of other sorts of organic growth. It follows that 
the rate of growth will coincide at certain points with the 
rate of interest. These small grains of truth in the pro- 
ductivity theories will be fully incorporated in our study 
at a later stage. 



I 



CHAPTER III 

COST THEORIES 



§ 1 

We turn now from those theories of interest based mainly 
on the idea of productivity to those based mainly on that of 
cost. 

The first of the cost theories to be examined resembles 
closely the productivity theories, the only difference being 
that the "cost of production of capital" takes the place of 
the value of capital. In the productivity theories, the rate 
of interest was sought in the ratio between the income 
from capital and the value of that capital. In the cost 
theory now considered, on the other hand, the rate of in- 
terest is sought in the ratio between the income from capi- 
tal and the cost of that capital. This theory is subject to 
many of the objections which apply to the productivity 
theories. In the first place, it is necessary, before the 
ratio of income to cost can be regarded as even commen- 
surable with a rate of interest, that income and cost shall 
have been reduced to a common denomination of value, 
as, for instance, dollars. A loom renders its return, or ser- 
%ice, by the operation called weaving. The cost of the 
loom, on the other hand, consists of mw materials, the use 
of tools, dies, lathes, and other machine-shop appliances, 
togethf^r with human labor. Only when these miscella-i 
neous items are reduced to some common standard of value ' 
docs the ratio of income to cost become a mere percentage 
like the rate of interest. But when this reduction to a 
common standard is effected, the suspicion immediately 
arises that, after all, the question of interest may have 

20 






r^ 



il 



30 



THE RATE OF INTEREST 



[Chap. Ill 



(been begged in the process,— that the labor, materials, 
and use of tools all derive their value as costs, in part, at 
least, from discounting the prospective product to which 
they contribute. In other words, since the cost of capi- 
tal must be obtained by a process of valuation, this valua- 
tion may involve the very rate of interest to be determined. 

Nevertheless, the theory which seeks the rate of interest 
in the ratio of return to cost of capital has certain advan- 
tages over that which seeks it in the ratio of return to value 
of capital; for there are some costs which are not merely 
the discounted value of expected services. There are 
two kinds of costs, (1) "interactions'" and (2) labor- 
and-trouble. The value of the former is always de- 
termined by discounting some future service; the value 
of the latter is determined (to the laborer) by theirksome- 
ness or "undesirability" of labor compared with the de- 
sirability of money. We are not called upon, however, 
to strengthen the cost theories by recourse to this distinc- 
tion between costs which involve discounting and costs 
which do not; for the cost theories as actually held and 
advocated take no account of such a distinction, and the 
costs usually cited are mainly costs which do involve 
j discounting, — in other words, interactions. Such costs 
certainly cannot be taken as a sufficient foundation for 
explaining the rate of interest. The tailor reckons among 
his costs the value of the cloth which he buys; the manu- 
facturer of the cloth reckons among his costs the value of 
the yarn; the producer of the yam reckons in his cost the 
value of the wool. But the value of the wool is found in 
part by discounting the value of the yarn to which it 
contributes; that of the yam, by discounting the value 
of the cloth; that of the cloth, by discounting the value 
of the clothes. 

It is seldom i)08sible in practice to find a case so pure 
as not to be obscured by a number of different ele- 
ments; but let us, for the sake of illustration, consider 

' Si^t- Tin Saiurt- of Capital and Income, Chaps. VII -X. 



Sec. 2] 



COST THEORIES 



31 



a dealer in trees, who buys saplings and sells taem after 
they are full grown. In this ca.se there are few other 
costs besides the cost of buying the saplings. We can here 
see clearly the fallacy involved in regarding the rate of in- 
terest as determined by the ratio of the value of the full- 
grown tree to the cost of the sapling ; for the cost of buying 
the sapling is evidently itself obtained by discounting the 
value of the tree. In fact, in this case the cost theory 
becomes identical with the productivity theory; for the 
cost of buying the sapling is nothing more nor less than the 
value of the sapling. 'Hie only distinction between them 
is a formal one : the cost of buying the sapling is regarded 
as pertaining to the income and outgo account ; the value 
of the sapling, to the capital account. Since, then, the 
cost of buying the sapling is the di. counted value of the 
tree, this cost can be computed only by di.«!counting, and 
discounting presupposes a rate of interest. In many 
cases, therefore, "cost" is merely the discounted value of 
"return." The cost, in these cases at least, depends on 
the rate of interest, not the rate of interest on the cost. 



§ 2 



It is true that an article sometimes costs less (or more) 
than the discounted value of the returns. Tlie ratio of 
future return to present cost ma> then temporarily differ 
from the rate of interest on loans. Thus, a manufacturer 
calculates that a newly invented machine will earn him 
$10 a year for twenty years. If we suppose he is willing 
to invest on a 5 per cent, basis, namely, that subjectively 
ho values this year's goods at a premium of 5 jx^r cent, 
compared with next year's gootls, then the price he is 
willing to pay for the machine is $125, this being the 
present worth, at 5 per cent., of $10 a year for twenty years. 
But it may be that the cost of obtaining the machine is 
not $125 bui, .say, $i(K), which corresponds to an 8 per 



J^ 



I if 



Hi I 



32 



THE RATE OF INTEREST 



[Chap. Ill 



cent, basis. Here seems to be a natural rate of interest of 
8 per cent., in defiance of an interest rate of 5 per cent, em- 
ployed by the manufacturer in discounting his returns. 
The manufacturer, by investing $100, makes 8 per cent. — 
not, apparently, because he or any one else discounts the 
future at that rate, but simply because of the productivity 
of the machine in relation to its cost. 

But such a disharmony between the 8 per cent, realized 
and the 5 per cent, employed in discounting will be only ta^^ 
porary. It will work out its own correction, for the manu- 
facturer who finds he can invest at 8 per cent, when he 
is willing to invest at 5 per cent, will increase his invest- 
ment until the returns fall to 5 per cent. He will buy 
more machines; but the more he buys, the less will he 
make from each successive machine. The tenth machine 
will not increase his income rate by $10 over and above 
what it would bf- with only nine machines, but by, let us 
say, only $6.25 This reduction may be due to outrun- 
ning his market and reducing the price he can get, or by 
increasing the cost of running, or in other ways. He will 
buy machines up to the point where the last increment 
earns 5 per cent., and by the "law of indifference" he will 
impute this same rate to all the machines. In other words, 
however much the ratio of return to cost may temporarily 
deviate from the rate of preference for present over future 
goods, such deviatiun is done away with at the margin of 
final choice. Excessive rates of return could never serve 
as a permanent basis for market values, for the rush to 
secure these excessive returns would reduce them. If, on 
the other hantl, the cost of the machine is $150, represent- 
ing a basis of about 3 per cent., while the manufacturer 
continues willing to invest only on a 5 per cent, basis, 
there may soeiii to lie a natural rate of 3 per cent. Here, 
too. the a()parent disharmony will work out its own cor- 
rection. The manufacturer will cease buying machines to 
replace the old ones which have worn out, until through 
such liinitation the returns have Increased to 5 per cent. 



Sec. 3] 



COST THEORIES 



33 



In either case, when equilibrium is established the value of 
the machine is the discounted value of its future uses. 
For the individual purchaser, the cost of the machine 
appears as a fixed quantity, and he so adjusts the number 
of machines that the return of the marginal machine is 
5 per cent, on this cost. For the market as a whole, how- 
ever, the situation is reversed ; the price of the machines is 
determined by their prospective return. 



§3 

So far as the cost theories of interest relate to labor 
cost, they are free from the objection of begging the ques- 
tion, which has just been offered to the more general cost- 
theor> ; and yet, the ratio of return on labor to the labor 
invested cannot, by itself, afford a sufficient basis for the 
rate of interest, for the reason that neither the return nor 
the labor are fixed quantities. With an increase in the 
amount of capital, the return will decrease, and the labor 
of obtaining it will uicrease. This, in fact, is the well- 
known "law of diminishing returns." 

To render our reasoning clear, we shall take a clas.sical 
illustration of Roscher's. Let the kbor sacrificed in produc- 
ing a fishing net be reckoned at 100 fish. This valuation of 
labor hy the laborer is not quite like the valuation of the 
machine. Instead of being the value of future income dis- 
counted, it is the value of present outgo in the form of 
effort. We cannot, therefore, maintain that in valuing the 
net the rate of interest is surreptitiously introduced. Our 
objections arc now confined to the fact that both the labor 
of making the net and its return are not fixed elements to 
which the rate of interest is adjusted, but are themselves 
adjustable to that rate. With the net, the fisherman is 
enabletl to catch 30 fish a day, whe. ? without it he could 
catch but 3. We may suppose that the net will last 90 
days, gelling In all 2700 fish. This is the return on the 



.-.il 



M 



34 



THE RATE OF INTEREST 



[Chap. Ill 



II 



I 1 

i 



1 

I 



labor invested, which has been reckoned at 100 fish. If 
the net requires care and attention, and this be reckoned 
at 3 fish a day, there is still an excess of 30 — 3, or 27 fish 
a day to be credited to the net itself. For the 90 days this 
amounts to 2430 fish. Even if, for other reasons, we 
make further reductions, the return may still be a very 
large one compared with the 100 fish invested, — let 
us say 2000 fish. 

The question now is, does the excess of this return 
over the labor invested explain interest? Certainly not. 
Granted that such an extraordinary return on one's labor 
invested were initially realized, it is evident that nets 
paying so handsomely would be made in large numbers, 
and that, as their numbers were increased, the labor 
and sacrifice of making each additional net would in- 
crease, or else the product obtained from each additional 
net would decrease, or both. In this way the excess 
of return over cost would be doubly reduced. Why should 
not this excess be reduced to zero? Evidently nothing in 
the physical nature of the net itself, or the condition of 
the fisheries, or the amount of labor involved in producing 
a net, will suffice to explain the point at which the process 
will cease and nets no longer be produced. On the con- 
trary, it is evident that physically it would be possible to 
greatly overproduce the nets. It is also clear that the 
fisheries could not continue to yield fish indefinitely. The 
result might be that, as the nets were increased in num- 
ber, the labor of obtaining materials and making nets 
would increase until, let us say, a net would cost labor 
reckoned equivalent to 1000 fish; at the same time the 
yield of each net might fall to, say, 10 fish a day for the 
90 days, or 900 fish in all. Here would be an invest- 
ment of 1000 for a return of only 900. The reason that 
this result would not, intentionally at least, be reached, is 
evidently not to be sought in any physical facts as to 
the net, the fish, and the labor of producing them, but in 
the fact that the net makers would of their own volition 



Sic. 4] 



COST THEORISS 



35 



cease producing nets before such a superabundance was 
put upon the market. In fact, they would even refuse to 
invest 1000 for an equal return of 1000. In other words, 
the production of nets would proceed only up to the point 
where the excess of return over cost corresponded to the 
relative preference for present over future fish. The rea- 
son, then, that the prorluct keeps above the cost is simply 
that those who make r. *ts decide to stop making them at 
a point earlier than that of equality between cost and re- 
turn, and their decisions so to do are based not on a 
physical but on a psychical fact— their relative valua- 
tions of present sacrifice and future return. 

Leaving our special illustration, let us put the matter 
in general terms. It is often stated by economists that 
any capital will be constructed only so long as its mar- 
ginal utility is equal to or greater than the marginal dis- 
utility or marginal cost of its construction. The greater 
the desire for its services and the less the cost of produc- 
tion, the more of it will be produced before its marginal 
utility falls to the level of its marginal cost. But the 
proper statement would be, not that the marginal utility 
of the services of a capital instrument tends to equal the 
marginal cost of the instrument, but that it tends to reach 
a level slightly above that cost, such that the present or 
dwcounted estimate of the marginal utility of future ser- 
vices will equal marginal cost. 



§4 

Sometimes the argument of the cost theorists takes a 
slightly different form. It is said that the net, for instance 
receives mterest because it "saves labor." If by "saving 
labor" is meant that the net costs less than it produces, - 
that the labor of constructing and tending the net, meas- 
ured m fish, is less than the number of fish caught by the 
net, —the argument is merely a repetition, in different 



ii lii 



r i 



t ' 



36 



THE RATE OP INTEREST 



[Chap. Ill 



words, of the argument which has just been stated and 
criticised, that the net receives interest because it produces 
something over and above its cost. If, on the other hand, 
by "saving labor" is meant simply that the net catches 
more fish than its owner could catch without it (30 fish 
a day instead of 3), the argument is superficial; it leaves 
entirely out of account the cost of constructing the net, 
which is evidently an essential factor in reckoning the rate 
of return. For aught which this statement of "labor- 
saving" contains, the net might have cost or be worth 
10,000 fish. Such a net, though "saving labor" for 90 
days, would never earn its original cost, and there could be 
no interest, m spite of this "saving of labor." 

The adherents of the labor-saving theory of interest 
may put their case in a third and stronger form. They 
may say (1) that the net first costs labor to produce, (2) 
that it afterward saves labor in operating, and (3) that the 
labor subsequently saved exceeds the labor originally ex- 
pended. The excess of the labor saved over the labor 
expended, both being measured, say, in fish, is, according 
to their theory, the source of mterest. There is an ele- 
ment of truth in the theory as thus stated, and this 
element will be incorporated into the constructive argu- 
ment in Chapter VIII. But the element of truth is in- 
adequate to form a complete theory of interest for the 
reason that the excess of labor saved over labor spent is 
not a fixed excess, but depends on the voluntary choice of 
the fishermen as to the number of nets they propose to 
make. Their choice depends on how much present labor 
they are willing to spend in order to save tht mselves a 
given amount of future labor; it depends, in other words, 
on their relative valuation of present and future labor. 



55 

In the example of the net, labor-sacrifice and return were 
both measured in a common objective standard, — fish. 



Sec. 5] 



COST THEORIES 



37 



A still more elementary case is that in which both cost and 
return are measured in a common subjective standard, — 
utility. The desirability of the fish and the labor-cost of 
obtaining them are comparable magnitudes, the one being 
utility (or desirability) and the other disutility (or un- 
desirability). 

To change our illustration, let Robinson Crusoe be 
suddenly placed on a fertile island suitable for banana 
growing. He will be able at first, owing to the great fer- 
tility, to get a high degree of satisfaction in consuming 
bananas by the expenditure of a low degree of labor in 
planting and cultivatmg the trees. But the same objec- 
tions apply as before ; for the excess of subjective satisfac- 
tion over subjective effort is no more fixed than any other 
excess of return over cost, and Crusoe may, if inclined, be 
so industrious in his raising of bananas as to vastly increase 
the labor of raising them, or, by satiating himself with them, 
decrease the satisfaction which they yield, or both. This 
process will proceed far enough to reduce the excess of satis- 
faction over effort to such dimensions as Crusoe's relative 
valuation of present effort and future satisfaction will 
allow. The stopping point is determined by him, not by 
any natural yield of the soil. The mere fact that the 
island is naturally fertile, so that labor is especially pro- 
ductive, cannot determine the degree of intensive culture 
which Crusoe may apply to it. 

The same principles apply to every unusually lucrative 
employment. Man is continually hunting, as it were, for 
bargains with Nature; but he deals at Nature's bargain 
counter only up to a definite point, — a point decided upon 
by him and not by Nature. We cannot obtain a true and 
complete explanation of interest without recourse to the 
psychological element of human choice. 

Those who have made the most successful use of the cost 
theory of interest are John Rae' and Adolphe Landry,* 

• The Soeiologictd Theory of CapiUd, edited by Professor C. W. Mix- 
ter, (Macmillan) 1905. 

» L'InUrU du Capital, Paris (Giard & Brifere), 1904. 



'U 






38 



THE RATE OF INTEREST 



[Chap. Ill 



and both of these expressly admit that the ratio of return 
to cost can influence the rate of interest only as the mar- 
gmal excess of retivn over cost harmonizes with the degree 
of preference for present over future goods. No objection 
is here offered to the general reasoning of Rae and Landry. 
Their results and those shown in the present book are for 
the most part in agreement. The chief difference, in so 
far as the present topic is concerned, grows out of the fact 
that neither Rae nor Landry made use of any definite theory 
of income, the relation of cost to income, and the distinc- 
tion between labor-costs and "interactions." 



M 

i 






1 f 



§6 

Some economists, whom Professor Bohm-Bawerk clas- 
sifies as the " labor theorists of the EngUsh school," have 
attempted to explain the rate of interest as a sort of wage 
for the labor of producing capital. This theory is very 
crude and does not need extended discussion ; for it is evi- 
dent that the labor which produces the capital very seldom 
receives the interest. Suppose that a tree twenty-five 
years old is worth $3, and was planted at a cost of $1 
worth of labor. The laborer was paid $1 when the tree 
was planted; evidently not he, but the capitalist who pays 
him, receives the $3 twenty-five years later and thereby en- 
joys an increase of value of $2. If this $2, which is inter- 
est, is produced by the laborer who planted the tree, why 
does he not get it ? It is quite true that the laborer pro- 
duces this "surplus value," and yet he is forced to let 
another receive it. 

This paradox has been made use of by the socialists, 
who maintain that interest ought to go to the laborers 
who produce the capital, but that they are robbed of it by 
the capitalist. This "exploitation theory of interest" con- 
sists virtually of two propositions: first, that the value 
of any product usually exceeds its cost of production ; and, 
secondly, that the value of any product ought to be exactly 



Sic. 6] 



COST THEORIES 



39 



equal to its cost of production. The first of these proposi- 
tions is true, but the second is false. Economists have 
usually pursued a wrong method in answering the social- 
ists, for they have attacked the first proposition instead of 
the second. The socialist is quite right in his contention 
that the value of the product exceeds the cost. In fact, 
this proposition is fundamental in the whole theory of cap- 
ital and interest. Ricardo here, as in many other places 
in economics, has been partly right and partly wrong. He 
was one of the first to fall into the fallacy that the value 
of the product was normally equal to its cost, but he also 
noted certain apparent "exceptions," as for instance, that 
tvine increased in value with years. As a matter of fact, 
as Bohm-Bawerk has fully shown, this increase of value, 
instead of being exceptional, is universal in the whole 
realm of production. It is just because the value of a 
Iproduct does exceed its cost that there exists tne possi- 
bility of any perpetual net income.' Not only, therefore, 
is there no necessity that cost should equal return, but 
on the contrary, it never can normally do so. By making 
cost of production a corner-stone of the theory of value, 
the classical economists weakened their system greatly.' 

In attempting to prove that the laborer should receive the 
whole product, the socialist thus stands on stronger ground 
than has sometimes been admitted. He cannot be an- 

' See Chap. II and its Appendix, where it is shown that if each ma- 
chine costs exactly what it returns, and if the up-keep of a group of 
machines is maintained, the net annual income from the group is zero. 

' Besides the error that the cost of production theory -^mits the 
interest element, there was the error that most costs of production — 
all "interactic.'ia," in fact — are themselves not the cause but the 
result of value, being future values discounted. See The Nature of Capi- 
tal and Income, Chaps. X, XIV, XVII. This objection to the cost 
theory of value does not apply to labor-cost; but even labor-cost in 
not a necessary or universal accompaniment of value. A mineral 
spring may produce a valuable water without labor-cost. Land 
also is largely costless except for the cost of transferring it, wliich is 
an "interaetinn." Other rlaxfJiral examples of articles which have 
no cost of production are autographs of Miltoi. and similar memora- 
bilia. 



40 



THE RATE OF INTEREST 



[Chap. Ill 



I f 



swered offhand by saying that capital aids labor, and that 
the owner of a plow deserves an interest payment for its 
use quite as truly as the laborer who operates the plow 
deserves wages for his labor. The socialist contends that 
the payment for the use of the plow should belong, not to 
the man who holds it, but to the man who made it. He is 
quite correct in believing that the value of the uses of the 
plow is entirely due to the laborers who made it, but 
that, nevertheless, the capitalist, not the laborer, enjoys the 
value of these uses. The capitalist is, as a matter of fact, 
always living on the product of past labor. A millionaire 
who gets his income from railroads, ships, and houses, all 
products of labor, is reaping what labor sowed. The capi- 
talists of to-tlay are receiving compound interest on the 
labor of yesterday, 

§7 

But it does not follow that in this any injustice has been 

done to the laborer. Let us revert to the case of the tree 

which was planted with $1 worth of labor, and 25 years 

■later was worth $3. The socialist virtually asks, \\liy 

1 should not the laborer receive $3 instead of $1 for his work? 

The answer is that he may receive it, provided he will wait 

j 25 years for the $3 ! As Bohm-Bawerk says : ' — 

"The perfectly just proposition that the laborer should receive 
the entire value of his product may be understood to mean either 
n that the laborer should now receive the entire present value of his 
|i product, or should receive the entire future value of his product 
|itn the future. But Rodbertus and the socialists expomid it as it 
.it meant that the laborer should now receive the entire future 
value of his product." 

To take another example : if a number of laborers work 
upon a railroad which requires 5 years before it can be 
completed, and which, when completed, is worth $7,00,000, 
there is no reason, if the laborers are willing to wait until 
the road is completed, that they should not own and 
' Capital and Interest, p. 342. 



&c. 7] 



COST THEORIES 



41 



operate it. They would then be receiving, in the future, 
the future value of their product. If, however, they are 
paid at the time their work is being done, they may be 
paid in one of two ways. One is by having assigned to them 
such parts of the road as they have created so that they may 
retain the same until it is a finished product to return 
in !ome to them in future years. The other method, and 
the one which they much prefer, is to be paid in casl , 
convertible immediately into food, clothes, and other en- 
joyable income. Under these circumstances the road, 
which is to be worth $7,000,000, will be paid for in wages, 
not by $7,000,000, but by, say, $5,000,000. distributed at 
the rate of $1,000,000 a year for the 5 years reqmred to 
build the road. 

Socialists would cease to think that this is extortion 
if they would try the experiment of sending a colony of 
laborers into the unreclaimed lands of the West, lettmg 
them develop and irrigate those lands and build railways 
on them, unaided by borrowed capital. The colonists 
would find that interest had not disappeared by any means, 
but that by waiting they had themselves reaped the benefit 
of it. They would need to wait, let us say, 5 years before 
their railway was completed. At the end of that time 
they would own every cent of its earnings, and no " capi- 
talist" could be accused of robbing them of it. But they 
would find that, in spite of themselves, they had now 
become capitalists, and they had become so by stinting for 
those 5 years, instead of receiving in advance, in the shape 
of food, clothing, and other real income, the discounted 
value of the raih-oad. This example was almost literally 
realized in the case of the Mormon settlement in Utah. 
Tliose who went there originally possessed little capital, 
and did not pay mterest for the use of other persons' cap- 
ital. They created their capita' and passed from the 
category of "laborers" to that of ' capitalists." It will be 
seen that capitalists are not robbers of labor, but labor- 
brokers who buy work at one time and sell its products at 



41 




i 



M 



I 1 



42 



THE RATE OF INTEREST 



rCHAP. Ill 



another. Their profit on the transaction (or ra* ler, that 
part of it which is interest) is due to the time elapsing 
between the labor and its return to the capitalist. 



§8 

Among those who have attempted to justify interest- 
taking on a labor basis is a peculiar group of theorists who 
maintam that interest does actually go to the laborer — not 
the laborer who produces the capital, but the laborer who 
manages it. In other words, the "entrepreneur," "under- 
taker," or "enterpriser" is the one who creates interest 
and therefore tleserves it. This is another of the many at- 
tempts to maintain that every economic product nmst be 
a mere equivalent for some corresponding labor-outgo. 
The only evidence the adherents of this school can offer 
for the truth of their theory is, however, that capital can 
produce nothing without proper management. If, they 
say, no one lifts a finger to make capital protluctive, it will 
not be productive, and the man who plans, organizes, and 
controls the use of capital is the one who creates interest 
and ought to receive it. This theory, however, is evidently 
fallacious, if not self-destructive. For the person who 
receives interest, par excellence, is not the active "entrepre- 
neur," but his "sleeping partner." If the active capitalist 
produces the interest on the capital he borrows from his 
sleeping partner, who "does not lift a finger," why does he 
surrender any of it to that partner ? Is the sleeping part- 
ner "exploiting" his active associate? Of course it is 
true that the mere investor could get no interest were it 
not for some intelligent, active management of capital. 
But this inaiiagcment is paid for in the shape of entre-" 
preneur's jirofits. The mere fact that the entrepreneur's 
work is usually indispensable to the production of income 
would not justify his receivmg all of that income. In fact, 
we may rnnver-^i'ly state that the capital intrusted to the 



Sec. 9] 



COST THEORIES 



43 



entrepreneur is quite as indispensable to him as is his work 
to the inactive capitalist. 



A 



§9 



^So determined have been the attempts to justify interest 
on the ground of some cost of production that, in the ab- 
sence of any other item which can be called cost, a special 
constructive cost called "abstinence" or "waiting" has 
been invoked to meet the emergency. Certam French 
economists have even gone so far as to call this the "labor 
of saving." The al)stinence theory in its various forms 
holds that the capitalist, by abstaining from the consump- 
tion of his capital, obU'.ios a reward in the shape of interest. 

T ^ abstinence theory bears a close resemblance to the 
"agi theory of interest, which is believed by the writer 
to be essential!^ correct. In fact, it has been claimed by 
some writers tlmt the abstinence theory differs from the 
agio theory merely in words. This claim is perhaps true 
of certam versions of the theory, and agamst these no criti- 
cism need here be offered, unless it be a verbal one. If by 
saymg that mterest is the reward of waiting or abstinence 
it is only meant that men prefer not to wait for the future, 
but to enjoy the present, the only objection which need be 
offeied is that the mode of statement is somewhat unhappy ; 
it implies, apparently, that future rewards are caused by 
making present sacrifices, rather than that present sacri 
fices are caused by the prospect of future rewards. 

But in the sense in which the abstinence theory is usually 
held, it differs from the agio theory not only in words but 
in essence. As Bohm-Bawerk has shown, it aasumea that 
"abstinence" is an independent item in cost of production, 
to be added to the other costs and to be treated in all ways 
like them. With this proposition issue is here joined. If 
"abstinence" or "waiting" or "labor of saving" is in any 
sense a cost, it is certainly a cost in a very different sense 
from ail other items which have previously been con- 



/■ 



44 



THE RATE OF INTEREST 



[Chap. Ill 



I i 



' I- 



sidered as costs. An illustration will make clear the dif- 
ference between true costs and the purely constructive 
cost of waiting. According to the theory that waiting is 
a cost, if planting a sapling costs $1 worth of labor, and in 
25 years, without further expenditure of labor, this sapling 
becomes worth $3, this $3 is a mere equivalent for the entire 
cost of producing the tree. The items in this cost are, it 
is claimed, $1 worth of labor and $2 worth of "waiting." 

According to the theory of the present book, however, the 
cost of producing the tree is the $1 worth of labor, and 
nothing more. The value of the tree, $3, exceeds that 
cost by a surplus of $2, the existence of ^v•hich as interest 
it is our business to explain. At first it would seem u mere 
matter of words whether we call the $2 a surplus above cost, 
or an item constituting another cost, known as "waiting." 
But examination will show that the two so-called "costs" 
are radically different. 

If waiting is a cost like other costs, it should be subject 
to the law of discount, according to which the capital- 
value of any article of wealth is equal to the discounted 
value of its expected income less the discounted value of its 
expected outgo. The value of the tree which has just been 
mentioned, taken, say, at the end of 14 years, will actually 
be about $2, and this is the discounted value of the S3 of 
uicome which the tree will yield at the end of eleven more 
years. According to our own theory, this $3 is the only 
future item of income or outgo. But according to the 
theory here criticised, besides this positive item of income, 
S3 due in eleven years, we have to deal with a series of 
eleven negative items called "waiting," distributed through 
these eleven years, and amounting to the interest, — 
about 10 cents for the first year and gradually increasing to 15 
cents for the last year. Now if these costs really exist, 
they ought to be discounted and their discounted value 
deducted from the discounted value of the S3 of expected 
income. But we should then have to assign a value to the 
tree not of $2, as it actually is, but of about $1, which is 



Sec. 10] 



COST THEORIES 



45 



erroneous. If the waiting-items were bona fide annual costs, 

— like, for instance, actual labor-costs of pnming the trees, 

— the process of discount would properly be applied to 
them. The fact that it cannot be applied to the so-called 
"cost of waiting" without leading to an erroneous result is 
a proof that the "cost of waiting" differs radically from 
true costs, y 

Thus, tWe theory that waiting is a cost or outgo is a fal- 
lacy exactly the inverse of the fallacy that saving is income 
explained in The Nature of Capital and Income.^ Both 
have to deal with the increase of capital- value ; the one 
theory regards this increase as income, the other as outgo. 
As a matter of fact, it is neither income nor outgo, but 
increase of capital only. 



§ 10 

As an answer to the objection just urged against treating 
waiting as a cost, namely, that it cannot be discounted, it 
might be pointed out by the abstinence theorists that while 
waiting-cost is certainly not a discountable cost, its inclu- 
sion in the list of costs obviates the necessity of discounting 
the other items of cost or of income. If all mcome and all 
cost items, including waiting, are counted at full value, 
capital may be valued simply by taking their net sum, 
without subjecting any item to the discounting process. 
To count "waiting" as a cost, then, appears as an pltema- 
tive method of keeping accounts. Accepting this answer 
for the sake of argument, we observe that while it obviates 
the objection to the abstinence theory of cost so far as its 
application to capital value is concerned, it leaves objec- 
tions equally great to its application to income. If wait- 
ing is a cost like other items, it must be included on the 
outgo side of the income account. To show how this 

' Chap. XIV. Cf. as to the fallacy here coniiideiwd^ Bdhm-Bawerk, 
lUetnt LiUrtUun on IttUntt (Macmiilan), 1903, p. 3S a. 



If 



46 



THE RATE OP INTEREST 



[Chap. Ill 



I f 



II i 



would apply to the cost of the tree, the following table is 
presented : — 



Income 


OUTOO 


Nkt 
Income 


Capitai- 

Value at 

End or 

TKbar 


1st year 

2d year 

3d year 

* * * « 41 * « 

14th year .... 

* * * * m 41 « 

25th ye ir. from sale 
of tree .... 


00.00 

00.00 
00.00 

* * 

00.00 

* * 

3.00 


Labor 1.00 
"Waiting" .06 
"Waiting" .05 
"Waiting" .05 

* * * ♦ » 

"Waiting" .10 

***** 

"Waiting" .15 


1.05 
1.10 

1.15 

* * 

2.00 

* * 

3.00 


Total .... 


3.00 


3.00 


00.00 





According to this method of accounting, we see that 
during the year in which the sapling is planted its cost con- 
sists of labor to the extent of $1, expended, let us say, at 
the beginning of the year, and 5 cents' worth of waiting 
suffered during the course of the year. During the second 
year a waiting cost of about the same amount is incurred, 
and so on for each succeeding year, the cost of waiting 
gradually increasing as the tables of compound interest 
would indicate, until in the fourteenth year it amounts to 
10 cents, and in the twenty-fifth year to 15 cents. The 
total CO.S. for the 25 years will then be $:i, and the 
return to the planter at the end, from the sale of the tree, 
will also l)e $3. Consequently, If we take the whole 
period from the first application of labor to the final sale of 
the tree, tlie net income will l)e zero. This result is, to 
say the least, somewhat surprising, but not so much so as 
some other results of the same bookkeeping, as the fol- 
lowing additional examples will show. 

Suppose .1 person owns an annuity amounting to $100 a 
year for 10 ytaru. According to any ordinary method 



Sec. 10] 



COST THEORIES 



47 



of keeping accounts, his income consists of this $100 a year 
each year. But if we count the waiting as a cost, we shall 
find that the income for each year is less than $100. The 
owner of such an annuity will, during the first year, have 
to suffer "waiting" to the extent of $39, supposing iilterest 
is at 5 per cent. ; for this is the increase in value of his an- 
nuity during that year, due to his waiting for the future 
instalments of income of which his annuity consists.' His 
net income during that year, therefore, according to such 
accounting, is not $100, but $100-$39, or $61. During 
the second year his income is somewhat greater, for the 
cost of " waiting " is only $35. His net income i.s, therefore, 
$100 -$35, or $65. Similar computations carried out for 
succeeding years result in the following table : — 




Ist year 
2d year 
3d year 
4th year 
5th year 
6th year 
7th year 
8th year 
9th year 
10th year 



, money, 

i money, 

! money, 

money, 

j money. 

I money, 

I money, 

money, 

money 

money, 



SlOO 
100 
100 
100 
100 
100 
100 
100 
100 
100 



"Waiting"* 39 

"Waiting" 35 

"Waiting" 32 

"Waiting" 29 

"Waiting" 25 

"Waiting" 22 i 

I "Waiting" IS 

I "Waiting" 14 

'"Waiting" 9 

j " Waiting " 5 



i Net 
Incoue 


Capital 
Value at 

BEGI,N.M.V<i 

or Year 


1 S 61 


1772 


; 65 


711 


68 


646 


71 


578 


75 


507 


78 


432 



82 
86 
91 
95 



$1000 



$228 ! $772 



354 
272 

186 
95 



Is it good bookkeeping to introduce a new and strange 
element of cost which results in making the net income 
of the annuitant not the $100 which he actually receives, 

'Thin is evident, since the value of his annuity, cnpitaJiied at S ncr 
cent, recltoned at f 1,.. boEinninsr. i.H f 772, a-h<^r=a=^, revkoned at the end 
or the first year, before his $100 is paid, it i.-* $811. 



48 



THE RATE OF INTEREST 



[Chap. Ill 



but the sums given in the table; namely, $61, $65, $68, 
and so forth ? 

To push this criticism to the limit, let us finally consider 
a perpetual annuity of $100 a year. In this case we shall 
find that the "cost of waiting" each year is $100; for 
the value of such an annuity, reckoned at 5 per cent., is 
$2000 reckoned at the beginning of each year, and $2100 
reckoned at the end. If this cost of waiting is to be re- 
garded as a deduction from income, like other costs, we 
are forced to conclude that the owner of such a perpetual 
annuity receives each year no income whatever! For, if 
we deduct from the $100 of money-income the $100 of 
waiting, the remainder each year is zero ! 

It may be said that we have not always a mere annuity 
to deal with but a definite capital such as a house or a 
factory which has involved cost in its construction and 
the " sacrifice " of waiting for an income, whereas the 
capital might have been consumed at once. In all such 
cases, however, we are dealing with the very same prin- 
ciple. The possession of the house or factory, like the 
title to the annuity, is valuable only because of the service 
or the income which it is expected to yield. If there is 
for the house or factory an initial labor-cost or expense, 
this is also true of the annuity. On the other hand, the 
one as well as the other may come by inheritance and so 
involves no cost to its owner. What it is desired to em- 
phasize is that in any case the present value is the dis- 
counted value of the expected future services or income 
and that it is not any sacrifice or cost of waiting which 
produces this value but that, on the contrary, it is the 
existence of this future value which prompts the waiting. 



§ 11 

'It 18 obvious that the theory which calls "waiting" a 
coat has worked out its own abnurJity. Tiie moal Uiat can 



r^mm^ ' .1 



Sic. 11] 



COST THEORIES 



49 



be said in its favor is that it makes the capital-value of / 
any article equal to its cost of production. The idea that''/ 
the value of an article should equal its cost seems to pos- 
sess a certain fascination for many, if not most, students of 
economics/ That it is false has been sufficiently shown 
by Bohm-Bawerk through reasoning somewhat similar to 
the foregoing. That it is absurd when carried to its logical 
conclusion is evident when we consider what happens if the 
same method of bookkeeping is carried out with respect 
to the future as well as the past. It is a poor rule which 
wiU not work both ways. This rule, applied to future 
expected income and outgo, yields the strange result that 
the capital value of any article is normally not less than, 
but equal to, the expected income. Thus, to revert to 
the case of the tree, let us take its value at the end of 
14 years. It is then worth $2, which, m the parlance 
of the abstinence theorists, is equal to its previous cost 
of production, consistmg of $1 worth of labor plus $1 
worth of waiting during the 14 years. It is also, in 
like manner, equal to the future income to be derived 
from it, which consists of $3 worth of actual receipts 
from the sale of the tree, due at the end of eleven 
more years, less the cost of waiting for those $3, which 
amoimts to $1. 

In the same way, the ten-year annuitant just consid- 
ered has, at the beginning, property worth $772. This, 
according to any proper bookkeeping, is the discounted 
value of the future income of $100 a year for 10 years, the 
total amount of which is $1000. But, according to the 
abstinence theorists, the income which he receives for the 
whole period is, as has been shown, not this $1000, but 
$772, which is just equal to the value of the property. 
Pursuing the method of limits, we find that for the owner 
of a perpetual annuity the same proposition would hold 
good. According to the true and ordinary method of reck- 
onmg, the total income from such an annuity is lnfii;ity, 
although its present capital value is only $2000. But 



/' 



' •!*! 



\V' J'\ 




50 



THE RATE OF INTEREST 



[Chap. Ill 



according to the abstinence theorists the income itself is 
not infinite, but only $2000.' 

Those who are enamored of the simplicity and neatness 
of the formula of the abstinence theorists, by which the 
capital value is not greater than past cost of production, 
but exactly equal to it, can scarcely be attracted by the 
exaggerated simplicity of the inverse theorem which is 
also involved ; namely, that the capital value of any future 
expected income is not less than that income, but exactly 
equal to it also. 

§ 12 

The fallacy of the abstinence theorists lies in the simple 
fact that waitirig has no independent existence as a "cost." 
We can never locate it in time, nor estimate its amount, 
without first knowing some other more tangible costs. 
Waiting means nothing unless there is something waited 
for, and the cost of waiting can only be estimated in pro- 
portion to the magnitude of what is waited for. 

It will doubtless take a long time for many to accept the 
doctrine that the value of capital is not only less than its 
future expected income, but normally greater than its past 
cost. Even to those who do not formally accept any cost 
theory of interest, the mterest itself will seem in some 
sense to be a cost; and in most books on economics, in- 
terest, however explained, is n'garded as one of the costs 
of production. It is trie that for a debtor who pays in- 
terest, the interest is, to him, a real cost, and is debited on 

' Lest the non-mathematical reader should be puzzled by this 
result, which seems to contradict the fact already brouRht out, that 
under the pseudo-reckoning of the abstinence theorists the net in- 
com .i zero every year, it must be remembered that this zero income 
i.-* repeated an infinite number of times, and that when we deal with 
infinity we can get reliable results only by the method of limits. 
The mathematical reader will find no difficulty in showing, by the 
method of limits, that there is a "remainder term" which will, in 
the supposed accounting, make the t^t.al income distributed through 
all eternity simply equal to the capita] value, 12000. 






Sec. 13] 



COST THEORIES 



51 



his books. But we need only to be reminded of the debit 
and credit bookkeeping which was considered at length in 
The Nature of Capital and Income to see that this item is 
counterbalanced on the books of the creditor, to whom this 
mterest is by no means a cost, but an item of income For 
society as a whole, therefore, even in the case of interest 
which IS explicitly paid, it cannot be said that it consti- 
tutes a cost of production. In the case of a person who 
works with his own capital, the t.nth of this statement is 
even more evident. Economists who state that the inde- 
pendent capitalist must charge off interest as one of his 
costs of production seem to forget that such self-paid 
interest must be charged back agam as income also. The 
fallacy of assuming that interest is a cost is doubtless due 
to the habit of regarding production from the point of 
view of the " enterpriser." Since he usually pays interest, 
he comes to think of it purely as a cost. 

We have devoted considerable space to the refutation of 
the abstmence theory, because its errors are so subtle and 
insidious as to beguile many of the best and most wary 
of economists. 



§ 13 

The results of the present chapter may be summed up 
by grouping the cost theories under ^wo hoads: those 
which regard interest as in some sense a cost; and t'uoat; 
which regard interest as a surplus above cost. As we have 
seen, the contention of the first group is erroneous, whether 
the concept of cost employed is the "cost of producing capi- 
tal the "cost of managing," organizing, or investing it, 
or the purely constructive cost of "waitmg," "abstinence " 
or ''labor of saving." The contention of the second group, 
which considers interest as a surplus above cost, is correct- 
but the explanations which are given of this surplus are in- 
correct, or at any rate, incomplete, whether those explana- 






52 



THE RATE OF INTEREST 



[Crap. Ill 



. -} 



tions take the fanciful form of the socialists that interest is 
extortion, or the mere statement of fact of the cost produc- 
tivity theories, that nature yields a surplus above cost. In 
this last statement, however, lies the only grain of truth 
which can be ascribed to the cost theories. Although 
nature does not of herself yield a fixed surplus r bove cost, 
which may be called interest, she offers a serie!^ of such 
opportunities of getting a surplus, of which opportunities 
man takes advantage, and with respect to which he adjusts 
his efforts to his returns vmtil the surplus yielded corre- 
sponds to his subjective preference for present over future 
goods. In other words, just as in the case of the theories 
based on productivity, we find that the theories based on 
cost have an element of truth only as far as the oppor- 
tunities presented by nature are reviewed in the mind of 
man and decided upon according to his time preference. 



Ill 



I i 



1^' 

CHAPTER IV 
bShm-bawerk's theory 



A 



§ 1 



In the preceding three chapters the most common of 
the existing theories of interest have been stated and criti- 
cised. There remains one, however, which has received 
a large degree of currency among economists. Hitherto, 
m order to condense our review, we have employed the 
impersonal method and have rarely discussed the special 
mterpretations which individual writers have made of 
the several theories. In the present chapter, however, we 
shaU depart from this practice. The reason for criti- 
cismg Bohm-Bawerk's specific theory is that, unlike the 
theory of any other mdividual writer, it has become widely 
accepted. Capital and Interest and The PosUive Theory 
of Capital have become economic classics. There can be 
no question that they deserve the high esteem in which 
they are held, for they contain the material, both in vheir 
destructive criticism and in their constructive argument, 'or 
a correct theory of interest. For the most part, Bohni- 
Bawerk's work wiU doubtless always stand. At only one 
vital point do we regard it as defective. 

Bohm-Bawerk's theory is called by him the " agi< theory "5 
of interest, since it finds the essence of the rate of interesti 
m the agio or premium on present goods when exchange* 
for future goods. This theory is in the main accepted by' 
the present writer as the natural and proper star ing- 
pomt for any rational discussion of the subject. Bohm- 
Bawerk has presented the agio theory clearly and forcibly, 
and has disentangled it from the crude and incorrect 

63 



■-i : 



54 



THE RATE OF INTEREST 



(Chap. IV 



f. -i 



ilH 



notions with which it had previously been associated. It 
b only when he attempts to add to it his special feature 
of a "technical superiority of present over future goods " 
that he has impau-ed rather than improved it. 

The agio theory may be said to have been foreshadowed 
by mediaeval writers, some of whom stated that mterest 
could be justified by mora or "delay"; and the theory 
appears in a crude form in the abstinence theories of Senior 
and others, which were discussed in the preceding chapter. 
In a more definite form it was advanced by John Rae in 
1834, in a work which has hitherto received far less atten- 
tion than it deserved ; * and in a less complete form, and 
quite independently of Rae, by Jevons,' Sax,» and Laun- 
hardt.* But excepting Rae, none of these writers can 
compare with Bohm-Bawerk for the thoroughness with 
which the theory is worked out. 

Bohm-Bawerk distinguishes two problems: (1) Why 
does mterest exist? and (2) What determines any par- 
ticular rate of mterest? In answer to the first problem, 
he states virtually that this world is so constituted that 
most of us prefer present ^oods to future goods of like kind 
and number. This preference is due, according to Bohm- 
Bawerk, to three circumstances: (1) the "perspective 

' Bubm-Bawerk reintroduced independently the main argument 
of Rae. Several years later Rae's book was unearthed and brought 
into prominence by Professor C. W. Mixter. The original being out 
of print, Professor Mixter has edited a reprint, rearranged for modem 
readers, under the new title. The Sociological Theory of Capital (Mac- 
millan) , 1905. Rae's work labored under the disadvantage, compared 
with BOhm-Bawerk's, of being written before the modem theory of 
value had been expounded. Its shortcomings are chiefly due to this 
fact. On the other hand, it surpasses B6hm-Bawerk's treatise in some 
respects, notably in its treatment of invention. See Bdhm-Bawerk's 
comments on Rae in Recent Literature on Intereet (Macmillan), 1903, 
and the reply by Mixter, "B«hm-Bawerk on Rae," Quarterly Journal 
of Economic*, May, 1902, pp. 385-412. 

' Theory of Politieal Economy, London, 3,* ed. (Macmillan), 1888. 

• OrunMegung der theoretiechen StaatetriHhechaft, Vienna, 1887. 

* Mathemaliicke Bcgriindung der Volk*wirUchafl»hhre, Leipsic, 
1885. . i~ , 



Sko. 2] 



BOHM-BAWERK'S THEORY 






underestimate" of the future, by wh.^h is meant the f::ct 
that future goods are less clearly perceived and therefore 
less resolutely striven for than those more immediately 
at hand; (2) the relative inatlequacy of the "provision" 
for present wants as compared with the p'^jvislun for future 
wants, or in other won' . ;:- relative scarcity of prewnt 
goods compared with i tir, goofjs; (3) the "technical 



superiority" of pref • t < 
Bohm-Bawerk con i-ei 
"capitalistic" pi, < , v 
nerative than t' ; s. - cl 

The first two fi ♦ t 's. 
pertinent, and . 'I -:, 
different form, ia l.j 
the third circumstance 
of present over future ^ 
essential errors.^ 



'■ti. 



s, or th'2 fact, as 



>f 



• t ! roundabout" or 
:'•;'! If I ; .,re more remu- 
-;«•;: iri:!)i'i',ui. J returns. 
(1 cu;' -tani'tsare 
i-K'nutil, a; der 

r tlio prudent booic. li is 

s'^-.' »!•:(] 'echnical superiority 

-"- Nvhi,'h ^fe believe to contain 



— tb 



ft 

undoubtedly \>^ir'f^ 
c somewliat {*^^^ 



§ 2 



'^According to Bohm-Bawerk, labor invested in long 
processes of production will yield larger returns than labor 
invested in short processes, and will therefore confer a 
"technical advantage" upon those who have the conmiand 
of that labor. In the reasoning by which Bohm-Bawerk 
attempts to prove this "technical superiority," thtrt are 
three principal steps. The first consipts of loslulating 
an "average production period" repre -ntinjt he length 
of the productive processes of the communitv; the second 
consists of the proposition that the longer this average 
production period, the greater will be the product; and 
the third consists in the conclusion that in consequence of 
this greater productiveness of lengthy processes, present 
goods possess a "technical superiority " over future goods./ 

We shall endeavor to show that the third of these steps 
contains a fatal error. The first step also is not wholly 
satiz-factory. 



-I 



i 



56 



THE RATE OF INTEREST 



[Chap. IV 



t if 



A serious defect in Bohm-Bawerk's concct of an aver- 
age production period is that it lacks sufficient definiteness 
to form a basis for the reasoning that he attempts toTJSse 
upon it. He begins by stating that every article is the 
result of the cooperation of land and labor, and (abstract- 
ing the element of land) he proceeds to consider the period 
of production for the element of labor. If, he says, an arti- 
cle costs 100 days' labor, of which 20 days must be spent 
10 years before the completion of the article, 20 days 
9 years before completion, and thereafter 5 days in each 
succeeding year until completion, whereupon 20 days' 
labor are spent in finishing touches, the production period 
for this article is the average age of these several brief 
terms of labor; namely, 

20j<10 + 20 x9-t-a><8-t-a»c7-t-gx8-t.8xB-t-8i>4->-8»< 3 ^■5^<2^■5»c 1 + 20x0 fiOO 

lOO "lOO 

or 5.6 years.* In other words, all the labor expended in 
the production of the article is regarded as concentrated 
at one point of time 5.6 years prior to its completion. 
This point is what mathematicians call the "center of 
gravity ' ' of the various portions of labor expended. First, 
in regard to the location of tlus point, we may ask 
why the particular method of averaging which Bohm- 
Bawerk employs is assumeil by him to be the correct one. 
His average is a "weighted arithmetical mean." There 
are many other possible methods of averaging any series 
of nuiiiljors. The particular kind of average chosen in 
any special problem is a matter of prime importance in 
cases, like the present, in which the numbers are widely 
divergent. In cases in which the numbers do not vary 
widely, there is little practical need of distinguishing be- 
tween the different methods of averaging. Experience 
with index numbers shows, for instance, that the arith- 
metical, geometrical, and harmonical "means" and an 

• Th<- Potitivt Theory ol Capital, Englislj tranalation, Londou (M«t- 
milUn), 1801, p. 89. 



Sk-!. 2] 



BOHM-BAWERK'S THEORY 



57 



infinite number of other "means," » wiU agree very closely. 
But where, as m the present case, some of the elements 
averaged are very smaU and others very large, their means 
will differ widely according to the different methods of 
averaging. Thus, in the example used by Bohm-Bawerk 
if we apply, instead of the weighted arithmetical, the 
weighted geometrical mean, we shall obtain years* 
instead of 5.6 years as the average. The weighted harmoni- 
cal mean will also be 0. 

But suppose the question of the correct formulation of 
the average production period for an individual article 
to have been satisfactorily settleti, in what manner is it 
proposed to combine the production periods of different 
articles? Here are involved, considerably magnified, aU 
the well-known difficulties of constructing a suitable index- 
number. Supposing the average production period of 
cloth IS 2 years and iron 5 years, how are we to obtain 
the average production period for cloth and iron? No 
one would maintain that in such averaging between tlif- 
ferent commodities, they should all be assumed as equally 
important. They must be u^/i/ed. To obtain the aver- 
age of 2 anil 5 for the cloth and iron, are we to weight 
these two commoilities according to the value of the 
amounts annually consumed? If so, will not the rate of 
interest l)e involved in the value of the cloth and the iron' 
Again, Bohm-Bawerk's theory of the production i)eriod 
requires us to combine a number of seemingly discon- 
nected time-elements. Tims, the "period of proiluction" 

Chlp^ w1 J^';*'""^"''*' staten-ent of thi. topic, sec ApfK-ndix to 

h,ilIthT^?:T'!'T 'l"i^ y'"*^^; '"r H is physically impossible to 
insL. » I '"".V*""'*"^ "' '«''«^ "*'n^'y. 20 days, all put in at an 
laSTv .r. ""•'•"•""-"k .peaks of this M days of labor a« immedi- 
lateJy pn.,HMl,n« the finishing of the productive process. It, Uke the 

fmm thr'" f ''*''"'' '•■' '"•^"'^ '" ^'^'^ P"-*' "^^^^ "a remoteness 
from the pHsenf .s very small, let us say one day, or A, years The^ 

the gP„m,.trio.»l moan would be, not .e,;, but •»»>''''"• ^^^° 

»VTO«.x«..x««x7.xO»x6»x4»x3«x!J»xl»x(,Ii)«rorl,3 years. 



o8 



THE RATE OF INTEREST 



[Chap. IV 






of obtaining water from a well is not, by Bohm-Bawerk's 
method of estimation, the time consumed m merely send- 
ing down and drawing up the bucket. His theory requires 
us to add to this interval of time some fraction of the time 
of digging the well, and to this, some fraction of the time 
of making the spade by which the well was dug, and then, 
some fraction of the time of making the machinery by 
which the spade was manufactured, and again, some frac- 
tion of the tinie of constructing the tools by which the 
machmery was made, and so on, thus carrying our calcula- 
tions indefinitely into the past. Waiving other objections, 
what is to insure that the items representing the distant 
past will bt, as Biihm-Bawerk alleges,* negligible quantities? 
Such an assertion as to the convergence of the mathe- 
matical series in question should receive substantiation. 

Professor Fetter' and others' have criticised Bohm- 
Bawerk's concept of a production periotl so fully that we 
need not mention adiiitional perplexities.* 



§ 3 

Passing over the second stejj.' to which no objection is 
offered, we come to the third and crucial step in Bohm- 
Bawerk's theory of the technical superiority of present goods ; 
namely, that the productiveness of long proteases confers 
a special "technical advantage" to the fMJSsessor of present 
goo<i8 or labor. This advantage protluces. so B<ihm-Bawerk 
Jjelieves, a i)reference for present over future goods which 
is entirely apart from and in addition to the preference 
due to the iKTspective underestimate of the future or 

' The Pomtiif Theitryo/Cnpitnl, p. 88 

' Sec "J ho Roundabout ProceM in the Intj-n-wt Theory,' by F A. 
FetUT, Quartcrh, Journal of Eeonoimet, Vol. .Wll (.Novoiiibcr 1902). 
p. 13 pattim. Cf Taunaig, Wagen and Capital, p. 12 

• Sep IvexiH, Jahrbueh fiir (ietla^ung, VerwaUung umi Volkt- 
wirUcha/t. 1895, pp 332-3.17; Borlku-wici, Md , 1906, p 69 

• See, however, Appendix to Ch-ip IV, } 2 

• Set- Appt-ndix to Chap IV, } 3 



S^^--' 



Sbc. 3] 



BOHM-BAWERK'8 THEORY 



59 



that due to the underendowment of the present. Grant- 
ing for the moment the vaHdity of the concept of a pro- 
duction period, and that the longer the period, the greater 
Its product, it may stiU be shown that no such "technical 
superiority" foUows. Since Bohm-Bawerk regards this 
part of his theory as the most essential of aU, and repeat- 
edly states that the theory must stand or fall by the truth 
or falsity of that part, it becomes necessary to examine his 
claim in considerable detail. 

Bohm-Bawerk supports his assertion of the existence of 
a "technical superiority" ' by elaborate iUustrative tables 
reproduced below: — ' 

A MONTH'S LABOR AVAILABLE IN 1888 YIELDS 



• or the 
Eoonomic Period 



Uniu of 
Product 



True Marginal :,,,.•. ''5"'?' J„ Amount of 
Utility ofl'uit 1 V"''*>' Knduced; Value of Entire 
i in Pertpective | Product 



1888 


100 


5 


1889 


200 


4 


1890 


280 


3.3 


1891 


350 


2.5 


1892 


«)0 


2.2 


1893 


440 


2.1 


1894 


470 


2 


1895 


500 


1.5 



5 

3.8 

3 

2.2 

2 

1.8 

1.5 

1 



500 
760 
840 
770 
800 
792 
705 
500 



A MONTH'.S LABOR AVAILABLE IN 1889 YIELDS 



For 
Eoonomic Period 



1888 
1889 
1890 
1891 
1892 
1893 
1894 
1895 



Uniu 



i True Marcinal I 
I Utility i 



Reduced 

Marsinal 

UtiUty 



Value 



100 
200 
280 
350 
400 
440 
470 



5 
4 

3.:} 

2.5 

2.2 

2.1 

2 

1.5 



5 

3.8 

3 

2.2 

2 

1.8 

1.5 

1 



380 
600 
616 
700 
720 
MK) 
470 



The PotiHv Theory of Capital, p 2M. 



i i 



60 THE RATE OF INTEREST [Chap. IV 

A MONTH'S LABOR AVAILABLE IN 1890 YIELDS 



For 
EeODomic Period 



1888 
1889 
1890 
1891 
1892 
1893 
1894 
1895 



UniU 



100 
200 
280 
350 
400 
440 



True Harcinal 
Utility 



5 

4 

3.3 

2.5 

2.2 

2.1 

2 

1.5 



Reduced 
Utility 



5 
3.8 

3 

22 

2 

1.8 

1.5 

1 



Value 



300 
440 
560 
fi30 
600 
440 



A MONTH'S LABOR AVAILABLE IN 1891 YIELDS 



For 
Eoonomic Period 


Unit! 


True Marginal 

Utility 


Reduced 

Marginal 

Utility 


Value 


1888 




5 


5 




1889 





4 


3.8 


— BHB 


1890 




3.3 


3 




1891 


100 


2.5 


2.2 


220 


1892 


200 


2.2 


2 


400 


1893 


280 


2.1 


1.8 


504 


1894 


350 


2 


1.5 


525 


1895 


400 


1.5 


1 


400 















Bejpnning with the fir.st tal)le we see that it represents, 
in the second column, the units of pro<iuct obtainable 
in various years through the investment of a month's 
labw in 1888. Thvw, a montii's labor in IHHH may l)e in- 
vftsteti 80 as to produce 280 units in the year 1890, or 470 
units in the year 1894. 

Tlie third column gives the marginal utility of the pro<l- 
uot to the investor in the various years, fliis column is 
formed on tht; assumption that the individual is in "grad- 
ually improving circumstances." so that in 1895 a unit 
of product will be estimated in his mind at 1.5 units of 
utility, whereas in 1888 the same unit would have been 
>*«timated at 5. 






Sbc. 4] 



BOHM-BAWERK'S THEORY 



61 



The fourth column shows the present valuation of the 
aforesaid marginal utilities. Thus, the unit of product 
in 1895, while worth 1.5 units of utility at that date, is, 
when foreseen in perspective, worth only 1. 

The fifth column shows the (subjective) value of the 
product. This is obtained by multiplying the number of 
units of product by the reduced marginal utility; that is, 
multiplying the items in the second column by the cor- 
responding items in the fourth column. 

Beginning with the first table, Bohm-Bawcrk selects the 
maximum figure (underscored) in the last column. This 
maximum signifies that a month's labor available in 1888 
would l)est be invested so as to mature in 1890, because the 
present value of the product attainable in 1890, but reck- 
oned in 1888, is the maximum, 840, of all the present 
values. In the same way it is seen from the second table 
that a month's labor available in 1889 wiU be so invested 
as to mature in 1893; for, when thus invested, it has its 
maximum present value (reckoned in 1888). But this 
maximum present value is only 720, which is less than the 
previous maximum present value of the product (840) if 
the labor were invested in 1888. There is, therefore, says 
B()hm-Bav, rk. a "technical advantage" in having the 
lalwr available in 1888 over having it available only in 
1889. In the same way, it is still less advantageous to 
have a month's labor available in 1890. as the product is 
m that case worth only m) in the pn^nt (1888). Like- 
wise, a month's labor available in 18<»1 is still less valuable 
having a value (in 18aS) of only 525. Tims we see that 
the longer the labor is deferred the loss the value of its • 
best pri'duct, as reckoned in the present (1SS8). 



§ 4 

The result is co-rcct ; but Hohm-Bnwerk is mistaken in 
i««ribing any part of the result to the fact tlmt the longer 



62 



THE RATE OF INTEREST 



[Chap. IV 



' I 



(processes are the more productive. In his tables he 
assumes the existence of one or both of the other two 
factors, — the relative overprovision for the future as 
compared with the present, and the perspective under- 
valuation of the future, due to lack of intellectual imagi- 
nation and of self-control. Examination will show thatj 
it is these elements, and these alone, which produce the/ 
advantage of present over future goods which the tables' 
display. 

Bohm-Bawerk has curiously deluded himself, as well as 
many of his followers, on this point. He says : * — 

"I repeat emphatically that this result is not an accidental one, 
such as might have made its appearance in consequence of the par- 
ticular figures used in our hypothesis. On the single assumption 
that longer methods of production lead generally to a rreater out- 
put, It IS a necessary result; a result which must have occurred, 
m an exactly similar way, whatever might have been the figures 
of quantity of product and value of unit in the different years." 

As a matter of fact, however, the result does not at all 
foUow from "the single assumption that longer methods 
of production lead generally to a greater output." It 
has nothing whatever to do with that assumption. In 
)ther words, it has nothing to do with the fact that the 
series of numbers in the second column of the tables in- 
creases, but with the fact that the scries of numljens in the 
fourth column decreases. 

If we should make the opposite assumption from that 
of Bfihm-Bawerk, namely, that the longer the productive 
process the smaller will be the return, the very same result 
would follow. The labor would still be invested at the 
earliest pos.sible moment. Let the figures in the second 
column (lecroase instead of increase; the only difference 
woul.l be that the months labor available in"lS88 would 
now \^o «) invested as to bring immediate returns instead 

' The Ponilirr Theory of Capital, p. 268. 



1-^ 



Sxc. 4] 



BOHM-BAWERK'S THEORY 



63 



of being invested in a two years' process as before. The 
present value, in 1888, of the investment of the month's 
labor of that year in an immediately returning process 
would be, as before, the product of 100 by the marginal 
utility, 5, or 500, whereas if the labor were invested for a 
year the present value would be less; for its amount is 
found, as before, by multiplying the number of units of 
product (now assumed less than 100) by the marginal 
utihy which IS less than 5). Likewise, the month's labor 
available in 1889 would also be invested so as to yield an 
immediate return and would possess a value of 100x3 8 
or 380. If similar calculations are performed for each year 
and the results are compared, it will appear that the invest- 
ment in 1.S88 yields the highest return, just as it did on tlie 
previous hypothesis. 

Again, the same result would follow if the productivity 
increased and then decreased in all the tables, as follows: 
100, 200, 230, 200, 100, etc. For examination will show that 
the labor available in 1888 would have a maxinmm value of 
200 X 3.8, or 760 ; that available in 1889, a value of 200 x 3 
or 600 ; that in 1890, a value of 230 x 2, or 460 ; that of 1891,' 
230 X 1.8, or 414, etc. These results, 760, 600, 460, 414 etc ' 
constitute a descending series, and show again the giiater 
desirability of labor which is available early as compared 
with labor which is available late. It is just as easy to 
show that if the productivity first decreases and then in- 
creases, the same advantage of present over future labor 
will result. 

Such illustrative figur s could be reproduced indefi- 
nitely. The reader can readily convince himself by trial 
that as long as the column of "re<lucod marginal utility" 
decreases, the column of "units of product" mav be "of 
any descnption wUtn^er, without in the least affecting 
the o.s.sential result that the oariior the month's labor is 
available, the higher is its value.' 



' For a mnthenmtical proof, s.v Appendix to Chap. IV, { 4. 



64 



THE RATE OF INTEREST 



§ 5 



[Chap. IV 



On the other hand, if the conditions are reversed and 
the fourth column of "reduced marginal utility" does not 
decrease, the earlier available labor will not have a higher 
value, whatever may be the character of the second column 
of "units of product." 

Bohm-Bawerk, however, specifically denies this : ' — 

" The superiority in value of present means of production, which 
is based on their technical superiority, is not one borrowed from 
these circumstances [i.e., the perspective underestimate of the future 
and the relative underendowment of the present] ; it would emerge 
of its own strength even if thes^ were not active at all. I have 
introduced the two circumstances into the hypothesis only to make 
it a little more true to life, or, rather, to keep it from being quite 
absurd. Take, for instance, the influence of the reduction due to 
perspective entirely out of the illustration, and we get the follow- 
ing figures: — 

A MONTH'S LABOR OF THE YEAR 







lasi 


iai9 


1800 


1S91 






1888 


500 




^v«> 








1889 
1890 


800 
924 


400 
660 


330 




H 

b 
< 


£. 


1891 


875 


700 


500 


250 


> 


§0 


1892 


880 


770 


616 


440 





a ?■ 


1893 


924 


840 


735 


588 


E 


•^■J 


1894 


940 


880 


800 


700 


ij 




1895 


750 


705 


660 


600 





It is, as Bohm-Bawerk remarks, still true that the month's 
labor available in 1888 is more highly valued than the same 
month's labor available at a later date. But he has care- 
fully retainotl in his illustration one of the "two circum- 
stances" whi( ..p stated could be discanlel; namely, the 

' The PonUive Theory of Capital, p. 268. 



Sic. 5] 



BOHM-BAWERK'S THEORY 



05 



relative overprovision for the future. To leave one of these 
two crcumstances effective mstead of both is merely to 
change slightly thesenes in the fourth column of the pre- 
vious tables; namely, to change it from the descendmR 

Zt ' ' f ' '•'' ^•'' '•'' 2' '■'' ^' change in the par! 
t ^r numbers ,s qmte immaterial as long as the seri^ is 
s m descending. It does not matter whether the descent is 
due to i^erspective, or to the relative overprovision for the 

n trr \^ 't- "^^ ^"^""^^ '^'' '- that the numbers 
m the fourth column stiU constitute a descending series. 
Tte only fair test of the independence of Bohm-Bawerk's 
third factor -the alleged technical superiority of pr^nj 
over future goods - would be to strike out Jth the oX 
elements (miderestimate and overprovision of the future) 
so that there should be no progressive decrease in rw- 
gmal utUities; m other words, to make the number, in 
the fourth column all equal. Bohm-Bawerk, for some 
reason, hesitates to do this. Hesays:>— '^ ^"^e 

,fJ5"*f «'«.^e'«.al«> to abstract the difference in the circum 
recewe the stamp of extreme improbabUity. even of self-contra- 

This is very true indee<l; for to abstract both the un.ler- 
estima te of the future and underprovision for the pr^^nt 

merely. Yet this is no reason for refusing to push the 
mquiry to i^ limit. The consideration of this'e^treme 
case W.U in fact show clearly the error of Br.h.n-BawT k 
or al hough we shall have abstracted all true foun lltil' 
or interest, there will I. left, what Bohm-Buwork"; o. 2 

make all the factors m the •'reduced utility" c-ohunn alike 

' ''"</ , p. -'69. 




66 



THE RATE OF INTEREST 



[Chap. IV 



A MONTH'S LABOR AVAILABLE 



Fob 

Economic 

Period 


IN 1888 YIELDS 


IN 1889 YIELDS 


Units or 

PROD0CT 


Reduced 
Utility 


Value 


Unitbof 
Product 


Reduced 
Utilitt 


Value 


1888 
1889 
1890 
1891 
1892 
1893 
1894 
1895 


100 
200 
280 
350 
400 
440 
470 
500 


5 
5 
5 
5 
5 
5 
5 
5 


500 
1000 
1400 
1750 
2000 
2200 
23.50 
2500 


100 
200 
280 
350 
400 
440 
470 


5 
5 
5 
5 
5 
5 
5 
5 


500 
1000 
1400 
1750 
2000 
2200 
2350 
2500 



;! n 



f t 



The figures in the value columns for 1888 and 1889 are 
here absolutely alike ; hence the maximum of the former, 
if there be a maximum, must be identical with the maxi- 
mum of the latter. 

Though Bohm-Bawerk did not consider this case in his 
tables, he speaks of it briefly in his text, but seems to be 
somewhat puzzled by it. He says : ' — 



if ; 



" If the value of the unit of product were to be the same in all 
periods of time, however remote, the most abundant prwluct would, 
naturally, at the same time be the most valuable. But since the 
most abundant product is obtained by the most lengthy and round- 
about methods of production, — perhaps extending over decades 
of years, — the economic center of gravity, for all present means 
of production, would, on this assumption, be found at extremely 
remot* periods of time — which is entirely contrary to all experi- 
ence." 



Bohm-Bawerk's confusion here is probably to be ascribed 
to his insistence on the indefinite increase of product with 



^ I 



' Ibid., p. 269. 



8kc. 5] 



BOHM-BAWERK'S THEORY 



67 



a lengthening of the production period. Had he admitted 
into his possibilities the particularpossibility that Sfe ptS 
uct would ultimately deci^ with a lengthening of t^t 
penod the en-or which he had committed would hfve made 
Jteelf too evident to escape his notice. As it was he fo,md 

ofTl '' r ' T "^ ^^'^ ««"^' ^"d a. the history 
of ma hematics shows, it is not easy in such inquiries t^ 
keep dear of pitfalls. Yet even in the hypothesisTa W 
of trulefimte mcrease in returns with mcrea^ length of 

C^'ir '' '"' ^^°^' ''^^'^ -^-^< ^^^^ -' 

In order not to tamper prematurely with any of Bohm- 
Wk'shypotheses let us then stiU a^ume th^ lawof ^- 
definite mcrease of value proportionately with the length of 

simply that productive processes indefinitely long would bei 

IS ^''^^'' "^ '^ ""' ^^^' ^<^"^d '^vest it in ^ 
infinite production process, -a result extremely fanta^tb 

thenZ fr''%'^''^''^- W« need not aiume that 
ttie pnxluct of an mfinite production period is itself infinite 
The ^crea^mg product may approach a definite limit' 

S t^f '' ^ r*' "".^ ^"™^' ^^^ "« ««"Jd not imag: 
me that a finite earth would have an mfinite produ^ 

S)W^ '^ri'o T '"PP^ '^' ^'^h «-<''^ y^r after 
1895, with which Bohm-Bawerk breaks oflF his table the 

i^t^tlT r^'^^'"^^ ^"^^ ^«» units, it 

In 1^? ^K. ^^^ P"^""' °^ 1^5) ^d 1000 miits. 
ete ?^. r .°T' '; "•'" "^^"^' «75' ^ 1898, 937.5. 
ete. The hmit of such a series is 1000 units. A month^ 

^ no^^ir"''?"'" ^'^"'' '^*^"y ^«»' ^<1 there wiU 
whatever «"P«"°"ty" in present over future goods 

It is noteworthy that in treatmg this case Bohm-Bawerk 
dufta his ground. For the case of undiminished nfar^ 



i 
I 



MKROCOPV RBOIUTION TfST CHART 

(ANSI and ISO TEST CHART No 2) 




HO 



m 






12.2 



1.25 ii.4 



1 1.8 
!■■■ 



>d 



APPLIED I^A^1GE Inc 

1653 tott Moin StrMi 

Rochesttr, N«w York U609 USA 

('16) ♦9J - 0300 - Phon. 

('16) 2M- %S89 - Fo. 






n 



1 1 

r 



68 



THE RATE OF INTEREST 



[Chap. IV 



utilities, the only comparison which he makes between the 
two series (that for 1888 and that for 1889) is not a com- 
parison between their maxima, such as he made in his 
previous cases, but a comparison between individual terms. 
He states in a footnote : ' — 

"... The month's labour of 1888 remains superior to that of 
1889. For, as regards any one remote period, say, the year 1988, 
the former, as employed ia a process longer by one year, could pro- 
duce a somewhat greater product than the latter." 

Such an individual comparison is, of course, beside the 
point; but granted that it should be made at all, why is it 
made between two items relating to the same calendar 
yeart Why not make it between two items relating to 
the same production period f Why conclude that a month's 
labor of 1888 is superior to that of 1889 because, say in 
1892, the first yields 400, whereas the second yields only 
350, rather than conclude that they are equal, since, in 
a four years' process, the labor of 1888 yields 400, and 
that of 1889 yields also 400 ? That the fruition is deferred 
one year m the latter case is no disadvantage under the 
present hypothesis, for we have expressly eliminated from 
consideration any overprovision or underestimation of 
the future; it becomes a matter of entire indifference 
whether the 400 is obtained in 1892 or 1893.* 



§ 6 



Thus far we have not altered any of Bohm-Bawerk's 
hypotheses; but if we allow ourselves to assume, as prac- 



\\ 



> Tbid., p. 260. 

'Cf. Bortkiewica, "Der Kardinalfehler der BOhm-Bawerkachen 
ZiQSth<H>rift," Jakibuck far OtMltgehung, VtrwUun^ wn4 VothMvpirt' 
tdtaft, 1906, pp. 71-73. 



-3. 



Sbc. 6] 



BOHM-BAWERK'S THEORY 



69 



tically we ought to assume, that sometime the product 
decreases, no matter for how long a production period, we 
shall have a more practical illustration of the fact that the; 
labor available in 1888 and that available in 1889 stand 
on a perfect equality. 

Let us assume that Bohm-Bawerk's table of products 
holds true as far as he carries it, 1895, but that thereafter 
the numbers decrease, as m the next table. In this table 
are also given the products of a month's labor available 
in 1889 and other years : — 



PRODUCT OF A MONTH'S LABOR AVAILABLE IN 



For the 














Economic 


188S 


1S89 


1890 


1891 


188S 




Period 














1888 


100 













1889 


200 


100 







_ 




1890 


280 


200 


100 









1891 


350 


280 


200 


100 







1892 


400 


350 


280 


200 


100 




1893 


440 


400 


350 


280 


200 




1894 


470 


440 


400 


350 


280 


UmTBOi' 
Prodcct 


1895 


500 


470 


440 


400 


350 


1896 


490 


500 


470 


440 


400 




1897 


480 


490 


500 


470 


440 




1898 


460 


480 


490 


500 


470 




1899 


430 


460 


480 


490 


500 




1900 


410 


430 


460 


480 


490 J 





If, as before, we suspend the operation of the two 
"circumstances " (overprovision and underestimation of 
future) and employ for the "reduced utility" the constant 
number, 5, we have the following table for the "value" 
columns : — 



70 



THE RATE OF INTEREST [Chap. IV 

A MONTH'S LABOR AVAILABLE IN 



Yields in 












Valce for 
THE Economic 


'8>S 


18S9 


1S90 


1891 


1899 


Period 












18S8 


500 












1889 


1000 


500 










1890 


1400 


1000 


500 








1891 


1750 


1400 


1000 


500 






1892 


2000 


1750 


1400 


1000 


500 




1893 


2200 


2000 


1750 


1400 


1000 




1894 


2350 


2200 


2000 


1750 


1400 


[ Valub 


1895 


2500 


2350 


2200 


2000 


1750 




1896 


2450 


2500 


2350 


2200 


2000 




1897 


2400 


2450 


2500 


2350 


2200 




1898 


2300 


2400 


2450 


2500 


2350 




1899 


2150 


2300 


2400 


2450 


2500 




1900 


2050 


2150 


2300 


2400 


2450 J 





II 



This table of values is simply the previous table of prod- 
ucts magnified fivefold, and is only given separately lest 
there be any possible room for doubt that the reasoning 
applies to " value " as well as to " product." We see clearly 
that the labor of 1888 will be invested m a seven-year 
productive process maturing m 1895, and having a present 
value, reckoned in 1888, of 2!m units of value; that the 
labor of 1889 will likewise be put into a seven-year pro- 
ductive process, maturing in 1896, and having a present 
value in 1888 of 2500. Similarly, the labor of each succeed- 
ing year matures seven years later, but is worth to-day 
(1888) its fuU value of 2500. 

Our conclusion is that if we eliminate the "other two 
■ circumstances " (relative underestimate of, and over- 
provision for, the future), we eliminate entirely the supe- 
riority of present over future goods, aid the supposed 
third circumstance of "technical superiority" therefore 
turns out to be non-existent. 

The fact is that the only reason any one can prefer 



Skc. 7] 



BOHM-BAWERK'S THEORY 



71 



the product of a month's labor invested to-day to the 
product of a month's labor invested next year is that 
to-day's mvestment will mature earlier than next year's in- 
vestment. If a fruit tree is planted to-day which will be.,f 
fruit in four years, the labor available to-day for plant- 
ing it is preferred rather than the same amount of labor 
available next year; because, if the planting is deferred 
until next year, the fruit will likewise be deferred a year, 
maturing in five instead of four years from the present. 
It does not alter this essential fact to speak of the possi- 
bility of a niunber of different investments. A month's 
labor to-day may, it is true, be spent in planting slow- 
growing or fast-growing trees; but so may a month's 
labor mvested next year. It is from the preference for 
the early over the late fruition of any productive process 
that the so-called "technical . 'periority of present over 
future goods" derives all its force. The imagined "third 
circumstance" producing a superiority in present goods 
is only the first two circumstances in disguise. 



•1-1 

m 
in 



§ 7 

' But our distinguished author attempts to prove that his 
"third circumstance" — the alleged technical superiority 
of present goods — is really independent of the first two, 
by tlie following reasoning : ' — 

"... If every employment of goods for future periods is, not 
only technically, but economically, more remunerative than the 
employment of them for the present or near future, of course men 
would withdraw their stocks of goods, to a great extent, from the 
service of the present, and direct them to the more remunerative 
service of the future. But this would immediately cause an ebb- 
tide in the provision for the present, and a flood in the provision 
for the future, for the future would then have the double advantage 
of having a greater amount of productive instruments directed to 



» Ibid., pp. 269, 270. 



rf 



11 
It 



liti 

ill 

fil 



* i . 
I I ■ 



n\ 



? ! 



I I 



72 



THE RATE OF INTEREST 



[Chap. IV 



its service, and those instruments employed in mire fruitful meth- 
ods of production. Thus the difference in the lircumstances of 
provision, which might have disappeared for the mordent, would 
recur of its own accord. 

"But it is just at this point that we get the best proof that the 
superiority in question is independent of differences in the circum- 
stances of provision : so far from being obliged to borrow its strength 
and activity from any such difference, it is, on the contrary, able, 
if need be, to call forth this very difference ... We have to deal 
with a third cause of the surplus value, and one which is independ- 
ent of any of the two already mentioned." 

The argument here is that if "the other two circum- 
stances" which produce interest, namely, underestimate 
of the i\xi\xK and underendowment of the present, are tem- 
porarily absent, they will be forced back into existence by 
the choice of roundabout processes. In other words, the 
"technical superiority of present goods" produces interest 
by restoring the "other two circumstances." But this is 
tantamount to the admission that "technical superiority" 
actually depends for its force on thede "other two circum- 
stances" and is not "independent." The essential fact is 
that its presence does not produce interest when the other 
two are absent. In short, the " technical superiority" of 
present goods is a delusion,* and the only way in which the 
existence of long processes of production acts on interest 
is by overendowing the future and underendowing the 
present, thus creating a "scarcity value" of present goods. 

Smce the foregoing criticism on Bohm-Bawerk's theory of 
the technical superiority of present over future goods was first 
written, very similar criticism has been made by Adolphe 
Landry' and by Ladislas von Bortkiewicz.' So far as 
the writer knows, Landry is the first to have set forth 
clearly and definitely the fallacy contained in Bohm- 

'Cf. Bortkiewicz, "Dnr Kardinalfehler der Bohm-Bawerkschen 
Zmstheoric," Jahrburh fur Gesettgebung, VerwaUung und Volkswirt- 
schaft, 1906, pp. 61-90. 

• L'InUrH du Capilnl. 

' Loc. cU., pp. Gl-CO. 



S«c. 7] 



BOHM-BAWERK'S THEORY 



73 






Bawerk's theory of "technical superiority." Every reader 
of Bohm-Bawerk, however, must have felt dissatisfied 
with his explanations; and sundry expressions of Bohm- 
Bawerk's suggest that he was dissatisfied himself. His 
theory of technical superiority stands out as incongruous 
with the rest of his work, and is more in keeping with 
the productivity theories which he has done so much to 
demolish. It would seem as though, like a successful 
warrior, he had been haunted by the ghosts of his slain 
enemies. As Professor Fetter has said : * — 

"It has been a surprise to many students of Bohm-Bawerk to 
find that he has presented a theory, the most prominent feature 
of which is the technical productiveness of roundabout processes . 
His criticism of the productivity theories of interest has been of 
such a nature as to lead to the belief that he utterly rejected them. 
But evidently such is not the case. Critics have pretty generally/ 
agreed that the theory of the roundabout process is a productivity! 
theory of interest." ' 

It is, therefore, somewhat strange to find Bohm-Bawerk 
strenuously insisting on the importance of his "technical" 
theory. He writes:* — 

"The statement of how the productivity of capital works into 
and together with the other two grounds of the higher valuation 
of present goods, I consider one of the most difficult points in the 
theory of interest, and, at the same time, the one which must decide 
the fate of that theory. It is just at this point that we discover 
the chief weakness in Jevons's otherwise suggestive work. None 
of the groups of phenomena concerned escaped his keen observa- 
tion ; what did escape him was the way in which they work into 
one another." 

And, referring to Launhardt, he says:' — 

"But, on the other hand, it is a sensible omission that the differ- 
ence between the values of present and future goods is traced 

' "The 'Roundabout Process' in the Interest Theory," bj Frank 
A. Fetter, Quarterly Journal of Economics, Vol. XVII November 
1902. ' 

» The Paaitive. Theory of Capital, p. 277, footnote. 

' Ibid, p. 278. 



'■m 



'.-^K 



74 



THE RATE OF INTEREST 



[Chap. IV 



^M 



excluflively to this factor, and that the much more important 
factor that cooperates with it, that of the greater productiveness, 
does not get even the scanty consideration it gets from Jevons." 

Before leaving the subject, justice requires that we should 
diasent from Bohm-Bawerk's opinion that he has made 
no substantial contribution to the theory of interest aside 
from his particular "technical" feature. His work in 
historical criticism is a model both for the historian and 
for the critical analyst, and hb enunciation of the agio 
theory, while partially anticipated by Jevons, Sax, and 
Launhardt, was so much more clearly and perfectly worked 
out that it gains an almost mdependent form in his 
hands. The only writer who has equaled Bohm-Bawerk 
was one with whom the latter was not acquainted, namely, 
John Rae. His valuable contribution to the subject was, 
through a curious chain of circumstances, lost to two 
generations of readers, and has only recently been revived 
and made accessible through Professor Mixter. 

If we cast out from the agio theory Bohm-Bawerk's 
special feature, his alleged "technical superiority of present 
goods," the theory which remains is believed to be correct. 
It is, however, still incomplete, for there remains the gap 
-vhich Bohm-Bawerk sought to fill, — the formulation of 
he exaci manner in which the "technique" or actual con- 
jlitions of production enter into the determination of 
interest. /In Part III we shall attempt to supply this 
deficien<^. 



It 
t 

I 



* i " 



PART II. First Approximation 

Chaptek v. Appkkciation and Interest 

Chapter VI. Time-Pkeference 

Chapter VII. First Approximation to the Theorv 

OF Interest (assuming income kioid) 





■ i =, 



III 



i i i 



» I i 



! t 



v^ 



CHAPTER V 



APPRECIATION AND INTEREST 



/ " 

In the four preceding chapters we have criticised those 
theories of interest which enjoy the greatest currency in 
present economic und business circles. Inasmuch as we 
have found radical defects in all of them, our best course 
now is to formulate de novo what seems to us to be the cor- 
rect theory. At the outset we need to note an oversight 
common to all the theories reviewed. In none of them is 
any accoimt taken of the fact that the number expressing 
the rate of mterest depends upon the monetary standard 
of value in terms of which that rate of interest is expressed. 
To say that the rate of interest is 4 per cent, means ' that 
the quantity of this year's goods which is worth $100 is 
equivalent to the quantit^' of next year's goods which is 
worth $104. In this statement we observe that the 
" goods " which are considered are expressed not in their own 
special units, — pounds, bushels, yards etc., — but in terms 
of a standard of value. Tht an-b'- 4 value chosen is 
usually money. This money, the $. lud $104, is nomi- 
nally exchanged; but actually it r 
"goods" which are exchanged. \M 
this year in order to obtain $104 n 
sacrificing not one hundred dollars e 
dred dollars' worth of goods such as 
or pleasure trips, m order to obtaii. 
hundred and four dollars in money, but 



four dollars' worth of other goods which 

' See Glossary at end of this volume ; also the 
of Capital and Income (Chap. XI), the nomenciMw 
followed in the present work. 

77 



-rely measures the 

a man 1 ads $100 

'? ir, h., is really 

<*■ ^ut one hun- 

jthing, books, 

SI year not one 

•ne Iiundred and 



desires,^ 

■r'sTke Nature 
"•hicb lie is 



'fel 



-* 



M 



. 



IB 



78 



THE RATE OF INTEREST 



[Chap. V 



■v 



Yet the fact that both sets of goods are measured in money 
introduces a monetary factor into the problem of interest 
Inferest, bemg a premium in the exchange between the 
money values of this year's and next year's goods, is there- 
fore not wholly an affair of goods, but is partly one of money 
The relation of the rate of interest to goods will form the 
subject of subsequent chapters. The present chapter 
is devoted to a study of the relation which subsis ts between 
the rate of mterest and the monetar^«fAnd.rrl .'n ,.^f 
which i^t IS expre ssed. 

The monetary standard affects the rate of interest in 
so far as there is a change in the value of that standard 
m reference to other standards. Could it always be as- 
sumed that the monetary standard was invariable in value 
with reference to aU goods, the rate of interest reckoned 
in money wouli be the same as though it were reckoned 
m terms of the goods themselves. But if money and goods 
are to change with reference to each other - in other words 
If the money standard "appreciates" or "depreciates"' 
— the number expressing the rate of interest wiU be affected 



u 



I ' f 

fc . # . I 

'II 

I ■ 
1^ 



§2 

TTie influence of monetary appreciation or depreciation 
on the rate of interest wiU be different accordmg to whether 
or not that appreciation or depreciation is foreseen If it 
is not foreseen, the appreciation cf money necessarily in- 
jures the debtor, because, the purchasing power of money 
bemg increased, the principal of his debt, when due, repri 
sents a larger quantum of goods than was anticipated when 
the debt was contracted. But if_ihe appreciation is fore- 
seen, any increased burden in the '>incipal'^^S^t 
bjia.: ^tion in tEelate-oTm^rest. Iliis7act, strangely 
enough, has seldom been recognized. The assumption 
has been tacitly made that contractmg parties are power- 
less to forestaU gams or losses due to an upward or down- 
ward movement of the monetary standard. Yet no reason 



Sec. 2] 



APPRECIATION AND INTEREST 



79 



has been given to show that it is any more difficult to make 
allowance for a change in the unit of value than for a change 
in any other unit. If the unit of length were changed, and 
its change were foreknown, it is clear that contracts would 
be modified accordingly. Suppose, for instance, that a 
yard were defined (as possibly it once was) as the length 
of the king's girdle, and suppose the king to be a child. 
Everybody would then know that the "yard" would 
probably increase with the king's age, and a merchant 
who should agree to deliver one thousand "yards" ten 
years hence would make his terms correspond to his ex- 
pectations. It would be strange if, in some similar way, 
an escape could not be found from the effects of changes 
in the monetary yardstick, provided these changes were 
known in advance. To^ffset a foreseen appreciation, it 
would only be necessary that the rate of interest be cor- 
respondingly lower, and to offset a foreseen depreciation, 
that it be correspondingly higher,' 

I f a debt is contracted op tionally in either nf two stand- 
a£Jijad--Qn£,of them jsjx^^tecU^ with reference 

tfl_the_()ther,Jhe rate of interest will hyjiQ. means be "the 
sanjejnjjoth. A few years ago, durbg the uncertainty 
as to the adoption or rejection of "free silver," a syndicate 
offered the United States government the alternative of 
some $65,000,000 of bonds on a 3 per cent, basis in gold, 
or on a 3i per cent, basis m " coin." Every one knew that 
the additional J per cent, in the latter alternative was due 
to the mere possibility that "coin" might not continue at 
full goli value, but sink to the level of silver. If the 
alternative had been between repayment in gold and a — 
not merely possible but actual — repayment in silver, 
the additional interest would obviously have exceeded 
i per cent. 

» For the history of the theory of appreciation and interest, see 
Appendix to Chap. V, | 1. 



•t 

■n] 






4 






80 



THE RATE OF INTEREST 



[Chap. V 



■l\ 



'I J'i 



■> i 









II 



§3 

The relation between the rate of interest and the rate 
of a foreseen appreciation or depreciation of money may 
be readily illustrated. In order to illustrate the theory, 
we may imagine two specified standards of value diverging 
from each other, in either of which loan contracts may be 
expressed. Let the two standards be gold and wheat, 
und let a bushel of wheat be first worth $1. If the two 
standards did not diverge, that is, if the price of wheat 
m terms of gold held good till next year, it is clear that 
the rate of mterest in a gold contract and a wheat contract 
would be the same; if it were 4 per cent, in gold, it would 
be 4 per cent, in wheat also. This may be expressed as 
follows : — 

If to-day 100 dollars is the equivalent of 100 bu. @ $1 per bu., 
then next year 104 dollars is the equivalent of 104 bu. @ $1 per bu. 

But let us suppose that the price of wheat rises from $1 
to $1.01. We then readily see that : — 

Whereas to-day 100 dollars is the equivalent of 100 bu. @ $1 per 
bu., next year 104 x 1.01 dollars is the equivalent of 104 bu. @ 11.01 
perbu. 

If we calculate out the 104 x $1.01, we shall obtain $105.04 
as the sum which next year should be repaid m gold to be 
equivalent to 104 bu. payable in wheat. In other words, if 
4 per cent, is the interest in the wheat standard, its equiva- 
lent is 5|g5 per cent, in the gold standard; or, again, if 

j the rate of interest in wheat is 4 per cent., an appreciation 
of wheat of 1 per cent, is exactly offset by a rise of 1^ J, per 

f cent, in the rate of interest in goKl. It is thus a matter 
of indifference whether, under our auppo.sed circumstances, 
a man who borrows $1000 expresses hid contract in gold 
and agrees to pay 5 y J j per cent, interest or translates the 
same contrnf h into t<?rms of wheat, borrowing the value of 



If 



Sec. 4] 



APPRECIATION AND INTEREST 



81 



1000 bushels and agreeing to pay 4 per cent, interest. By 
the first form of contract he pays back $1000 of gold prin- 
cipal and $50.40 of gold interest; by the second, he pays 
back the value of 1000 bu. as principal and of 40 bu. as 
interest. At the end of a year his debt by the one » 
/reckoning is $1050.40, by the other, 1040 bu., and these! 
/are equivalent. 

It is to be noted that we have been regarding gold or 
wheat as standards of value and not as media of exchange. 
In either contract the actual liquidation need not be made 
either in actual gold or wheat. The speculator who sells! 
wheat "short" comes very close to using wheat as a 
standard, but not as a medium. 

The relative change in the two standards may be spoken 
of either as an apprpniatinn nf wljgat relatively Jo gold, 
or as a depreciation of g old relativBJyjn whPRt We are 
not compelled to inquire which is the "absolute" change. 
If we use the first of these two modes of expression, we may 
say that since one bushel changes in value from $1 to $1.01, 
wheat has appreciated 1 per cent. ; if we use the second mode 
of expression, we may say a gold dollar has fallen in its 
wheat value from one bushel to Jg^ of a bushel, and has 
therefore depreciated by ^Jj or .99 ^Jy per cent.' 



§ 4 

In our numerical example, the appreciation (1 per cent.) 
of one standard relatively to the other, and likewise the de- 
preciation (.99-iJy per cent.) of the latter standard relatively 
to the former, are not quite so great as the difference 
(hh per cent.) in the rate of interest. This slight disparity 
must always exist so long as the rate of interest is reokoned 
annually or discontinuously. But the shorter the period of 
"compounding," the less the disparity; that is, the more 

• For thfi general formula eoaaeetiiig the rates of interest iu «uiy 
two diverging standards, see Apijoudix to Chap. V, | 2. 
u 



in 



II 



III 



; 



\U 



I'- 

i ' 



i'it 



' 



1 1 ■ 

f i 




82 



THE RATE OF INTEREST 



[Chap. V 



nearly equal are the two magnitudes: (1) the rate of 
divergence between the two standards, whether measured 
as appreciation or depreciation, and (2) the difference 
between the rates of interest in the two standards. When 
the rates are "reckoned continuously," the disparity dis- 
appears altogether.' 

§5 

Having established the truth and generality* of the 
prmciple connecting the rates of interest in two standards 
and the appreciation of one of them relatively to the other, 
we next inquire what limits, if any, are imposed on the 
three magnitudes; namely, the two rates of interest in 
the respective standards and the rate of relative apprecia- 
tion between the standards. From what has been said 
it might seem that, when the appreciation is sufficiently 
rapid, the rate of interest in the upwanl-moving standard, 
in order to equalize the burden, would have to be zero or 
even negative. For instance, if the rate of interest in gold 
is 4 per cent., and if wheat appreciates relatively to gold 
at 4 per cent, also, the rate of interest in wheat, if perfectly 
adjusted, would have to sink to zero ! But we know that 
zero or negative interest is practically impossible. Wheat 
would be hoarded, and this action would effectually pre- 
vent the rate of interest in terms of wheat from passing 
below tho zero mark. But this very limitation on the 
possible rate of interest carries with it a limitation on the 

' For the mathematical demonstration of this proposition, see 
Appendix to Chap. V, { 3. For the significance of "continuous" 
reckoning, see The Nature of Capital and Income, Chap. XII; also 
Chap. XIII and Ap^iendix. We have here an example of the fact 
there observed that, considered mathematically, the analytical rela- 
tions connected with the rate of interest are simplest when that rate 
is reckoned continuously. Since, however, the rate of interest reck- 
oned continuously is so rarely used in practice, we shall adhere, in 
the remainder of our discussion, to the system of annual reckoning. 

' For mathematical pronfg. numerical iUustratinn.i, and fomuli? 
see Appendix to Chap. V, || 4 to 9 inclusive. 



^ 



Skc. 5] 



APPRECIATION AND INTEREST 



83 



possible rate of appreciation. IfjntereaL_orLjnoneyj_for 
inatAnpfi, w e re 4 4)eaijffiQt._^ it woiJd^ impossible fo r whea t 
t o have a fore k nown app reciation of iQ^per j^.43fir_an- 
num relativ ely money'; fo r it would immediately h a 
bougM ana^HeiaTorJ^;n^^tjwpuld therefore rise at 
on^lo'tSe ^ couBted-YaJiieL_a£ itsJutureexpectedjaJjufiT 
a^jts mifififtftHing ^risejcouJd not exceed the rate of inte r- 
est} In other words, if mterest is 4 per cent., it is impos- 
sible that wheat should be worth $1 to-day and $1.10 next 
year foreknown to-day. For, under these circumstances, 
holding for a rise would give a sure return of 10 per cent. 
The lowest price of present wheat possible would be the 
$1.10 discounted at 4 per cent., or about $1.06. At this 
figure the rate of mterest in gold is 4 per cent., but in 
wheat it is zero per cent. We should have : — 

To^lay $ 106 equivalent to 100 bu. @ $ 1.06 per bushel. 
Next year $ 110 equivalent to 100 bu. @ $ 1.10 per bushel. 

and the two alternative forms of contract would be : for 
$106 this year $110 are returned next year, or (about) 4 
per cent., and for 100 bu. this year 100 bu. are returned 
next year, or zero per cent. Every case of holding wheat 
or land or other wealth for a rise may be, in fact, regarded I 
as a case of zero mterest in terms of these articles as\ 
standards of value. 

The same principle which prevents the rate of interest 
in wheat or land from being negative also prevents a 
negative interest in money. A lender, rather than ex- 
change $101 to-day for $100 next year, would hoard his 
$101. It is important to emphasize the fact that t he limit s 
i mposedo n the jates of interest and ^ipreciation come 
fcom the powuhility nf hmtrHing mnnfj withouLlsss. If 
money were a perishable commodity, like fruit, the limit 
would be pushed mto the region of negativre quantities. 

' See The Nature of Capital and Income, on the rate of rise of " dis- 
count curves," Chap. XIII. 









IP 



84 



THE RATE OP INTEREST 



[Chap. V 



One can imagine a loan based on strawberries or peaches, 
jcontracted in summer and payable in winter, with negative 
linterest.' Or, again, we may define a "dollar" as consist- 
ing of a constantly increasing number of grains of gold, 
the weight of which is to double yearly. Such "dollars" 
cannot be hoarded voithout necessarily becoming fewer vnth 
time, and if interest in the old fixed-weight dollars is 5 per 
cent., it will be minus 47} per cent, in the new dollars of 
increasing weight; for he who borrows $100 (2580 grains) 
to-day will need to pay back only $52.50 (2709 grains) 
one year hence. 

§6 

The relation existing between interest and apprecia- 
tion implies, then, that the "rate of interest" is always 
relative to the standard in which it is expressed. The 
fact that interes t^ in money is high, say 15 per cent ^may 
m erely indicate _^that_general prices are expe^tecTto rise 
atlhe rate of 1 per cent., ah^ lHat the r ule of mterest in 
t ernis ^goods is not lilgh. but onlY_4j_£er ccAt. "" 

We thus need to disthiguish between interest in terms 
of money and interest in terms of goods. The first thought 
suggested by this fact is that the rate of interest in money 
is "nominal," and that in goods "real." But this distinc- 
tion is not sufficient, for no two forms of goods maintain, 
or are expected to maintain, a constant price ratio tow- 

Iard each other. There are therefore just, as many rates I 
of interest in goods as there are forms of goods diverging inl 
value. ^ 

Is there, then, no absolute standard of value, as utility, 
in terms of which "real" interest should be expressed? 
To this we reply that any absolute standard is absolute 



onlvjo r a particu larJnJmcjuaj.' Tim fnpi. that a dollar 

' Cf. Bolun-Bawerk, The Positive Theory of Capital, pp. 252. 297- 
Landry, L'Intirit du Capital, p. 49. ' 

' M;tr-ha!!, Prindplts of Eemonics, Voi. I, SU t-d. New York 
(Macnullun), 1895, p. 198, and Royal Cammisiion on DepreaHon o/ 



* i 



Sec. 6] 



APPRECIATION AND INTEREST 



85 



is a smaller unit to a millionaire than to a poor laborer 
has as its consequence that, as the millionaire grows poorer 
his dollar grows larger, while as the laborer grows richer 
his dollar grows smaller. On account of such changes in' 
personal fortunes, the dollar will be constantly appreciat-,' 
ing and depreciating in different degrees among different; 
men and classes. But if the dollar appreciates in terms 
of absolute utility in the eyes of one man, and depreciates 
in a corresponding standard of utility in the eyes of another, 
the rates of interest in the men's "absolute" standards 
must be different in the two cases; for the_iat eg of in - 
terest to both persons inj erms of objective units, such a s 
money, mmt by the o pemtUmst of thp mnrt-^f tw \ h^_^nr«0j 
If, in the gold standard, $100 to-day is equivalent to $104 
due one year hence, both for him who is growing richer 
and for him who is growing poorer, the rates in terms of al)- 
solute utility will be different for the two men. Thus, sup- 
pose that the dollar to-day is worth to each man one unit of 
utility, but that one year hence, to the man who is growing 
richer, the dollar will be worth slightly less —let us say, 
/s^jj of one unit of utility. Consequently, when he considers 
$100 to-day as equivalent to $104 due next year, he is 
virtually contrasting in his mind 100 units of utility to-day 
with 104 X .99, or about 103 units of utility next year. His 
rate of interest, therefore, in terms of absolute utility, is 
3 per cent. Similar calculations for the man whose for- 
tunes were declining, and to whom the marginal utility of 
the dollar was increasing 1 per cent, per annum, would 
show that whereas $100 to-tlay is equivalent in his esti- 
mation to $104 next year, 100 units of present utility are 
equivalent to about 105 units of next year's utility. To 
him, therefore, the rate of interest in the absolute standard 
would be 5 per cent. 

"^J^*, 1886, p. 423; the writer's "Mathematical InvestiRationa in 
the Theory of Vah.P and Prices," Ttanzadioru oj the ConnecUcul 
Academy, New Haven, 1892, pp. 11-23, 8fr-89; A. C. Pigou, "Some 
Remarka on Utility," Economic Journal, March, 1903, p. 60 



i 



86 



THE RATE OF INTEREST 



[Chap, V 



:;fi. 



t i " 



From this explanation it is very evident that if we seek 
to postulate an absolute standard of value in which the 
rates of interest are to be reckoned, we cannot fix one 
which will be uniform for all the int 'viduals in the market. 
i Supply and demand operate only to make objective rates 
( equal. Hereafter we shall confine ourselves to a study of 
objective mterest; and since the objective standard usually 
employed is money, the rate of mterest, imless otherwise 
specified, will be taken in this book to mean the rate of 
interest in terms of the money standard. 

As was observed at the beginnmg of this chapter,. it 

makes a great difference whether the relative divergence of 

the different standards is or is not known in advance. 

iln actual fact it usually happens that future appreciation 

— *=A)r depreciation is neither entirely foreseen nor entirely 

I ^foreseen: An intermediate condition is usually mam- 

tained. When prices are rising, the rate of mterest is 

usually high, but not as high as it should be to compensate 

I for the rise ; and when prices are fallmg, the rate of interest 

is usually low, but not as low as it should be to compensate 

! for the fall. The facts as they are actually found m the 

market will be given m Chapter XIV. 



t 



I 



.1 



J 



CHAPTER VI 



TIME-PREFERENCE 



§1 

In the last chapter we saw that the num'^er expressing 
the rate of interest depends on the standard of value in 
which present and future goods are expressed. We saw 
how the rate of interest in one standard is to be derived 
from the rate of interest in any other standard. 

It is clear that this translation of the rate of interest 
from one standard t/ ) another does not constitute a com- 
plete determinat im QJ the ral e-«f~dat£rest in^^nmy^ .<iffiri<i<jrd 
whaiever ; for it assxmies that the rate in some one stan3arc 



is already known, and merely enables us on the basis of 
this known rate to calculate the rates in other standards. 
The case is similar to the conversion of temperature from 
the Fahrenheit system into the Centigrade or the Reaumur, 
which clearly does not determine temperature itself; or, to 
the conversion of the price of cotton in dollars into its price 
in shillings or francs, which does not determine the price of 
cotton itself. The relation which has been shown between 
appreciation (or depreciation) and interest therefore solves 
merely the problem of translating the rate of interest from 
one standard into another; but the problem of determining 
the rate of interest is still left imtouched. This problem 
— the problem of determining the rate of interest — now 
demands attention. 

In our theory we shall find a place for each of the partial 
truths which we have found in the foregoing review of the 
productivity, cost, and agio theories. Our presentation 
may, in fact, be classified as a form of the agio theory, differ- 
ing from Bohm-Bawerk's version chiefly by the omission of 

87 



9 
C 



I 






88 



THE RATE OF INTEREST 



[Chap. VI 



the "technical advantage of present over future goods," 
aiid from agio theories in general by the explicit introdu' 
tion of the income-concept. The income-concept plays the 
central role. 

The theory of interest bears a close resemblance to the 
theory of prices, of which, in fact, it might be regarded as a 
part; for, as was shown in The Nature of Capital and 
Income, Chap. XII, the rate of interest expresses a price 
in the exchange between present and future goods. Just 
as m the onlinary theory of prices the ratio of exchange 
of any two articles is based on a psychological or sub- 
jective element, — their comparative marginal utility, — 
so in the theory of interest the rate of interest, or the pre- 
mium in the exchange between present and future goods, 
is based on a subjective prototype; namely, the preference 
for present over future goods. 

This "time-preference" is the central fact in the theory 
of interest.' It is what Rae calls the "effective desh-e for 
accumulation," and very nearly what Bohm-Bawerk calls 
the "perspective undervaluation of the future." » It is the 
(percentage) excess of the present desirability » of present 
goods over the present desirability of an equal amount of 
future goods. 









I [ ■■ 



' Cf. Bullock, Introduction to the Study of Economics (Silver, Bur- 
dett & Company), 1900, p. 390; Fetter, Ec4>nomics, New York (Centurj- 
Co.), 1904, p. 135. 

' At least, as applied to objective goods. Bohm-Bawerk applies 
It to subjective pleasures, which he translates into objective goods 
at a ratio depending on the "relative provision for present and future 
needs. As we have seen in | 6 of the preceding chapter, it is possible 
to translate the rate of interest (and, it might have been added the 
rate of prcfi-rence) from an objective to a subjective standard, or'»tce 
versa, proAidcd we know the rate at which the two standards are 
diverging. We prefer to base our reasoning in this book on rates of 
preferenro and rates of interest expressed in terms of an objective 
monetary standard. As we have seen, the rate of preference ex- 
pressed m terms of subjective standards will be different for different 
individuals . 

' Or '-.yhelimity," or "utility." See The Nature of Capital and 
Income, Chap. III. 



Sec. 2] 



TIME-PREFERENCE 



89 



■f, i^mf^ 



/, 



52 



But what are these "goods" which are thus contrasted? 
At first sight it might seem that the "goods" compared 
may be indiscriminately wealth, property, or services} It is 
true that present machines are preferred to future machines ; 
present houses to future houses; land possessed to-day 
to land available next year; present food or clothing to 
future food or clothing; present stocks or bonds to future 
stocks or bonds; present music to future music, and so on. 
But a slight examination will show that some of these 
cases of preference are reducible to others. ^Vhen present 
capital (whether capital-wealth or capital-property) is pre- 
ferred to future capital, this preference is really a prefer- 
ence for the income of the first capital as compared with 
the income of the second. The reason we would choose a 
present fruit tree rather than a similar tree available in 
ten years is that the fruit production of the first will occur 
earlier than that of the second. The reason one prefers 
immediate tenancy of a house to the right to occupy it in 
six months is that the uses of the house begin six months 
earlier in one case than in the other. [ In short, capital- 
wealth available early is preferred to capital-wealth of 
like kind available at a more remote time, because the 
income of the former is available earlier than the income 
of the latter. For the same reason, early capital-property 
is preferred to late capital-property of the same description. 
For property is merely a claim to future income; and the 
earlier the property is acquired, the earlier will the in- 
come accrue, of the right to which the property consists! ' 

Thus, all time-preference resolves itself into the prefer- 
ence for early income over late income. Moreover, the 
preference for present income over future income resolves 
itself into the preference for present final income over future 
iirud income. The income from an article of capital which 

' For definitions of these terms, see Glossary. 



.■1' 



1 1 



ifii 



'i 



I 'A \ 



90 



THE RATE OF INTEREST 



[Chap. VI 



consists merely of an "interaction" > or "preparatory ser- 
vice'" is desired for the sake of the final income to which 
that interaction paves the w.iy. We prefer present bread 
baking to future bread baking because the enjoyment of the 
resulting bread is available earlier in the one case than in 
the other. Present weavmg is preferred to future weaving, 
because the earlier the weaving takes place the sooner will 
the cloth be manufactured, and the sooner will the clothmg 
made from it be worn by the consumer. 

When, as is usually the case, exchange mtervenes be- 
tween the weaving and the use of the clothes, the goal in 
the process is somewhat obscured by the fact that the 
manufacturer feels his preference for present weaving over 
future weaving, not because the clothes will be more early 
available, but because he will be enabled to sell the cloth 
earlier. To him, early sales are more advantageous than 
deferred sales, because the earlier the money is received the 
earlier can he spend it for his own personal uses, — the shel- 
ter and the comforts of various kinds constituting his real 
income. It is not he, but his customers, those who buy 
the cloth he manufactures, that base their preference for 
present cloth over future cloth on the earlier availability of 
the clothes which can be made from it. But in both cases 
the mind's eye is fixed on some ultimate enjoyable income 
to which the interaction in question is a mere preparatory 
step. We thus see that all preference for present over 
future goods resolves itself, in the last analysis, into a 
preference for early enjoyable income over late enjoyable 
income. This simple proposition would have received 
attention before had there been at hand a clear-cut con- 
cept of income. 

§3 

In The Nature of Capital and Income * it was shown 

that income ultimately consists of the stream of conscious- 

' See Glossary. 

' Sets The Nature of Capital and Income, Chap. IX 
• Chap. X. > I' • 



Sac. 3] 



TIME-PREFERENCE 



91 



ness. Or, if we prefer to stop just short of this subjective 
mcome, we may say that income consists of the objective 
services which impinge upon our persons and are on the 
poini of producing the subjective effects on consciousness. 
In short, the income-stream consists of nourishment, cloth- 
mg, shelter, amusements, the gratification of vanity, and 
other miscellaneous items. It is this income-stream upon 
which attention now centers. Henceforth, instead of 
speaking vaguely and loosely of the preference for pre -t 
"goods" over future "goods," we shall speak of the p 
ence for present enjoyable income over future enjoyah 
come. "Present" and "future" are, of course, used 
comparative sense only; in a more accurate statemre 
should substitute "early" and "deferred." 

It should be noted that the preference for present • 
future goods, when thus reduced to its lowest terms, -tos 
the values of the contrasted present and future goo.fe of 
the interest element. When any other goods than enjoy- 
able income are conside' ' their values abready imply a 
rate of interest. When w t 'at interest is the i»^ tnium 
on the value of a present house er that of a future lOUse, 
we are apt to forget that the value of each housp > itsetf 
based on a rate of interest. We have seen * that e pri ^ 
of a house is the discounted value of its future in( ne. In 
the process of discounting there lurks a rate of intermit 
The value of houses will rise or fall as the rate of interest 
falls or rises. Hence, when we compare the values of presen t 
and future houses, both ternr of the comparison involve 
the rate of mterest. If, thei 'ore,we undertake to make 
the rate of mterest depend on the relative preference for 
present over future houses, we are making it depend on 
two elements, in each of which it already enters. The same 
is true of all capital, and also of those items of income 
which we have called mteractions; for the value of an 
interaction is the discounted value of the ultimate income 

' See tupra, Chap. II, and The Nature of Cajrital and Income, 
Chap. XIII. 






92 



THE RATE OF INTEREST 



[Chap. VI 



to which that interaction leads. We could not rest satisfied 
in the statement that interest is the premium on the 
, value of present tree-planting over that of future tree- 
planting; for the value of each tree-planting itself depends 
on the rate at which the future income from the tree is 
discounted. But when present vitinuUe income is com- 
pared with future ultimate income, the case is different, 
for the value of ultimate income mvolves no interest what-' 
ever. We see, therefore, that the reduction of the problem 
of mterest to a comparative value of present and future 
enjoyable mcome avoids the difficulty of making interest 
depend on magnitudes which themselves depend directly 
on interest. 



t r 



. , i. B 



§4 

Having seen that time-preference is really a preference 
for early enjoyable mcome compared with remote enjoy- 
able mcome, we next note that this preference depends 
on the entire future income-stream, that is, the amount of 
mcome and the manner in which it is distributed in time. 
It depends on the relative abundance of the early and 
remote incomes — or what we may call the time-shape of 
the mcome-stream. If future income is particularly abun- 
dant, its possessor would evidently be willing to sacrifice 
a large amoimt of it for the sake of a relatively small 
J amount of present mcome.* Thus, in winter, the possessor 
of a strawberry patch might be wiUing to sell two boxes of 
strawberries, due in six months, for one available to-day, 
while in strawberry season he might, on the contrary, be 

' It is noteworthy that, though lacking any definite theory of 
income, those writers who have made the most successful analysis 
of the rate of interest have, in substance, made it depend, to some 
extent, at least, on income. Thus B6hm-Bawerk, as has been observed 
gives as one of the "three circumstances" aflFecting the "preference 
for present goods" the "relative provision for present and future »• 
and Landry virtually states the same relation, on p. 55 of L'InUrH 
au Capital. 



Sbo. 4] 



TIME-PREFERENCE 



93 



willing to give up two boxes of his then abundant crop for 
the right to one box in the succeeding winter. 

It is, therefore, not necessary here to distinguish, as 
Bohm-Bawerk does, between the principles which lead to the 
existence of interest an ' those which regulate the rate of 
interest; for to determine the rate of interest will include 
the determination of whether the rate must necessarily 
always be greater than zero. As a matter of fact, the rate 
may theoretically be negative, as in the case just mentioned 
of strawberries in otrawberry season, or in the case cited by 
Bohm-Bawerk hi.Mself, of ice in wmter. The reason such 
negative interest is not actually encountered in the market 
is that perishable articles such as ice and strawberries are 
never used as standards of value. We express our rates 
of interest m money, even if our contracts relate to 
strawberries or ice. But money possesses durability, and 
may be hoarded without loss. This explains why the 
rate of mterest m terms of money can never be 
negative.' 

The proposition that the preference of any individual 
tor present over future income depends upon his pro- 
spective enjoyable income corresponds to the proposition in 
the theory of prices, that the marginal utility of any article 
depends upon the quantity of that article; both proposi- 
tions are fundamental in their respective spheres. 

When it is said that the time-preference of an individual 
depends on his enjoyable income, it is meant that the rate 
of preference for, say, $100 worth of this year's enjoyable 
income over $100 worth of next year's enjoyable income 
depends upon the entire character of the mdividual's in- 
come-stream. 

An income-stream is made up of a large number of 
different elen ints, aome of which contribute to nourish- 
ment, others ^o shelter, others to amusement, etc. In a 
complete enumeration of these elements, we should need 
to distinguish the use of each different kind of food, the 
' See Supra, Chap. V, § 5. 



C 

z 

s 






■' 



I 

I 

i 3 



ml 



.1 f 



f :■ 

- -I 






94 



THE RATE OF INTEREST 



[Chap. VI 



gratification of every variety of human want. TTn^jj of 
these constitutes a particular filament of the income- 
stream, extending from the present out into the indefinite 
future and varying at different points of time in respect 
to size and probability of attainment. A man's rate of 
tirne-preference, therefore, depends on the size and prob- 
ability at various moments of the entire collection of 
income-elements. For the graphic representation, how- 
ever, of size and distribution in time, it is simpler to lump 
together these innumerable elements of income, expressed 
iri terms of money. We may say, therefore, that an indi- 
vidual's time-preference depends on the following four 
elements : — 



1. On the size of the income-stream. 

2. On its distribution in time,— accordrng as it accrues 

evenly or unevenly, and if unevenly, according to the 
periods at which it is expected to be relatively abun- 
dant and the periods at which relatively scarce. 

3. On the composition of the income-stream,— what part 

consists of nourishment, what part clothing, what 
part shelter, etc. 

4. On the probabiiity of the income-stream and its con- 

stituent elements. 



We shall consider these in order, 



15 



/ 



Our first step, then, is to show how a person's time- 
preference depends on the size of his income. In general, 
it may be said that the smaller the income the higher is 
the preference for present over future income. It is true 
that a small income implies a keen appreciation of future 
wants as well as of immediate v&nts. Poverty bears down 
heavily on all parts of a man's life, both that which is im- 



s» 



%''^&i; 



Sac. 6] 



TIME-PREFERENCE 



95 



mediate and that which is remote. But it enhances the 
utility of immediate income even more than of future in- 
come. This result is partly rational, because of the im- 
portance, by supplying present needs, of keeping up the 
continuity of life and the ability to cope with the future; 
and partly irrational, because the pressure of present needs 
blinds one to the needs of the future. As to the rational 
side, it is clear that present income is absolutely indispen- 
sable, not only for the present, but even as a precondition 
to the attainment of future income, "A man must live." 
Any one who values his life would prefer to rob the future 
for the benefit of the present, so far, at least, as to keep life 
going. If one has only one loaf of bread he would not 
preserve it for next year; for if he did he would starve in 
the meantime. A single break in the thread of life suffices 
to cut oflf all the future. And not only is a certain mini- 
mum of present income necessary to prevent starvation, 
but the nearer this minimum is approached the more 
precious does present income appear, relatively to futiu« 
income. 

As to the irrational side, the effect of poverty is often 
to relax foresight and self-control and tempt one to "trust 
to luck" for the future, if only the all-absorbing clamor of 
present necessities is satisfied. 

We see, then, that a low income tends to produce a high 
time-preference, partly from lack of foresight and self-con- 
trol, and partly from the thought that provision for the 
present is necessary both for itself and for the future 
as well. 









§6 

We come next to the influence upon time-preference of 
the distribution of income in time — the time-shnpe of the 
income-stream. The concept of the time-shape of ore's 
ineome-strpftm is firndamental in the following chapters. 
Four different types of time-shape may be distinguished : 



.■r 



.'I 



III 



96 



THE RATE OF INTEREST 



[Chap, VI 



uniform income, as represented in Figiire 2;* increasing 
income (Fig. 3) ; decreasing income (Fig. 4) ; and fluctuating 



' u 



Fio. 2. 



income (Fig. 5). The effect of possessing an increasing in- 
come is to make the preference for present over future 



Fio. 3. 



income higher than otherwise, for it means that present 
income is relatively scarce ami future income abundant. 



?rj 



Fio. 4. 

A man who is now enjoying an hicome of only $1000 a 
year, but expects in ten years to be enjoying one of 
810,000 a year, will prize a dollar to-day far more than a 
dollar due ten years hence. He may, in fact, borrow 

• In these curves, time is represented horiiontally and rate of 
Chip Xm'"'' ''"''''''^^^- " '" ^*^ '"^'"^«- "/ <^"/«^°^ ='«'■ income, 



Sec. 6] 



TIME-PREFERENCE 



97 



money to eke out this year's income, and make repayment 
by sacrificing from the more abmidant income ten years 
later. Reversely, a gradually decreasing income, making, 
as it does, present income relatively abimdant and future 
income scarce, tends to reduce the preference for present 
as compared with future income. A man who has a salary 
of $10,000 at present, but expects to retire in a few years 
on half pay, will not have a very high preference 
for present income over future. He will want to save 
from his present abundance to provide for coming 
needs. 

The extent of these efifects will of course vary greatly with 
different individuals. Corresponding to a given ascend- 




l^ 




Fig. S. 

ing income, one individual may have a preference of 10 per 
cent., and another only 4 per cent. What we need here 
to emphasize is merely that, given a descemling instead 
of an ascending income, both of these individuals would 
experience a reduction of time-preference, — the first, say, 
to 5 per cent, and the second, say, to 2 per cent. 

If we consider the combined effect on time-preference of 
both the nze and time-shape of income, we shall observe 
that those with small incomes are much more sensitive to 
time-sha{)e in their feeling of time-preference than are 
those with large incomes. For a poor man, a very slight 
stinting of the present suflSces to enhance enormously his 
preference for present over future income: and reversely, 
a very slight increase in his present income will suffice to 







98 



THE RATE OP INTEREST 



[Chap. VI 



enormously lessen that preference. A rich man, on the 
other hand, requires a relatively large variation in the 
comparative amounts of this year's and next year's in- 
come to suffer any material change of time-preferer?ce. 

It is clear that the dependence of time-preference on 
time-shape of income is practically identical with what 
Bohm-Bawerk calls the "first circumstance" making for 
the superiority of present over future goods : * 

"The first great cause of difference in value between present and 
future goods consists in the different circumstances of want and 
provision in present and future. ... If a person is badly in want 
of certain goods, or of goods in general, while he has reason to hope 
that, at a future period, he will be better off, he will always value 
a given quantity of immediately available goods at a higher figure 
'" ^n the same quantity of future goods." 






§7 

We come next to the influence of the composition of the 
income-stream on the time-preference of its possessor. An 
income worth $5000 may, for one individual, comprise 
one set of enjoyable services, and for another, an entirely 
different set. The inhabitants of one country may have 
relatively more house-shelter and less food-element in 
their incomes than those of another. Tliese differences 
will havo an influence in one direction or the other upon 
the time-preference. Diminution of any one constituent of 
income would have an effect upon the time-preference 
similar to the effect of diminution of income in general. A 
decrease of the food element would be felt especially, both 
because this element usually forms a considerable part of 
income and because it is a prime necessity. 

Were we to pursue the subject in detail, we should need 
to resolve a person's income into the elements of which it 
is composed, —nourishment, shelter, clothing, and other 
gratifications. As we have seen, the income-stream is a 
complex magnitude consisting of a large number of sepa- 

' The Poailive Theory of Capital, p. 249. 



Sec. 8] 



TIME-PREFERENCE 



99 



rate filaments, one for each separate constituent. ' Any 
individual's rate of preference depends on this complex 
magnitude in its entirety. < Theoretically a change in 
any of these individual partial income-streams will in- 
fluence the rate of preference. A bread famine, a large 
wheat crop, the outlook for the fuel supply, electric light 
service, shoes, or diamonds, all should be taken into ac- 
count in a statement designed fully to cover the influence 
of the income-stream upon time-preference. 

It is not necessary to formulate the concept of "com- 
position " of an income-stream in such a way as to divorce 
it from the concepts of size and time-shape ; for the com- 
position of an income-stream is included in a statement 
of the size and time-shape of each filament of which that 
income-stream consists. We content ourselves by con- 
sidering all these elements of income lumped together in 
a single sum of money value. We need not here concern 
ourselves with the principles which govern the valuation 
of the sum. These principles constitute the theory of 
prices, not of interest; and these prices, as we have 
already observed, being prices of final or enjoyable 
elements of income, do not, like the prices of capital 
or of interactions, embarrass us by direct dependence on 
the rate of interest which we are seeking to solve. As- 
suming, then, the elements of which incomes are composed 
to be adjusted according to the principles which regulate 
prices, we shall hereafter usually treati an income-stream as 
a homogeneous quantum expressible in terms of gold or 
some other monetary standarrl. Our task is therefore re- 
duced to answering the question : Enjoyable incomes being 
expressed in terms of money, what determines the rate of 
interest in terms of this same money ? 






m 



We come fumiiy to the element of risk. ' Income, being 
future, is always subject to some uncertainty, and thin un- 



'f 



100 



THE RATE OP INTEREST 



[Chap. VI 



llici 



certainty must naturally have an influence on the rate of 
time-preference of the possessor, t We have seen that time- 
preference ia the preference for $1 certain added to im- 
mediate income over $1, also certain, added to income 
one year hence. iThe influence of risk on time-preference 
therefore means the influence of uncertainties in the 
anticipated income of an individual upon his relative 
valuation of present and future small increments of In- 
come, both increments being certain: The manner in 
which risk operates upon time-preference will differ accord- 
ing to the particular periods in the future to which the risk 
applies. (If the possessor of income regards the income 
of the immetiiate future as fairly well assured, but fears the 
loss of income in more remote perioils, he may be aroused 
to a high appreciation of the needs of that remote future and 
save from his present certain abundance in order to provide 
for the later possible scarcity. . Income in which this sort 
of risk exists tend,?, therefore, to produce a low rate of 
time-preference for income which is immediate and cer- 
tiun as compared with income which is remote and uncer- 
tain. In actual fact, such a type is not uncommon. The 
remote future is usually less known than the immediate 
future. This means that the risk connected with distant 
income is greater than that connected with income near 
at hand. The chance of disease, accident, disability, or 
death is always to be reckoned with, but under ordinary 
circumstances is greater in the remote future than in the 
immediate future. Consequently there is usually a ten- 
dency toward a low time-preference. This tendency :s 
expressed in the phrase to "lay up for a rainy day." 

But the influence of risk is not always in the direction of 
lowering time-preference. Sometimes the relative un- 
certainty is reversed, and immediate income is subject 
to higher risk than remote income. Such is the case 
in war or other temporary threat of misfortune.' Such is 
also the case when an individual is assured a permanent 
position with a Salary after a certain time, but in the mean- 



Sic. 8] 



TIME-PREFERENCE 



101 






time must obtain a precarious subsistence. In these cases 
'the effect of the risk element is to enhance the estimation 
in which immediate income is held. Again the risk may, 
instead of applying especially to remote periods or espe- 
cially to immediate periods, apply to all alike. Such a con- 
dition largely explains why salaries and wages are lower 
than the average earnings of those who work for themselves. 
Those who choose salaries rather than profits are willing 
to accept a low mcome in order to get rid of a precarious 
one. Since a risky income, if the risk applies evenly to 
all parts of the income-stream, is nearly equivalent to 
a low income, and since a low income, as we have seen, 
tends to create a high time-preference, rl^k, if uniformly 
distributed in time, must tend to raise time-preference. 

\\e see, then, that risk tends in some cases to increase 
and in others tc decrease the rate of time-preference. But 
there is a common principle m all these cases. Whether 
the result is a high or a low time-preference, the primary 
fact is that the risk of losing the income in a particulw- period 
of time operates as a virtual impoverishment of the income 
in that period, and hence increases the estimation in 
which it is held. If that period is a remote one, the risk 
to which it is subject makes for a high appreciation of re- 
mote income; if the period is the immediate future, the 
risk makes for a high appreciation of immediate income; 
if the risk is in all periotls of time, it acts as a virtual de- 
crease of income all along the line. 

There are, however, anomalous individuals in whom 
caution is absent or per\-°rte<L Upon these, risk will have 
quite the opposite effects. Some persons, who see great, 
speculative chances m the remote future, may treat that 
future as though it were especially well-endowed, and there- 
fore be willing to sacrifice a large amount of their "great 
expectation"" in the future for the sake of a relatively 
small addition to their present income. In other words, 
they will have a high time-preference. The same individ- 
uals, if receiving an income which is risky foi all period.s 



i 



C 

z 

I 



102 



THE RATE OF INTEREST 



[Chap. VI 



Hi' 



■ i : 



of time alike, might have, as a result, a low instead of a 
high time-preference. 

The income to which risk applies may be either the in- 
come from articles of capital external to man, or the income 
from man himself. In the latter case the risk of losing 
the mcome is the risk of death or invalidism. This risk — 
the uncertainty as to human life and health — differs 
somewhat from the uncertainty of income dependent on 
objective capital ; for the cessation of life not only produces 
a cessation of income from the human machine, but a ces- 
sation of the enjoyment of all income whatsoever. Fer 
persons who have children whose future welfare they have 
at heart, this consideration loses much of its force. A man 
with wife and children is willing to pay a high insurance 
premium in order that they may continue to enjoy 
an income after his death, while an unmarried man, or 
a man who cares only for self-indulgence and wishes to 
"make the day a.id the journey alike," will not try to con- 
tmue the income after his death. Uncertainty of life in the 
latter case is especiaUy calculated to produce a high degree 
of time-preference. Sailors offer a good example. They 
are natural spendthrifts, and vnen they have money use 
It lavishly. The risk of shipwreck is constantly before 
them, and then- motto is, "A short life and a merry one." 
The effect of risk, therefore, is manifold, according to the 
degree and range of appUcation of risk to various periods 
of time; according to the cautious or incautious character 
of the individual; according to whether or not the risk in 
question applies to human life, and if so, aecordmg to 
whether or not the mdividual's interest m the future ex- 
tends beyond his own lifetime. The manner in which 
these tendencies operate upon the rate of interest will be 
C scussed in Chapter XI. 

§9 

The proposition that the preference for present over 
future income depends upon the income, its size, time- 



Sec. 9] 



TIME-PREFERENCE 



103 



shape, composition, and probability, does not deny that 
it may depend on other factors also, just as, in the theory 
of prices, the proposition that the marginal utility of an 
article depends upon the quantity of that article floes not 
deny that it may depend on other elements as well. But 
the dependence of time-preference on income is of most 
importance, foretime-preference is a preference fcrr incomet 
It is in the same way that the dependence of the marginal 
utility of bread on the quantity of bread is more important 
than its dependence on the quantity of some other com- 
modity, such as butter. As to the dependence of this time- 
preference for mcome on other factors than that income, 
these other factors may conveniently be regarded as affect- 
ing the " form of the function" which expresses its depend- 
ence on income. In this light may be considered the 
I mfluence of "the personal equation,'^ It is clear that the 
rate of time-preference which corresponds to a specific 
income-stream will not be the same for everybody, r One 
man m.ay have a time-preference of 5 per cent, and another 
10 per cent., although both have the same income; The 
vdifFerence will be due to the personal characteristics of 
the individuals.' These characteristics are chiefly five in 
number:* (1) foresight, (2) self-control, (3) habit, (4) ex- 
pectation of life, (5) interest in the lives of other i)ersons. 
We shall take these up in orrler. 

(1) Fu-si, as to foresight. Generally .speaking, the greater 
the foresight, the less the rate of time-preference, and vice 
versa} In the case of primitive races and uninstructed ' 



4 



' Cf. Rae's Sociological Theory of Capital, p. 54. Also IV>hm- 
Bawerk, The Positive Theory of Capital, Book V, Chap. III. 

' To be exact, we should observe that lack of fore.«ii;?ht m.iy either 
increase or decrease time-prcferfmce. Although most pfrs^ms who 
lack foresight err by failing to give due weight to the imfxjrtaTice of 
future needs, or, what amounta to the same thing, by overestimating 
the pro\-iaion existing for such future needs, cases are not lacking in 
which the opposite error is committed ; that is, the individual exagger- 
ates the needs of the future or underestimates the provision likely to be 
made for them. In order not to complicate the text, only the former 



104 



THE RATE OF INTEREST 



[Chap. VI 






it:H^i 



classes of society, the future is seldom consitlered in its 
true proportions. The story is told of such a person that 
he would not mend his leaky roof when it was raining, for 
fear of getting more wet, nor when it was not raining, be- 
cause he did not then need shelter. Among such persons, 
the preference for present gratification is powerful because 
their comprehension of the future is weak. In regard to 
foresight, Rae states:' — 

"The actual presence of the immediate object of desire in the 
mind, by exciting the attention, -oems to rouse aU the faculties, 
as It were, to fix their view on it, and leads them to a very lively 
conception of the enjoyments which -t offers to their instant pos- 
session. The prospects of future good, which future years may 
hold out to us, seem at such a moment dull and dubious, and are 
apt to be slighted, for objects on which the daylight is falling 
strongly, and showing us in all their freshness just within our grasp. 
There is no man, perhaps, to whom a good to be enjoyed to-day 
wou d not seem of very different importance, from one exactly 
sunilar to be enjoyed twelve years hence, even though the arrival 
of both were equally certain." 

The sagacious business man represents the other ex- 
treme; he ;^ constantly forecasting. These differences in 
degrees of foresight produce corresponding differences in 
the dependence of time-preference on the character of in- 
come. Tlius, for a given income, say $1000 a year, the 
reckless might have a time-preference of 10 per cent., when 
the forehanded would experience a preference of only 5 per 
cent. In both cases the preference will depend on the size 
of the mcome, being higher the lower the income; but the 
particular rates corresponding to a particular income in 
the two cases will be entirely different. LTherefore the 
rate of preference, in general, will be higher m a com- 
munity consisting of reckless mdividuals than in one 
consisting of the opposite type." 

and more common error wiU be hereafter referred to when " lark of fore- 
sight IS mentioned. But the reader may in each .suoh c;>so readily 
add the po.ssibility of the contrary error. 
' Sociological Theory of Capital, p. 54. 



Sec. 0] 



TIJIE-PREFEREXCE 



105 



(2) We come next to self-control. This trait, though 
distinct from foresight, is usually associated with it and 
has very similar effects. Foresight has to do with think- 
ing, self-control with willing. A weak will usually goes 
with a weak intellect, though not necessarily, and not 
always. The effect of a weak will is similar to the effect 
of inferior foresight. Like those workingmen who cannot 
carry their pay home Saturday night, but spend it on the 
way in the grogshop, many persons carmot deny themselves 
any present indulgence, even when they know definitely 
what the consequences will be in the future. Others, on 
the ntrary, have no difficulty in stinting themselves in 
tne tace of all temptatiou.. 

(3) The third characteristic of human nature which needs 
to be considered is habit. That to which one is accustomed 
exerts necessarily a powerful influence upon his valuations 
and therefore upon his time-preference. This induence 
may be in either direction. ^ Rich men's sons, accustomed 
to the enjojTnent of a large income, are apt to put a higher 
valuation on present compared with future income than 
would persons of the same income who were brought up 
under different conditions. If they suffer a reverse of 
fortune, they find it harder *o live moderately than those 
of equal means who have risen instead of fallen in the 
economic scale ; and this will be true even if foresight and 
self-control are the same in the two cases. 

(4) The fourth circumstance which may influence the 
form of the function by which time-preference depends on 
the character of income has to do with the uncertainty 
of life of the recipient of that income. We have already 
seen in a different connection that the time-preference of an 
individual will be affected by the prospect of a long or short 
life, both because the termination of life brings the termina- 
tion of the income from labor, and because it also ter- 
minates the enjoj-ment of all income. It is the latter fact 
in which we are here interested ; the expectation of life af- 
fects the dependence of time-preference on income. There 



1.: 




tp 



£•4 



106 THE RATE OP INTEREST [Chap. VI 

will be differences among different classes, different indi- 
viduals, and different ages of the same indivMual So far 
as age isconcemed, the usual course of events is as 
follows : The time-preference in the early periods of life 
IS high because foresight and self-control are weak 
UiUdren are notorious spendthrifts. A little later, when 
the mdividual has acquired some self-control and fore- 
sight, he will still have a high rate of preference, but 
for another reason, -the prospect of an ascen.ling in- 
come-stream. His present income is small, but he looks 
forwaatl to having an ample income in five or ten years 
As the time of marriage and middle life approaclies, the 
opposite tendency may assert itself. Foreseeing the needs 
of middle life and anticipating no increase in the provision 
for those needs, he wiU cease to borrow and begin to save 
After he has passed middle age, when hi.s children have 
become self-supporting, and he looks forward tc de- 
clinmg years, matters are reversed again. He wiU want 
to enjoy his income whHe he may, the income bevond 
his death bemg of no significance to him except as it 
can be bequeathed to his descendants. The prospect 
Oi death plays an important role in the thoughts of 
the old. One evidence of this L^ the prominence given 
to It m all philosophical and religious systems > The 
philosophy of Horace, for mstance, was summed up in the 
maxim "oarpe diem;' which is practicaUy the same as 
the still older maxim, "eat. drink, and be rnerr^-, for to- 
morrow we die." The chance of death may be said to 
be the most important ratimal factor tending to make 
the rate of time-preference high, and anything that would 
tend to prolong hmnan life would tend at the same time 
to reduce the rate of time-preference. .\s Rae says : » — 

''Were life to endure forever, were the capacity to enjoy in per- 
fection all .ts good., both mental and corporeal, to be prolon'^d 

i^r^'^:?;^^'' 'f •^-' ^^^ tr-"lation. New York 
' The Sociological Theory of Capital, pp. 53-54. 



L 



Sic. B] 



TIME-PREFERENCE 



107 



m 



with it, and were we ^ided solely by the dictates of reason, there 
oould be no limit to the formatif " of means for futuif» (gratification, 
till our utmost wishes were supplied. A pleasure to be enjoyed, 
or a pain to be endured, fifty or a hundred years hence, would be 
considered deservinji the same attention aa if it were to befall 
ua fifty or a hundred minutes hence, and the sacrifice of a smaller 
present good, for a greater future good, would be readily made, to 
whatever period that futurity might extend. But life, and the 
power to enjoy it, are the most Lncertain of all things, and we are 
not guided altogether by reason. We know not the periwl when 
death may come upon u.^, but we know that it may come in a few 
days, and must come in a few years. \\'hy then be providing 
goods that carmot be enjoyed until times, which, though not very 
remote, may never come to us, or until times still more remote, 
and which we are convinced we shall never see? If life, too, is 
of uncertain duration and the time that death comes between us 
and all our po-ssesaions unknown, the approaches of old age are at 
least certain, and are dulling, day by day, the relish of every 
pleasure." 

The shortness of life thus tends powerfully to raise the 
rate of time-preference. Thi.s Is especially evident when 
the income-streams compared are long. A lover of masic 
will prefer a piano at once to a piano available next year, 
hecau:se, smce either will outk.st his own life, he will get 
one more year's use out of the piano available at once. 

From what has been said it is clear that there are three 
periods in his life when a man's time-preference is espe- 
cially high: (1; in early Hfe it Is high because of youthful 
recklessness; i2) in the preparatory- stage, because future, 
income seems relatively abundant: and (3j kte in life, 
because future income seems relatively superfluous. 

(5) But whereas the shortness or uncertainty of life tends 
to raise the rate of time-preference, its effect is greatly 
mitigated by the fifth circumstance, the care for the welfare 
oTposterity. Probably the most ^werful cause tending to 
reduce the rate of interest is the love of one's children and 
u e desire to pro\nde for their good. 3^'hen these sentiments 
^cfcay. as they did at the time of th decline and fall of '''.e 
Roman Empire, and the fashion i^ : e.xhauat wealth m 






108 



THE RATE OF INTEREST 



[Chap. VI 



:!' 



i> ' 



self-indulgence and leave little or nothing to offspring, 
the rate of time-preference and rate of interest will be 
high. At such times the motto, ".\f^er us the deluge," 
indicates the feverish desire t^o s-;.uuaor in the Drcsf^nt, at 
whatever cost to the future.' ) 

In a community like the Uni M States, w ,^re parents 
regard their lives as continuing al^i den-'b in the lives of 
their children, there exists a high appreciation of the needs 
of the future which tends, therefore, to produce a low rate of 
time-preference. It is this sentiment which is responsible 
for the enormous extension of life insurance. At present 
m the United States the insurance on lives amounts to 
$20,000,000,000. This represents, for the most part, an 
investment of the present generation for the next. The 
mvestment of this sum springs out of a low time-preference, 
and tends to produce a low rate of interest. 

Not only does the regard for posterity lower interest, but 
the increase of posterity has in part the same effect. So 
far as an increase in the size of a family reduces the income 
per capita of that family, it operates, like impoverishment, 
to mcrease time-preference. So far as it adds to future 
needs rather than to immediate needs, it operates, like a 
descending income-stream, to diminish time-preference. 
Parents with large families feel the in^portance of providing 
for future years far more than parents otherwise similar but 
with small families. They try harder to save and to take out 
life insurance. In other words, their rate of preference 
for present over future income is lowered. An increase of 
population, therefore, will, other things being equal, reduce 
the rate of interest. This proposition must not be thought 
to conflict with the reciprocal proposition that the same 
prudent regard for the future which is created by the re- 
sponsibilities of parenthood itself tends to diminish the 
number of offspring. An increase of population tends 
toward a low time-preference, but reciprocally a low 

' Sec Rac, The Sociological Theory of Capital, p. 97, 



Sec. 10] 



TIME-PREFERENCE 



109 



time-preference tends to check such increase. Hence it is 
that the thrifty Frenchman and Scotchman have small 
families. 

§ 10 

Time-preference, therefore, depends for each individual 
on his income; that is, its size, time-shape, composition, 
and probability; but the form of this dependence differs 
according to the various circumstances of the individual. 
The circumstances which will tend to make his time- 
preference high are (1) shortsightedness, (2) a weak will, 
(3) the habit of spending freely, (4) the shortness and 
uncertainty of his life, (5) selfishness, or the absence of any 
desire to provide for posterity. The reverse conditions 
will tend to make his rate of preference low; namely, 
(1) a high degree of foresight, which enables him to give 
to the future such attention as it deserves; (2) a high 
degree of self-control, which enables him to abstain from 
present income in order to increase future income; (3) 
the habit of thrift; (4) the probability of long life; (5) 
the possession of a family and a high regard for their 
welfare after his death. 

The resultant of these various tendencies in any one in- 
dividual will determine the degree of his time-preference 
tn relation to any particular income. This result will differ 
as between individuals, and as between di" mt times for 
the same individual. The essential fact • »vever, is that 
for any given individual at any given timt, his tim^-prefer- 
ence depends in a definite manner upon the size, shape, 
composition, and probability of his income'Stream. i 



§ 11 

This view, that the rate of time-preference and conse- 
quently the rate of interest depend upon income, needs 
to be contrasted with the common view, which makes the 



110 



THE RATE OP INTEREST 



[Chap. VI 



til 






111 



rate of interest depend iwre / on the scarcity or abundo-ce 
of capital. It Ls commonly biiievefi that where capital » 
scarce, interest is high, and where capital is plentiful, in- 
terest is low. In a general way there is undoubtedly some 
tr^th in this proposition ; and yet it contains a misinterpre- 
tation of borrowing and lending. It is true that when and 
where men are anxious to lend, interest is low, and when 
and where men are anxious to borrow, interest is high. 
But it is not true that the more capital a man has the more 
anxious he is to lend, and the less capital he has the more 
anxious he is to borrow. The willingness to lend or bor- 
row depends primarily, not upon the amount of one's 
capital, but uix)n the character of the income which he 
gets from it.— whether this income is large or small, im- 
mediate or deferred, of what elements it consists, whether 
it is certain or uncertain. 

The prop<isition that abundance of capital tends to 
lower interest Is thus ver>- superficial : ' for abimdant 
capital merely means abundmt income. Capital- value is 
discountet,! income. Behind, or rather beyond, a capital 
of $100,000 is the income which that capital represer":.-^. 
To fix attention on the $I(30.(XX) capital instead of on 
the income is to use the capit;il as a cloak to over up 
the real factor in the case. Moreover, capital-value is 
itself det>endent on the rate of interest. The capital-value 
of a fami will be doubled if tht» rate of inten>st is halved. 
In such a case there would be found more capital in 
farm-; for the farms in a cornnn mi tv would rise -say from 
$10.000,U.\ to 120,000.000. But it" w not the rise "in cap- 
ital wluoh produces the fall in interest. On the contrar\-. 
it is the tall in the interest rate which pnxluces the rise in 
the valuiition of capital. If we attempt to make the rate of 
interest .iej.H-nd on capital-value, then, since capital-value 
depen.ls on two factors. — the prospective income and the 
rate of mtereat. —we thereby nuke the interest rate depend 

oa itsi'if. The de(.>fiideuce 



iijifUv !>r>, !nc<3?Be and 



~.j _. 



on itsi'lf is of course nugatory, and we are brought back to 



3ec. 11] 



TIME-PREFERENCE 



111 



its dependf^nce on incor ,• as tne only fact of real signifi- 
cance. 

But even as tha* amende<i and explained, the proposition 
that the rate of interest depends on the amount of capital 
b not satisfacton-. The mere amount of capital does not 
tell 113 much about the income for which that capital stands. 
To know chat one man has a capital worth $100,000, and 
another $200.fX)0. shows, to be sure, that the latter man 
may have an income of double the value of the former; but 
it tells us absolutely nothing a3 to the " time-shapea" of 
the two inconies; and the time-shape of income has, aa 
we have seen, a most profound mfluence on the time- 
preference of its possessor. 

Let us suppose two communities similar in population, 
distnbution of wealth, and ail other particulars except in 
the amotmt of their capital and the character of the income 
which that capital represents. One of these two communi- 
ties we shall suppose has a capital of 1100,000 invested, aa 
in N'eva.b, in n.iaes and (Quarries nearly e.xhau^teti, while 
in the .nlier community there is $200,000 of capital invested 
in young orchards and fore^'s. aa in Flori'ia. According 
to tiie tiieor>- that abunriance of capital makes interest low. 
we sho'ild expect the Neva^ia commionity to have a high 
rate oi interest compareii with the Flori'ia community. 
But it is evident tiiat. unle-s other circu.-astances .^hould 
bterfere. the opposite would be the case ; for Nevada hitd 
to cotiremplate a decreasing future income, and in order to 
offset the^ dopre«:iation of capital whi.ii foil.nvs from thia 
condition.' she wo'ild be seeking to lend or invest part of 
the income of the present or irame-liate future, in the hope 
of ofT^tting the 'lecreasel pr'>luct of the min»fs in the more 
remote f-uure. The Florida planters, on the contrary', would 
be iui'liaeil to borrow againat their tuture crops. If the two 
comn\tiiiitiea are supposed to be rommer»;iaiIy connecte*!. 
it would be Nevada which would lend to Flori'la, notwith- 
otandiuii the fact that the lending comniunity waa the 
' See The .\%uurt o/ Capital an.i Irxfomt. Ch^ip KIV. 






I 



112 



THE RATE OF INTEREST 



[Chap. VI 



il 






III' 



poorer in capital of the two. From the illustration it is 
clear that the mere amount of capital-value is not only 
a misleading but a very inadequate criterion of the rate of 
interest.' 

Apologists for the common statement that abundance 
or scarcity of capital lowers or raises interest might be in- 
clmed to argue that it is not the total capital, but only the 
"loanable capital" which should be included, and that the 
Nevada community had more "loanable capital" than the 
Florida comnmnity. But the phrase "loanable capital" 
is merely another cloak to cover the fact that it is not 
the amount of capital, but the decision to lend or 
borrow it, which is important. To give this proposition 
meaning, "loanable capital" must be taken, not in the 
literal sense of capital which can be lent, — for all capital 
is loanable in this sense; but in the sense of capital which 
persons are wUUng to lend. Hence, to state that hi any 
community there is abundance of loanable capital is merely 
to state that there is in that community a willingness to 
lend a great deal of capital. Consequently, the proposition 
that the rate of interest, or preference for present over 
future goods, is low when loanable capital is abundant 
becomes reduced to the platitude that the rate of preference 
for present over futiu^ goods is low when men wish to lend. 

But it may be said, surely in a money market there exists 
at one time a large visible supply of loanable money and at 
another time a small visible supply, and this supply affect" 
the rate of interest. This, again, is a true but a superficial 
statement. A little examination will show that the abun- 
dance or sliortage of loanable bank funds is merely a 
measure of the decision of merchants to discount or deposit, — 
in other wonls, to borrow or lend, —and does not give us any 
clew as to the reason why they do so. The money or credit 

• One of the few defects in Rae's analysis of interest is his em- 
phasis on the accumulation of capital. Since this accumulation i« 
merely in anticipation of future income, the emphasis belongs on the 
latter. 



Sec. 12] 



TIME-PREFERENCE 



113 



is, of course, the mere vehicle by which the bank acts as an 
intermediary or broker between borrowers and lenders, and 
does not represent any independent factor in the case. 

We end, therefore, by emphasizing anew the importance 
of fixing our eyes on income and not on capital. It is only 
as we look through capital-value, beyond to the income 
which it represents, that we reach the efficient causes which 
operate upon the rate of interest. The absence hitherto of 
a definite theory and conception of income has prevented 
economists from doing this. Borrowing and lending are 
in form a transfer of capital, but they are in fact a transfer 
of income of which that capital is merely the present 
value. In our theory of interest, therefore, we have to 
consider not primarily the amount of capital of a com- 
munity, but the income for which that capital stands. 



§ 12 

Unfortunately for purposes of exposition, the relation 
between time-preference and hicome cannot be expressed 
in a simple schedule or curve, as can the relation between 
demand and price, or supply and price, or utility and ciuan- 
tity consumed, for the reason that income means not a 
single magnitude merely, but a conglomtrution of a number 
of magnitudes. As mathematicians would express it, to 
state that time-preference depends on the character of 
income, its size, shajx^, composition, and probability, is 
to siate that time-preference is a fimc'ion of all the 
different magnitudes which need to be specified in a com- 
plete description of tliat hiconie. A geometrical represen- 
tation, therefore, of the dependence of time-preference on 
the various magnitudes which characterize income, would 
be impossible. For a curve can only represent th;.' depend- 
ence of a magnitude on one indeix*ndent variable; even 
a surface can only represent dej)enaence on two; but for 
uur requirenionto wc .shoviM nrod a apace of n tlimensions. 
We may represent the relation between trme-pref-nmce 
I 



;t'.? 



114 



THE RATE OF INTEREST 



[Chap. VI 



and income by a "schedule" like the ordinary "demand 
schedule and "supply schedule," if we make a list of all 
possible mcomes, specifying for each individual mcome all 
ite characteristics. - its size, time-shape (that is, its relative 
magnitude for each successive time-mterval considere^l) its 
composition (or the amount, at each period, of each 'in- 
dividual constituent, as nourishment, shelter, etc ) and 
the certainty or uncertainty attached to aU these elements 
Having thus compUed a list of aU possible incomes, it would 
only be necessary for us to assign to each of them the rate of 
time-preference pertaining to it. Such a schediUe would 
be too comphcated and cumbersome to carry out in detail • 
but the foUowing will roughly indicate some of the main 
groups of which it would consist. In this schedule we have 
represented by the three vertical lines three different classes 
of mcome, -two extreme types and one mean tvpe -so 
that the corresponding rates of time-preference ra^ge them- 
selves m a descending series of numbers. We have also 
represented by the three vertical columns three different 
clasps of individuals, two being of extreme types of in- 
dividuals, and the third of a mixed or medium t>Te Thus 
the numbers in the table descend as we proceeti ' either 
down or toward the right, the lowest number of all boin- 
in the lower right-hand comer. " 



Sic. 12] 



TIME-PREFERENCE 



115 



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c * C = ^ 
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116 



THE RATE OF INTEREST 



[Chap. VI 



Out of the large number of possible incomes represented 
in such a schedule, of course only one can be the actual 
incone of the individual. The one which exists in any 
case -s to a large extent a matter of choice, as we shall see 
in the next chapter. Since time-preference may be varied 
by voluntarUy varying the character of the mcome-stream 
on which it depends, it follows that the shortsighted, weak- 
willed spendthrift individual may not have, as a matter of 
fact, any higher rate of time-preference than his farsighted, 
self-controlled, abstemious brother. In fact, where a loan 
market is in full operation, the tendency is for the two in- 
dividuals to select such income-streams as will bring their 
time-preference into unison. How this is accomplished 
will form the subject of the following chapter. 




CHAPTER VII 

FIRST APPROXIMATION TO THE THEORY OF INTEREST 
(assuming INCOME RIGID) 



§ 1 

In the last chapter we saw that the rate of preference for 
present over future goods was, in the last analysis, a prefer- 
ence for present over future income; that this preference 
depends, for any given individual, upon the character of his 
income-stream, — its size, time-shape, composition, and 
probability, — and that the nature of this dependence varies 
with different individuals. The question at once arises, 
will not the rates of preference of different individuals be 
very different, and if so, what relation do these different 
rates have to the rate of interest ? John Rae assumed that 
the rates differed widely, and that the rate of interest was 
a sort of average of their different magnitudes. But this is 
incorrect. In a nation of hermits, in which there was no 
mutual lending and borrowing, the time-preferences of 
individuals would diverge widely; but in modem society, 
borrowing and lending tend to bring into equality the rates 
of preference in different minds. It is only because of 
the limitations of the loan market that absolute equality 
is not reached. 

The chief limitation to lending is due to the risk involved, 
and to the difficulty or impossibility of ob' .ning the se- 
curity necessary to eliminate or reduce that risk. Those 
who are most willing to borrow are oftentimes those who 
are least able to give security. It will then happen that 
these persons, shut off from the loan market, experience a 
higher rate of time-preference than the rate of interest ruling 

117 



Is! 



A 






If.*'. 



I . % ; 






lif ^ 



IfffP 



118 THE RATE OF INTEREST [Chap. VII 

in that market. If they can contract loans at all. it will 
be only through the pawn shop or other high-rate agencies 
Hut for the moment, let us assume a perfect market 
in which the element of risk is entirely lacking, both with 
respect to the certainty of the expected income-streams 
belonging to the different individuals, and with respect to 
the certainty of repav.nent for loans. In other words, we 
assume that each individual is initially possessed of a fore- 
known income-stream, and that he is free to exchange 
any^t of it to some other person, in~^^^ild;;:itrorSf 
receiving back at some future time an addition to his in- 
conie for the prospective period. We assume further that 
^ to buy and sell various parts of his income-stream (bv 
loans, etc.), is his only method of altering that mcomL 
stream. Prior to such exchange, his income-stream is 
ngrd, t-c. fixed in size, time-shape, and composition. The 
capital-mstruments which he possesses are each capable 
of only a smgle definite series of services contributing to 
his mcome-stream. These assumptions that each man's 
mcome-stream is initially certain and Med, will be used in 
our first approximation to the theory of interest. 

§2 

Under these hypothetical conditions, the rates of time- 
preference for different individuals would be perfectly 
equahzed. Borrowing and lending evidently affect the 
time-shape of the incomes of borrower and lender: and 
since the time-shape of their incomes affects their time- 
preference, such a modification of time-shape wiU react 
upon and modify their time-preference, and bring the 
market into equilibrium. 

If, for any particular individual, the rate of preference 
differs from the market rate, he wiU, if he can, adjust the 
tune-shape of his mcome-stream so as to harmonize his oref- 
erence rate with the interest rate. Those who, for a riven 
income-stream, have a rate of preference above the market 



Skc. 2] 



FIRST APPROXIMATION 



119 



1 rate, vdll sell some of their surplus futiu-e income to obtain 
?] an addition to their present meager income. This will have 
the effect of enhancing the value oif the future income and 
decreasing that of the present. The process will continue 
until the rate of preference of this individual is equal to 
the rate of interest. In other words, a person whose 
preference rate exceeds the current rate of interest will 
borrow up to the point which will make the two rates equal. 
Reversely, those who, with a given income-stream, have a 
preference rate below the market rate, will sell .some of their 
abundant present income to eke out the future, the effect 
being to increase their preference rate until it also harmo- 
nizes with the rate of interest. 

To put the matter in figures, let us suppose the rate of 
mterest is 5 per cent,, whereas the rate of preference of a 
particular individual is 10 per cent. Then, by hypothesis, 
the individual is willing to sacrifice $1.10 of next year's 
income in exchange for $1 of this year's. But in the 
market he is ahU to obtain $1 for this year by spending only 
$1.05 of next year. This ratio is, to him, a cheap price. 
He therefore borrows, say, $100 for a year, agreeing to 
return $105; that is, he contracts a loan at 5 per cent, 
when he is willing to pay 10 per cent. This operation, 
by increa.sing his present income and decrea.sing his future, 
tends to reduce his time-preference from 10 per cent, to, 
say, 8 per cent. Under these circumstances he will borrow 
another $100, being willing to pay 8 per cent., but having 
to pay only 5 per cent. This operation will still further 
reduce his time-preference, until it has been finally brought 
down to 5 per cent. Then, for the last or "marginal" 
$100, his rate of time-preference will agree with the market 
rate of interest. As in the general theory of prices, this 
marginal rate, 5 per cent., being once established, applies 
indifferently to all his valuations of present and future in- 
come. Every comparative estimate <..f present and future 
which he actually makes must be "on the margin" of his 
income-stream as actually determined. The above-men- 



f? 



111' 



I 




120 



THE RATE OF INTEREST 



[Chap. VII 



tioned 10 per cent, and 8 per cent, rates are not actually 
experienced by him ; they merely mean the rates of prefer- 
erence which he would have experienced had his income 
not been transformetl to the time-shape correspondent to 
5 per cent. 

In like manner, if another individual, entering the loan 
market from the other side, has a rate of preference of 
2 per cent., he will become a lender instead of a borrower 
He will he mlling to accept $102 of next year's income for 
$100 of this. But in the market he is able, instead of the 
$102, to get $105. As he can lend at 5 per cent, when he 
woidd gladly do so at 2 per cent., he jumps at the chance 
and invests, not one $100 only, but another and another 
But his present income, being reduced by the process, is 
now more highly esteemed than before, and his future 
income, being increased, is less highly esteen.ed. The result 
will be a higher relative valuation of the present, which 
under the influence of successive additions to the sums lent' 
wiU rise graduaUy to the level of the market rate of interest' 
In such an ideal loan market, therefore, where every in- 
dividual coulil freely borrow or lend, the rates of preference 
for present over future income for all the different indi- 
viduals would become equal to each other and to the rate 
of interest. 



To Illustrate thl^ -easoning b- a diagram, let us suppose 
the income-stream t.. W renresf-ued as in Fisure 6, and that 
the pos.ses8or wish» s onait a small item A" of imme- 
diately ensuing .aira8». -nr ^ .^mewhat larger item X" 
later on. He tajs^ore asoiiiiies his income-stream from 



ABCl 



MBL,. Bsax 



^■image will evidently produce 



, . . — — ■■"■b ^ ""i cviucuiiy proauce 

a chamr^ ir te mm-pj^^^^^Bx^. If the rate of time-pref- 
erence ^ir^aniiii^ IS tffi. iiEom^-stream represented by 
tiie un...uL=. xuir * ir iiH- ces:., tne rate of preference cor- 
respon-aig m the ttghsi ^ will be somewhat less, say 



nww 



Jit 



Sec. 3] 



FIRST APPROXIMATION 



121 



8 per cent. If the market rate of interest is 5 per cent., 
it is evident that the person will proceed to still further 
borrowing. By repeating the operation several times he 



E 
A 




Fio. 6. 



can evidently proiluce almost any required conformation 
in his incoine-stream. If, instead of borrowing, he wishes 
to lend (Fig. 7), he surrenders from his present income- 



A 

E 




Fio. 7. 

stream the amount X' for the sake of the larger amount 
X" at a later time. He will engage in the former series 
of npprations if, at the start, hh subjective preference 
for present goods exceeds the market rate of interest, 
and in the latter, if it falls short of that rate. After 



m 



122 



THE RATE OP INTEREST 



[Chap. VII 




Fio. 8. 



B 



the operations are completed and the final conformations 
of the income-streams are determined, the rates of time- 
preference are all brought into conformity with the market 
rate of interest. 
The loan is effected mider the guise of money. We do 

not confessedly borrow~and 
lend incomes, but money. Yet 
money— that universal me- 
dium in practice and universal/ 
stumbling-block in theory 
— merely represents capitalized income. A hundred dol- 
lars mean the pwwer to secure income, — any mcome the 
present value of which is $100. , 
When, therefore, a person '^ ""--^ 

"borrows" $100 to-day and A 1^:*^ 

returns $105 next year, in ac- 
tual fact he secures the title Tm.9. 
to $100 worth of future income — immediately future, 
perhaps —and parts with the title to $105 worth of income 
more remotely future. 
There are six prmcipal types of individuals in a loan 

market. In the first type 
(Fig. 8) the individual is sup- 
posed to be possessed of an in- 
creasing income-stream AB 
which in his mind results in 
a rate of preference above 
the market rate. Tliis leads 
him to borrow, and relatively 
to level up his ascending income-stream to such a position 
as A'S*. The second type of individual aheady possesses 
a uniform income-stream AB (Fig. 9), but, nevertheless, 
being of a spending type, experiences a rate of preference 
also above the market rate, and will therefore modify his 
income-stream to the curve A'B^. The third type is rep- 
resented in Figure 10. This individual has a rate of pref- 
erence in excess of the market rate, even with a descending 




Fio. 10. 



^^B' 



I 



Sxc. 3] 



FIRST APPROXIMATION 



123 



.B' 



R 



curve AB. The consequence is that by borrowing he 
obtains a curve A'B' of still steeper descent. 

The preceding three cases are of borrowers. In like man- 
ner there are three types of 
lenders. Figure 11 represents 

a descending type of income /! -^^^x^- b' 

AB which, by lending present 

income in return for future x P 

income, is converted into a Fm. ii. 

relatively uniform mcome A'B'; Figure 12 represents a 
imiform income converted, by lending, into an ascend- 
mg income; and Figure 13 an ascending income converted 
into a still more steeply ascending income. 

In all cases we see that the borrowers change their income 
curve by tipping it down in the future and up in the present ; 

whereas the lenders tip their 

income curves in the opposite 

direction. Of the three types 

^^ of borrowers and of lenders, 

A '"' pio 13 *^® ^^ ^ ^^^ group of three 

(see Figs. 8 and 11) is the 
usual and normal case. In both these cases the effort is 
to transform the given income into a more uniform one, 
the rising curve (Fig. 8) being lowered and the falling 
curve (Fig. 11) being raised toward a common horizontal 
position. Figure 10 and Figure 13, on the other hand, 
represent extreme and unusual 
cases. The former (Fig. 10) 
typifies the spendthrift who, 
in spite of lessening income, 
borrows, and the latter (Fig. 
13) typifies the miser who, in 
■pite of rapidly increasing in- X""' 
come, saves even more. Km. i3. 

But whatever the personal equation, it remains true that, 
for each individual, the more ascending his income curve 
the higher his rate of preference, and the more descending 



.B' 



':i; 



' ^'J 






124 



THE RATE OF INTEREST 



[Chap. VII 



the curve, the lower the rate. If the descent is sufficiently- 
rapid, the rate of preference could be made zero or even 
negative. In these cases, the income is such that its 
possessor would sacrifice present income to future, even if 
the market rate of interest were zero.' 

These are, of course, not the only types which could be 
considered, but they are some of the most important. To 
them we may add the type of fluctuating income, as rep- 
resented in Figure 14, which may result in alternate bor- 



li 




Fio. 14. 

rowing and lending so as to produce a more nearly uniform 
income-stream. 

It must not be imagined that the classes of borrowers and 
lenders correspond respectively with the classes of poor 
and rich. Personal and natural idiosyncracies, early 
training and acquired habits, accustomed style of living, 
the usages of the country, and other circumstances dis- 
cussed in Chapter VI, will, by influencing foresight, self- 
control, regard for posterity, etc., determine whether a 
man's rate of preference is high or low, and therefore 
whether he becomes a spender or a saver. So far as the 
character of the income-stream itself tends to place an 
individual in one or the other of these classes, the nature of 
the influence is in accordance with the principles stated in 
Chapter VI in respect to the four features, size, time-shape, 
composition, anil probability. As to size, the larger the 
income the more likely, in general, is its possessor to become 
a lentler, because large incomes, in general, reduce the rate 
of preference for present over future income; as to time- 

• This is the cane mentioned by Carver (Theory of DittribtUion, 
pp. 232-236), when he remark* that a man with S!00 in his pwket 
would not think of spending It all on a dinner to-day, but would save 
at least some of it for to-morrow. 



Sec. 4] 



FIRST APPROXIMATION 



125 






shape, ascending incomes are apt to make the possessors 
borrowers, and descending incomes to make them lenders; 
as to composition, incomes well endoved with the food 
element are less apt to make then- possessors borrowers 
than incomes of the contrary type ; and as to probability, 
incomes which are uncertain tend sometimes to make 
their possessors borrow, sometimes to lend. 



§4 

j But borrowing and lending are not the only ways in which 
'^Zone's income-stream may be modified. The same result 
" may be accomplished simply by buymg and selling property ; 
for, since property rights are merely rights to particular in- 
come-streams, their exchange substitutes one such stream for 
another of equal value but differing in time-shape, composi- 
tion, or certainty. This method of modifying one's income- 
stream, which we shall call the method of sale, really includes 
'the former method of loan ; for a loan contract is at bottom 
Y I'a Jale, as Bohm-Bawerk has so clearly shown. That is, 
I it is the exchange of the right to present or immediately 
ensuing income for the right to more remote or future in- 
come. A borrower is a seller of a note of which the lender 
is the buyer. A bondholder is regarded iutlifferently as a 
Tender and as a buyer of property. The concept of a loan 
may therefore now be dispensed with by beuig merged in that 
of sale. By sellmg some property rights and buying others 
it is ix)ssible to transform one's income-stream at will, 
whether in time-shape, composition, or probability. Thus, 
if a man buys an orchard, he is providing himself with future 
income in the use of apples; if, instead, he buys apples, he 
is providing himself with similar but more immediate 
income. If he buys securities, he is providing himself 
with future money, convertible when receive<l into true 
income. If hi8 security is a share in a mine, his income- 
Btreatn is less lasting, though it should be larger, than if 
the securily is stock in a railway. Purchasing the right to 



■■■^'^\m\ 



n 



' ■^J 




126 THE RATE OP INTEREST [Chap. VU 

remote enjoyable income is caUed investwg; to immediate 
enjoyable mcome, spending. These, howevTr are puTerrd! 
atnre concepts, for "remote" and "immediate" a^e relative 
terms Buymg a wmter overcoat or a carpet may be caUed 
mvestmg, and on the other hand, buying a^actory or lit 

spending" money and "investing" is important; it is 
the antithesis between immediate and remote income The 
adjustment between the two determmes the time-shape of 

oZ' rrT'^r- ^P""^^S ^^«^«^« immediate in- 
come but robs the future, whereas investing provides for 

the future to the detriment of the present 

in mf7 T^" ^f ^'T^ "^^y ""^^'^ terms and phrases 
m this field, most o; which, like "spending" and "in- 

To ?h; Jhile containing meaning of importance, include 
also the alloy of misconception. Thus, the phrase "caoital 
seekmg investment" means that capitklists havTprZ^ 
for which they desire, by exchange, te substituS S 
property, he income from which is more remote. It doL 
no mean that the inanimate capital has of itself any pow^ 

hardTn 1 rTT'"' '' '°^^ "°t ^'^^ th-t there i^Iy 
ha^d and fast Ime between invested and miinvested capital 

be iTf "^' -';^^^^E money which would otherwise 
be spent for immediate enjoyable income in order to ex- 
change it for remoter income ; it does not mean the creatbn 
of new capital, though it maylea.1 to it. Many nid Lsscr 
roversi^ have centered about the phenomenon of" s^^- 

From what has been said it is clear that by buying and 
sellmg property an mdividual may change the coZmatbn 



Seo. fi] 



FIRST APPROXIMATION 



127 



of his income-stream precisely as though he were specifically 
lending or borrowing. Thus, if a man's original income- 
stream is $1000 this year and $1500 next year, and if, 
selling this income-stream, he buys with the proceeds 
another yielding $1100 this year and $1395 next year, he 
has not, nominally, borrowed $100 and repaid $105, but 
he has done what amounts to the same thing, — increased 
his income-stream of this year by $100 and decreased that 
of next year by $105, the $100 being the modification pro- 
duced in his income for the first year by selling his original 
income-stream and substituting the final one, and $105 
being the reverse modification in next year's income 
produced by the same operations. The very same dia- 
grams which were used before may be taken to represent 
these operations. A man sells the income-stream ABCD 
(Fig. 6) and with the proceeds buys the stream EBD. 
The X' and X" are, as before, $100 and $105, but now 
appear explicitly as differences in the value of two income- 
streams instead of direct loans and returns. 



m 



^ 



§6 

In passing we may note that interest-taking cannot be 
prevented by prohibiting loan contracts. To forbid the 
particular form of sale called a loan contract would 
leave possible other forms of sale, and, as was shown 
in The Nature of Capital and Income, the valuation of 
every property-right involves interest. If the prohibition 
left individuals free to deal in bonds, it is clear that they 
would be still borrowing and lending, but imder the name 
of " sale " ; and if " bonds" were tabooed, they could change 
the name to "preferred stock." It can scarcely be sup- 
posed that any prohibition of interest-taking would extend 
to all buying and selling ; but as long as buying and selling 
of any kind were permitted, the virtual effect of lending and 
borrowing would be retained. The possessor of a forest 
of young trees, not being able to mortgage their future 



< 



'JJ 



1^ 




128 



THE RATE OP INTEREST 



[Chap, VII 



return, and bemg in need of an income-stream of a lesL 
deferred type than that receivable from the forest itself, 
would simply sell his forest and with the proceeds buy, say' 
a farm, with a uniform flow of income, or a mine with a 
decreasmg one. On the other hand, the possessor of a 
capital which is depreciating, that is, which represents an 
mcome-stream great now but steadily declining, and who 
is anxious to "save" instead of "spend," would seU his 
depreciating wealth and invest the proceeds in t \ch instru- 
ments as the forest ah-eady mentioned. 

It was m such a way, as for instance by "rent purchase," 
that the medieval prohibitions of usury were rendered 
nugatory. PracticaUy, at the worst, the effect of restrictive 
laws is simply to hamper and make difficult the finer ad- 
justments of the income-stream, compelling would-be bor- 
rowers to sell wealth yielding distant returns instead of 
mortgaging it, and would-be lenders to buy the same, 
instead of lending to the present owners. It is conceivable 
that "explicit" interest might disappear under such restric- 
tions, but "implicit" interest would remain. The young 
forest sold for $10,000 would bear this price, as now, because 
It IS the discounted value of the estimated future income; 
and the price of the farm bought for $10,000 would be de^ 
termined in like manner. The rate of discount in the two 
cases must be the same, because, by buying and seUing, 
the various parties in the community adjust their rates 
of preference to a common level, —an implicit rate of in- 
terest thus lurking m every contract, though never specifi- 
cally appearing thereb. Interest is too omnipresent a 
phenomenon to be eradicated by attacking any particular 
form; nor would any one undertake it who perceived the 
substance as well as the form.* In substance, the rate of 
mterest represents the terms on which the earlier and later 
elements of income-streams are exchangeable. 

'Cf Fetter. Principle! of Economict, New York (Century), 1904. 
pp. 134, 135. 



Sxo. 6] 



FIRST APPROXIMATION 



129 



§6 



The fact that, through the loan market, the marginal 
rate of time-preference for each individual is made equal 
to the rate of interest, may be stated in another way, 
namely, that the total present desirability or utility of the i\ 
individual mcome^stream is made a maximum. For, con- 
sider again the individual who modifies his original fixed 
income-stream by borrowing imtil his rate of preference is 
brought into vmison with the rate of interest. His rate of 
preference was at first 10 per cent. ; that is, in order to 
secure an addition of $100 to his present income, he was 
willing to sacrifice $110 of next year's income. But he 
only needed to sacrifice $105 ; that is, he was enabled to get 
his loan for less than he would have been willmg to pay. 
He was therefore a gainer to the extent of the present de- 
sirability of $5 of next year's income. The second $100 
borrowed was equivalent, in his present estimation, to 
$108 of next year's income, and the same reasonmg 
shows that, as he pays only $105, he saves $3; that is, he 
adds the present desirability of $3 due next year to the 
present " total desirability" or " total utility " of his mcome- 
stream. In like manner, each succepl /e increment of loans 
adds to his present total desirability, so long as he is 
willing to pay more than $105 of next year's income for 
$100 of this year's income. But, as he proceeds, hia gains 
and his eagerness diminish until they cease altogether. 
At, let us say, the fifth instalment of $100, he finds himself 
barely willing to pay $105; his present total desirability 
is then a maximum, and any further loan would decrease 
it. A sixth $100, for instance, is worth m his estimation 
less than $105, say $104, and as, in the loan market, he 
would have to sacrifice $105 next year to secure it, the con- 
tracting of such a loan would mean a loss of desirability 
to the extent of $1 due in one year. Thus, by borrowing up 
to the point where the rate of preference for present over 



M 



m 



130 THE RATE OP INTEREST [Chap. VII 

future income is equal to the rate of interest, the individual 
secures the greatest "total desirability " 

Similar reasoning, applied to the individual on the other 
«de of the market, whose rate of preference is initially 
^ than the market rate of interest, wUl show that he also 

to thrn^r^ '' E'^''"' "^"^^ desirability by lending up 
to the point where his rate of preference corresponds to the 
rate of mterest. At the begimimg, $100 this year has to 
him the same present desirabUity as $102 due one year 
hence whereas m the market he may secure $105 It is 

f im h/5n 1^' y««f he^ce- By lending each successive 
$100 he will add something to his total present desirability 

r^iin ?"" 1 P?'^^"^^ ''' P-sent over futuretcS 
is raised to a level equal to that of the rate of interest 
Beyond that point he would lose by further lendmTTut 

tm t'h?T' K ""'"^ '^^P' "^^ ^^ P'^^^* t°^l desi^bUity 
wUl therefore be a maximum. 



iU 



57 

We are now in a position to give a preliminary answer 
to aie question, What detennmes the rate oflterel" 
T^us far we have regarded the mdividual only, and have 
seen that he conforms his rate of preference to he rate of 
interest. For him the rate of interest is a relativel^fi^ 
fact, since his own time-preference and resulting action 
can affect ,t only infinitesimally. His rate of preference 
.8 the variable. In short, for him individually thTrate o^ 
interest is cause, and the rate of preference, "Effect Po 
society as a whole, however, the order of cau^e and eff^ 
^ reverb, 'n.is change is like the corresponding bveS 

re^rr' """T '" ''' ''^^ °^ P"«-- Eachlndlvidial 
regards the market price, say, of sugar, as fixed, and adjusts 

formmg the market, we know that the price of sugar is due 



Sec. 7] 



FIRST APPROXIMATION 



131 



to its marginal utility to the consumer.* In the same way, 
while for the individual the rate of interest determines the 
rate of preference, for society the rates of preference of 
the individuals determine the rate of interest. The rate 
of interest is simply the rate of preference, upon which the 
whole community may concur in order that the market 
of loans may be exactly cleared. 

To put the matter in figures : if the rate of interest is 
set very high, say 20 per cent., there will be relatively 
few borrowers and many would-be lenders, so that the 
total extent to which would-be lenders are willing to 
reduce their income-streams for the present year for the 
sake of a much larger future income will be, say, 100 
million dollars; whereas, those who are willing to add to 
their present income at the high price of 20 per cent, 
interest will borrow only, say, one million. Under such 
conditions the demand for loans is far short of the supply 
and the rate of interest will therefore go down. At an 
interest rate of 10 per cent, the present year's income 
offered as loans may be 50 millions, and the amovmt which 
would be taken at that rate only 20 millions. There is 
still an excess of supply over demand, and interest must 
needs fall further. At 5 per cent, we may suppose the 
market cleared, borrowers and lenders being willing to take 
or give respectively 30 millions. In like manner it can 
be shown that the rate would not fall below this, as in 
that case it would result in an excess of demand over 
supply and cause the rate to rise again. ,y' 

liius, the rate of intei;est is the common market rate of •'^ I 
preference for present over futufis income, as determined by | 
the supply and demand of present and f utvu« income. Those ' 
who, having a high rate of preference, strive to acquire 
more present income at the cost of future income, tend to 
raise the rate of interest. These are the borrowers, the 



m 



i 

'fi 



t: 





> See the author's " Mathematical Investigations in the Theory 
of Value and Prices," Traruactiona of Connecticut Academy, New 
Haven, 1892, p. 28. 







132 



THE RATE OF INTEREST 



[Chap. VII 



il. 



spenders, the seUere of property yielding remote income, 
such as bonds and stocks. On the other hand, those who' 
having a low rate of preference, strive to acquire more 
future income at the cost of present income, tend to lower 
the rate of mterest. These are the lenders, the savers 
the investors. ' 

The mechanism just described will not only result in a 
rate which wiU clear the market for loans connectmg the 
present with next year, but, applied to exchanges between 
the present and the remoter future, it wiU make similar 
adjustments. While some individuals may wish to ex- 
change this year's mcome for next year's, others wish to 
exchange this year's income for that of the year after next, 
or for a portion of several years' future mcomes. The 
rates of interest for these various periods are so adjusted 
as to clear the market for aU the periods of time for which 
contracts are made. 

If we retain our original assumption that every man is 
mitially endowed with a fixed and certain income-stream 
which, by borrowmg and lending, can be freely bought and 
sold and thereby redistributed in time, the foregomg dis- 
cussion gives us a complete theory of the causes which 
determme the rate of interest, or rather, the rates of interest 
for vanous time-periods. These rates of interest would, 
under these circumstances, be fully determined by the fol- 
lowmg four conditions, to which aU the magnitudes m the 
problem of interest must conform :— 

(1) The rate of time-preference of each individual for 
present income, as compared with remoter income, depends 
upon the character of his income-stream, as finally modified 
and determmed by the very act of borrowing or lending 
buying or selling. 

(2) Through the variations in the income-stream pro- 
duced by loans or sales, the rates of preference for all 
mdividuals in the market are brought into equaUty with 
each other and with the market rate of interest. 

This condition is equivalent to another; namely, that 



^liw 



8BC.7] 



FIRST APPROXIMATION 



133 



each individual exchanges present against future incomt, 
or vice versa, at the market rate of interest up to the 
point of maximum desirabUity. 

(3) The market rate of interrat will be such as will just 
clear the market; namely, will make the loans and borrow- 
ings cancel each other for each period of time. 

(4) All loans are repaid with interest ; that is, the present 
value of the payments, reckoned at the time of contract, 
equals the present value of the repayments. More gener- 
ally, the modifications or departures from a person's origi- 
nal income-stream effected by buying and selling are such 
that the algebraic sum of their present values is zero. 

These four conditions not only determine the rate of 
interest, but determine also all the other variable elements 
which enter into the problem ; namely, the individual rates 
of preference (equal to the rate of interest) and the 
amounts which are borrowed and lent. 

The formulation of these four determining conditions 
constitutes our first approximation to the theory of interest. 
The sufficiency of the four conditions and their coordination 
may be made clear by means of the mathematical statement 
contained in the Appendix to this chapter. 



rr 



! 




m 



t Hi 



PART III. Second and Third Approximations 
Chapter VIII. Second Approximation to the theory of 

INTEREST (assuming INCOME FLEXIBLE) 

Chapter IX. Classes of Options 
Chapter X. Invention 

Chapter XL Third Approximation to the theory f 
interest (assuming income uncertain . 



:i::? 



CHAPTER VIII 



second approximation to the theory of interest 
(assuming income flexible) 



t-i-' 



*i 



§1 

Hitherto we have assumed that the income-stream 
flowing from any given article of capital is both' fixed and 
certain. We now abandon the first part of this hypothesis, 
^ t iill ni ""'"i i"g *^''* "'• '"^^mft-Rtirams ar e certain, that is , 
c an be definitely fores een, we now introducejhe h ypothc^ 
t hat they are not fixed^tut flexible y~tHat is, that the owner 
of any capital-wealth or capital-property is not restricted 
to a single use to which he may put it, but has open to his 
choice several different uses, each of which constitutes a 
separate optional income-stream. 

For instance, t he owner of Jand TTifty Uflfi it in "'""^ 
tha n one way . He may use it to grow crops, graze animals, 
plant forests, extract mmerals, support buildings, or for 
other purposes. Again, the owner of a building may use 
it for office purposes, for apartments, or for stores. Most 
raw materials can be used for any one of a number of pur- 
poses. Iron may be wrought into steel rails or into ma- 
chinery, implements, tools, armor for ships, or girders for 
buildmgs. A derrick may be used for quarrying stone, 
building a house, or unloading a boat. A ship may be used 
to carry any sort of cargo, and over any one of numerous 
different routes. Hammers, saws, nails, and other tools 
may be used in almost numberless ways. 

Perhaps the most adaptable of all mstruments of wealth 
b man himself. He may be simply a passive enjoyer or 

137 



fi 



.*■•■ 



IB .1 






II'- 




138 THE RATE OF INTEREST [Chap. VIII 

'' transformer" ' of the services of other wealth, and as such 
derive his satisfactions in sensual, esthetic, intellectual, or 
spiritual ways; or he may also be an active producer, Lid 
as such perform physical or mental work. If his woik is 
physical. 1 may consist in anything from wielding a pick 

emnlnvT! *?.'^' ^f "^'^'P^^tion of the inst^niment. 
employee' m the jeweler's art. If his work is mental he 
n^y be a bookkeeper, clerk, superintendent, director kw- 
yer, physician, editor, teacher, or scientist 

In consequence of such a range of choice, the same set of 
productive mstruments may result m very different income- 
streams. Their energies may be directed at wiU to pro- 
duce cheap frame houses or durable stone ones; to equip 
a city ..-ith horse cars, trolleys, or underground mpid 
transit; to secure an income-stream which shaU consist 
to^ly of the pl^ures of the table, or of the amusements of 
the theater, or of the gratification of social vanities, -in 
snort, to select one particular income-stream out of 1 

s.S^lT'^'l'"'""'""'''^'"' diffenlng^bdi:^^ 
sition^and time-shape, as weJl « in probability, thouriTin 
thaJiaE^rUiee^.,^^ 

Owmg to this great range of choice, the own^r^^T^tal 
may modify the income-stream he derives from it. not 
simply by the devices of borrowing and lending or of seU- 
mg and buymg, but also by changmg the use or employ- 
men, to which his capital is put. It should be noted 
however, that this third method of modifving «n inp^^f ' 
fij^ra r^llfJad^^ Just as buyin7 

a«.a selling virtually mclude boirowinft and lendi ng, solh^ 
change from one use of cafiita) to aimthetmajU^ik^ 
mclude buying and seUing^and^lhereforeSSSS 

o^rn^flfr'r'''^. ^-i-videntifwZSS 
one method of employuig capital is to sell it. In fact a 
merchant regards himself as "using" his stock in the ex- 
elusive sense of selling it. 
This method of modifying the income-stream is therefore 
• See The \atur, of Capital and Income, Chap. X. 



Sec. 2] 



SECOND APPROXIMATION 



139 



a general one. But, while it includes the other methods, 
it includes much else so different from the methods of 
borrowing and lending or buying and selling that we shall 
need to distinguish the new method from the old. There 
are t wo principal rea sons for k eeping the new metho d 
separate. First, the former ^n d narrower methods of 
modTfymg income-strea ms cannot be applied to society as 
a whpJe."Society as a whole cannot borrow and lend, nor 
buy and sell; and yet it can radically change the character 
of its income-stream by changing the employment of its 
capital. Secondly, when borrowing, and le nding or ord i- 
nary buying and selli ng are employed to modify a n 
incorae-streamj the presftnt values of the original m- 
come-stream and of the^ mo dified iacom ft-atrpam are the 
same. But when an income-stream is modified by a 
change in the use of the capital yielding it, its present 
value may not remain the same. 






J2 



The choice '^m"" P ; ^^^^ vftri oua optional income-stream s 
will fall on the o ne which has the nmximum desirab ility. As 
among in'-ome-strpams of diflereni sires but allRe in com- 
position and time-shape, the most desirable will of course 
be the largest ; as among income-streams of different com- 
position but alike in other respects, the most desirable will be 
that in which the marginal desirabilities of the different con- 
stituents are proportional to their several prices, in acconlance 
with a fundamental principle in the theory of prices ; finally, 
as among income-streams differing in time-shape, the most 
desirable is found in accordance with the principles which 
govern the rate of interest. It is therefore with the (Mer- 
ences in time-dhape that we are here chiefly conccme«l. 

^IHustrate these differences, let us 3U[)pose an individual 
possessed of a piece of land almost equally good for lumber- 
ing, farming, or mming. He thu.'* has the option of using 



•~m 






w^^^ 



140 



THE RATE OF INTEREST 



[Chap. VIII 



It m any one of three diflFerent ways: (1) in farming 
which, let tw say, will give him a regular and indefiniS 
succession of crops with an income-stream of the type A m' 

fnfT^^fi ' /? ^' ^T* P"^"""'' ^^'^ ^^^ «"ght returns 
for ^e first few decades, and larger returns in the futm^ 

^indicated by the cxirve B; (3) for mming purposes, ii; 

which case we shall suppose that, as the mining plant is 

abeady set up and the richest ore lies close to the surface 

the mcome is greatest for the early years and thereafte^ 

padualy decreases untU the mine is exhausted. This is 

tTl^^ T!I' ?■ .^^' ^'^ *^^ P"°«'Pl«« upon which 
the owner of the land chooses among these three income- 
streams? 



I 



B 




Fio. IS. 



We sha 1 suppose, as heretofore, that there k a uniform 
rate of mterest and that any individual is free either to 

Lnder this hypothesis thejshoiceamong the options will 

present value, jsglconcd at the mark et rate of in<!^ 
TJus If the use of the land for forestry mioses yiedslhe 

hid «^T^r~/"^*^'^' twoyeare.$3i)for the 
third, $400 for the fourth, $500 for the fifth, and $500 

thereaf^r forever,-then the value of the land if the^Se 

of mterest is 5 per cent., will be $8820. If the land is used 

for mmmg purposes, it wiU yield an income-stream of 

quite a different character, let us say, as follows: $2000 



II 



See. 3] 



SECOND APPROXIMATION 



141 



the first year, $1800 the second, $1600 the third, and so 
on diminishing annually by $200 to the point of exhaustion. 
The present value of these sums b $9110. If, finally, the 
land is used for farming purposes and yields a net income 
of $450 a year perpetually, the present value will be $9000. 
Under these conditions the choice will evidently fall on the 
mmmg use, because, for mining purposes, the land is worth 
$9110, which is greater than $8820, its value for forestry 
purposes, and than $9000, its value for farming purposes. 
The particular income-stream selected will leave its im- 
press on the time-shape of the total income-stream of the 
individual who owns it. For, as was seen in The Nature 
of Capital and Income,^ the total final income-stream of 
any individual is simply the sum of the mcomes flowing 
from all the articles of property belonging to him. Hence, 
if one selecta the mining use for his land, whereby the 
income-stream gradually decreases, its tendency will be 
to produce a similar decrease in the total income-stream 
possessed by the individual. This tendency may, of course, 
be counteracted by some opposing tendency, but will have 
full sway if the income from all other capital than the 
land remains the same in value and time-shape. 

It Lb true that the income from the mine is not final 
enjoyable income, but consists of "mteractions." But 
these interactions are readily transformed, through a cham 
of credits and debits, into final enjoyable income. The 
ore of the mme is exchrnged for money, and the money 
spent for enjoyable services or for commodities which soon 
yield enjoyable services, so that the "enjoyable" income 
follows closely behind the "intermediate" income from the 
mine, and almost exactly copies it in time-shape.* 

§3 

Yet the possessor of the mine is not compelled to copy in 
his final enjoyable income the mine's fluctuations of natural 

• Chaps. VII-X, XVII. 

• See Tht Saturt of Captial and Income, Clutpi. VIII, IX, XVII. 



■'1^ 






142 



THE RATE OF INTEREST 



[Chap. VIII 






mcome. He may, for instance, prefer aa his model an even 
flow of mcome such as he could get from the farm-use of 
his land. He will not, however, on that accomit choose 
this farm-use m preference to the mming-use; for the min- 
mg-use has the lai^ger present value, and the midesirable 
tim^shape of ita mcome-stream can be remedied by the 
methods explamed in the previous chapter, -by lendina 
at mterest the proceeds of its earlier output and postponing 
enjoyable income to later years; or, more geneml^^, by 
huyxng with the early proceeds such pro^rty as^S^ 
yield returns at such future times as are most desired - 
in short, by "investing" instead of "spending."* The 
difference IS merely that if he "spends" the yield from his 
imne, he is exchanging it for property from which enjoy- 
able mcome comes promptly, whereas if he "invests " he 
IS exchanging it for property from which enjoyable income 
comes more tardily. If he "spends" the mine's mcome 
as fast as he receives it, for food, clothing, shelter travel 
amusements his "enjoyable" mcome simply shadows S 
mtermediat«" mcome from the mme; but if he "invests" 

or stiU better, dweUmgs, or stocks and bonds, his enjoyi 
able mcome lags further behmd the income from the mine 

hL1"L • T""^"' "^^ ^^ P^'P^^ manipulation can be 
distributed m time m any desired manner, - for mstance 
evenly, as above supposed. ' 

Since the mining-use has the higher present value, there 
l^K f ^^'I^^ "» ««'««ting it rather than the farm-use 
which has the more desirable time-shape; for after the 
mmmg income is converted into the same time-shape as 
the farming mcome, it will be greater in magnitude, iTtiie 
ratio of theu- present values,* 9110:9000. 

' See Chap. VII, } 4. 

^iTJt^T^?^^- ".' '°' ""* "^^K '°«"°«. "^te' convenrion 
cent., 1455 50, in.tead of the 9450 which the fum-u-e yield! "ffe 



Sec. 3] 



SECOND APPROXIMATION 



143 



Again, it may be that the mine owner prefers, not a 
steady, but an ascending income-stream, and as in the case 
just considered, he may secure such an income by modify- 
ing the income by means of properly graduated investments 
of the early parts of the mine's income. He can secure, if 
he likes, exactly the same time-shape as though he had 
chosen the forestry use, with the advantage that his income 
will be larger. Thus, he may invest all of his first two years' 
income of $2000 and $1800 respectively, $1290 in the third 
year, $987 in the fourth year, and so on, reducing his 
annual investments by the proper gradations; and, proceed- 
ing at the proper time to "reaUze" on these investments, 
he may obtain, as the final result of these operations, 
an income of precisely the same time-shape as that which 
he would have obtained from the forestry use. But the 
size of the income will be larger ui the ratio of the present 
values of the mining and forestry income-streams, 9110: 
8820. The following table exhibits these operations : — 











As AGAINST 




Receives 
FROM Mines 


From which 
HE Invests 


So THAT 

HIS Income 

IS 


WHAT THE 

Forest Use 

would have 

Yielded 


1st year 


2000 


2000 


000 


000 


2d year 


1800 


1800 


000 


000 


3d year 


1600 


1290 


310 


300 


4th year 


1400 


987 


413 


400 


5th year 


1200 


684 


516 


500 


6th year 


1000 


484 


516 


500 


7th year 


800 


284 


516 


500 


8th year 


600 


84 


516 


500 


9th year 


400 


-116 


516 


.500 


10th year 


200 


-316 


516 


500 



mine owner needd simply to invest annually the excess of his income 
above 8455.50; namely, 91544 50 in the first year, •1344.50 in the 
•econd year, etc. When the ninth year is reached the investment 
ceases, for the mine then yields only §400. This ia then eked out 
by t55..V) from the amounts previously invested, and the same 
methods are pursued therealter. 



']W 



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1- 



^ 



if 
J 



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1: *h 



144 



THE RATE OF INTEREST 



[Chap. VIII 



Smceany t ime-ahape may be transformed into any o ther 
no one need be deteniairom seleclingan JncomR Lr.«.,BA 
ofit^ tmie^khape. but m JFcEbose it exclusivehT^J he 
basis of majdmu m present va lue. On t.h«> nth^r hmd 
wereitm^t for the possibiUty of modifying the tune-shape 
of his mcome-stream by borrowing and lendmg or buying 
and sellmg, the land owner would not feel free to choose 
toe one from among the three optional employments of 
his land which possessed the highest value, but might be 
forced to take one of the others. We assume in this 
c hapter that, after the most valuable option has heftn 
chogen, it is possible to borrow .and lend_ or to buy and 
^Oadmtum. It wiU then happen that his income as 
fanaUy transformed will be larger than it could have been 




Fio. 16. 



if he had chosen some other use which afforded that same 
time-shape. 

To illustrate this by a diagram, let AB and A'B' m Figure 
16 be alternative income-streams, of which the descending 
mcome-stream AB has a larger present value than the as- 
eendmg mcome-stream A'B\ The choice will then faU on 
AB, even though the mdividual prefers the time-shape of 



Skc.4] 



SECOND APPROXIMATION 



145 



"-Mm 



the other income-stream A'B'. He will then lend some of 
the early receipts from the income-stream AB and receive 
back some of the later, converting his income AB of imde- 
sirable shape into the income-stream A^B" which has 
the desired shape. Consequently this final income A*B* 
combines the virtues of both the original alternative incomes 
AB and of A'B' ; it possesses the superior shape of A'B' 
and the superior present worth of AB. As compared with 
A'B' it has the same shape but a greater size. 

We see, then, that *^ti:;Tftft1i°^ rPflphpa hia final income 
t hrough the co6peration of two separate kinds of choice of 
i ncomes, — first, the choice of the mcome-stream whic h 
h as the highest present value, and second, the choice amon g 
differgnt_poaaibte- modifi c ation o -ef- thio moomo - Htrenm hy 

}^^^l^v^T;rin|r_nr|f^ Ipnf^ing nr hnying and SPllinfT TheSO tWO 

kinds of choice are distinguished from each other by the 
fact that th ft first is a «»Wfinn amnnfr optional incomes of 
( di fferent market valueSf and the second is a selection amon g 
{opti onal inco mes of the same market value . 

§4 

Since this double choice, when it is made, results in a 
perfectly definite income-stream, it might seem that the 
situation does not materially differ from the case of a rigid 
mcome-stream discussed in the preceding chapter. But 
the two cases differ materially; fo r in the present case o f 
optional inpnmA^trPflma, the particular choice deyend st 

i w^JTlKe rale of interest. A ch ange.. in. ihai_rate_may shiftj 
t)] P ohnJPft o f p)aviT r»nm prpspnt value to some Other alter- l 
native. Thus, in the example cited, if the rate of interest 
should be 4^ per cent, instead of 5 per cent., the order of | 
choice would be changed. The value of the land for fores- 
try use would be $9920, for farming use, $10,000, and forj 
mining use, $9280. The farming use would now be the best 
choice. Agam, if the rate of interest should be 4 per cent, 
instead of 4 J per cent., the present value of the use of the 



- ". in- ■ 



J 



■M^. 



)•, 



146 THE RATE OF INTEREST [Chap. VIII 

land for forest purposes would be $11,300, for farming 
purposes, $11,250, and for mining purposes, $9450. In 
this casf the forestry use would be chosen. We see, then 
that it pays best to employ the land for mining if the rate 
of mterest is 5 per cent., for farming if it is 4^ per cent., 
and for forestry if it is 4 per cent. 

The various options open to the owner of the land at 
different rates of interest are summarized m the foUowine 
table:— ^ 



Optional Usm 


Present Valuk 


AT 




5% 


4i% 


4% 


For forestry 

For fanning . . . 

For mining .... 


8,820 
9,000 
9,110 


9,920 

10,(X)0 

9,280 


11,300 

11,250 

9,450 



Tims a change in the rate of interest results in a change 
m the choice of income-streams. A high rate of interest i 
will encourage investment m the quickly returning in- 
comes, whereas a low rate of interest wiU encourage invest- 
ment m mcomes which yield distant returns. As the busi- 
ness man puts it, when interest is high he can less afford 
to wait for a remote return because he will "lose so much 
interest." 

An investor wUl, therefore, make very different choices 
accordmg as mterest is at one rate or another. Conse- 
quently the existence of optional uses of capital mtroduces 
a new variable into the problem of interest-determination, 
lo the mdividual, the rate of interest will determine the 
choice among his optional income-streams; but for society 
the order of cause and effect is reversed, — the rate of in- 
terest will be influenced by the existence of the options, 
lo trace this influence is the purpose of the present chapter. 



Ssc. 61 



SECOND APPROXIMATION 



147 



time- j ^^ 
lice of f^ 
e jusTi 



§5 

At first sight it may appear that we are reasoning in a 
circle: the rate of interest depends on mdividual rates of 
preference; th e^ rates of preference depend on the time- 
shapes of individual income-streams; and the choic e 
these time-shapes ot income-gtrfams le pend, we have 
seen, on the rate of mte resl itselT 

' It IS perfectly true that tne rate of interest depends 
on a series of factors which finally depend on the rate of 
interest. Yet this series is not the vicious circle it seems, 
for the last step is not the inverse of the first. 

To distinguish between a true and a seeming example 
of a circular dependence we may contrast the following two 
simple problems : We wish to find the height of a father 
who is known to be three times as tall as his child. To 
solve this we need to know something about the height of 
ihe child. If we are told that the child's height differs 
from his father's by twice itself, the problem is circular 
and insoluble, for the last step is reducible to the first, being 
merely a concealed inversion of it. The problem essen- 
tially states that the father's height is three times the 
child's and the child's one third of the father's,- an ob- 
vious circle. But if the dependence of the father's height 
or the child's were essentially different from that of the 
child's on its father's, there would be no circle. Thus, 
supi. X as before that the father is three times as tall as 
the child, but that the child's height differs from the 
father's by four times the child's, less four feet. This 
sounds as circular as the first problem, — the father's 
height is expressed in terms of the child's, and the child's in 
terms of the father's; but here the second expression is not 
reducible to the first. The heights are entirely determinate, 
that of the father being six feet and that of the child, two. 
The mere fact that each of these magnitudes is specified m 
terms of the other does not constitute a vicious circle. 



148 



THE RATE OF INTEREST 



(Cbap. VIII 



! 



1 ;• 



1 1 



!} ! 



11 , J 

I."* "allv 

/■:;!>• ;n 



The same is true in our present problem. Real examples 

of circular reasoning in the theory of interest are common 

enough, and many of them have, in fact, been noted in earlier 

chapters, but the dej^endence above stated, of interest on the 

range of options and of the choice among those options on 

mterest, is not a case in point. The logical principle holds 

true that any problem is determinate if only there are as 

many determining conditions as there are unknown . | .,..-)- 

titles; it is only necessary that these condition.- w iJ 

"mdependent"; in other words, that no on 

derivable from the others. That this is mat ;< 

the case under our present hypothesis is s\ \.i 

the Appendix to this chapter. For our pre ;;• 

need only present the matter to the reader's ■. .'in 

a series of successive approximations. 

To find out the rate of interest on which tht ;.ip . i ; 
finaUy settle, let us try successively a number oi' diff;;. nf 
rates. First, suppose a rate of 5 per cent. This i^io v.i 
determme the choice of income-streams for each indiviauiii. 
The landowner formerly supposed wiU, as we have seen 
choose the mining-use. Every other individual in the 
market, in like manner, will select that particular use for 
his capital which will give him the maximum present worth. 
With these choices made, the different individuals will then 
enter the market of loans or sales, desiring to modify the 
time-shapes of their income-streams to suit their particular 
desu-es. The amount which the would-be lenders are will- 
ing to lend at 5 per cent, out of this year's instalment of 
their chosen income-stream will be perfectly definite, and 
likewise the amount which the would-be borrowers are 
willmgtotake. This we saw in the preceding chapter. In 
; other words, the demand and supply of loans for the present 
J year for the given rate of interest, 5 per cent., will be definite 
1 quantities. Should it happen that the demand for loans 
IS less than the supply, it follows that 5 per cent, cannot 
be the correct solution of tho rate of interest, for it is too 
high to clear the market. 



k; 
^ 



I,' 



8bc. 6] 



SECOND APPROXIMATION 



149 



s 



I 



In that case, let us suppose a rate of 4 per cent. Follow- 
ing the same reasoning as bfjfore, we find that the landowner 
will now select the forestry use for his land. Other capital- 
ists will select likewLse their definite income-stroams, and 
on the basis of these income-streams there will oe the con- 
sequent desire to borrow and lend. Should it then hapfxjn 
that the demand and supply of loaas, on the hoMS of 4 
per cent., are not equal, but that this time the demand ex- v 
ceeds the supply, it is a proof that not 4 per cent, is the true \ 
solution, but some higher rate. By again changing our 
trial rate back toward 5 per cent, we may o 'ideutly reach 
some intermediate point, let us say 4i per cent., at which 
rate not only tvill all individuals choose definite income- 
streams, but aho, at the same time, the demand and supply 
of loans engendered by these income-streams will exactly 
dear the market. 

' The introduction, therefore, of flexibility into our in- 
come-stream still leaves the problem of interest entirely 
determinate. Though the income-streams arc now a mat- 
ter of choice, there is one definite choice corresponding 
to each rate of interest. The particular rate of interest 
which will solve the problem is that which will both deter- 
mine the choice among income-streams fliffering in present 
value, and also bring it abr at that individual departures 
from such income-streams shall mutually cancel each otl ,r, 

I —in other words, that the markets for loans an<l sales / 
shall be cleared. 

§ 6 

For the determination of the rate of interest we have 
therefore to modify the various conditions a.s given in the 
previous chapter. The modifications which are intrwluced 
are, (1) that m place of the single fixed incor.T>-stream 
fcrmerlv a^ume^i, there now exi-'^t"- a given range of choice 
between different income-streams; and (2) that whereas 
formerly the mdividual had no choice of income-streams, 



r.- 



hi 



m 



i.k^ 



150 



THE RATE OJ? INTEREST 



[Chap. VIII 






I 

J 



^ 



he now chooses out of those available the one which pos- 
sesses the majdmum present value. We therefore have ax 
conditions determining the rate of interest, as follows: 

(1) Tliere exists for each mdividual a given series of 
possible mcome-streams among which he may choose; 

(2) Each mdividual's preference rate depends upon his 
income-stream,— its size, shape, composition, and proba- 
bihty; (3) The rates of preference of dififerent individuals 
must be equal to each other and to the rate of interest in 
the market; (4) Out of aU available mcome-streams, that 
one is selected which has the maximum present value for 
the rate of interest finaUy determined; (5) The rate of in- 
terest must be such as will equalize supply and demand, or 
exactly clear the market; (6) The additions to and deduc- 
tions from each income-stream, brought about by borrowing 
and lending or buymg and selling, must be such that their 
net present value is zero. 

As to the first condition, viz., the existence of a range of 
choice, it is worth noting that some of the optional income- 
streams would never be chosen under any circumstances. 
These are the income-streams the present value of which 
could not be the maximum, no matter what the rate of 
interest might be. We have seen that the land, in our 
example, would be most profitably employed for farming, 
for mining, or for forestry, according to the rate of interest! 
But it would not be employed, let us say, for a quarry, no 
mattei what might be the rate of mterest. TTie optional 
uses which are thus out of the question may be called 
ineligible. We nerd consider only the eligible options. 



i 7 

The six conditions for det«>mining interest just enu- 
merated differ from those given in the preceding chapter 
chiefly by the introduction of number four, —that the use 
of capital which yields the maximum present value will 



|ll 



Sic. 71 



SECOND APPROXIMATION 



151 



be selected. This additional condition is of so much impor- 
tance that it should be restated in two other forms. 

To illustrate these, let us recur to the example of the 
land, which could be used in any one of three ways. We 
found that when the rate of interest was 4 per cent., the 
use chosen would be forestry, as this possessed the greatest 
present value. If we now compare, year by year, the in- 
come from the land when used for forestry purposes with 
the income which it might have yielded if used in one of 
the other ways, — as farming, — we shall see that in some 
years there is an excess in favor of the forest use, and in 
other years a deficiency, as shown in the following table : — 





Annual Vauik of Uei» fob 


DirnsRENCB ik 

Favor of 

Forest Ubb 




FoBBSTRT 


Famunq 


Ist year 

2d year 

3d year 

4th year 

5th year 

6th year 

7th year 

8th year 

9th year 

10th year 

11th year 

Each year after . . . 


300 
400 
500 
500 
500 
500 
500 
500 
500 
500 


450 
450 
450 
450 
450 
450 
450 
450 
450 
450 
450 
450 


-450 
-4,50 
-150 
-50 
+ r)0 
+ .50 
+ 50 
+ .50 
+ .50 
+ .50 
+ .50 
+ .50 



Here we see that for the first four years there is a com- 
parative disadvantage or sacrifice (amounting to |45(), $450, 
$150, $50 in successive years) from the use of the land for 
forest purposes as compared with farm uses, but that this 
disadvantage is made up later by an advantage or return oi 
$50 per annum. If we now take the total present value, 
at 4 per cent., of the deficiencies marked with a minus sign, 
we shall obtain $1024, whereas the present value of the 
excesses (continuing in perpetuity), indicatetl by a positive 



I 



*■'■-- 

I:. 



h 



'■^i^fi 



■ ■^— .-»..^^,... -. >..»■ 



if 






»•• 



152 



THE RATE OF INTEREST 



[Chap. VIII 



Sign, will be $1070. Thus the present value of the gains 
exceeds the present value of the sacrifices by the difference 
between $1070 and $1024. In other words, as reckoned in 
present estunation, the gains outweigh the sacrifices. We 
may say, therefore, that, the rate of interest being 4 per 
cent., forestry is preferable to farming because of a 
surplus of advantages over disadvantages reckoned in 
present value. But if the rate of interest were 4^ per 
cent, we should find the present value of the sacrifices 
to be $1017, and the present value of the gains, $930, 
showing a preponderance of the sacrifices. That is, if 
the rate of interest is 4 J per cent., the sacrifice in using 
the land for forestry rather than mining outweighs the 
gains. The land would, therefore, in that case, not be used 
for forestry purposes. 

The general principle is, ther'>^ re, that out of the various 
incomr-streams at the dispo . the capitalist, he chooses 
the mo 4 advantageous, or, more fully expressed, the 
one whlih, compaiod with any other, offers advantages 
winch, reckoned in present estimation at the given rate of 
mterest, outweigh the disad.-antages; and this is evidently 
merely a new formulation of the origmal principle that the 
use chosen will ho. that which has the maxinuun present 
value at the given rate of int-erest. 

There is yet a third mcthoil of stating this princi[ile. 
Tins method may also best be shown by an example. W'e 
have seen in the previous illustration that if the rate of 
interest is 4 per cent., the net advantage is in favor of the 
forest use; and if the rate of interest is 4J per cent., the 
mlvaiKage is in favor of the farming use. It h evident 
that at some intermediate rate of interest the comparative 
acivantages of the two uses would be e<iual. Tliis inter- 
me<hat(' rate is approximatdy 4.2 per cent. To show the 
nature and importance of such an equalizing rate, we mav 



M mM 



;«t ■ 




'3?tfi--'-^; 



Sbc. 8] 



SECOND APPROXIMATION 



153 



vary the example given to the foUowing simple illustra- 
tion: — 





Annual Valui: or Uses foh| 


Difference in 
Favor or 




F0BE8THT 


Farming ! 


FoREBTRY 


l8i year 
2d year 
3d year 
4th year 
Each subsequent year 


000 
210 
100 
100 
100 


100 1 

100 

100 

100 

100 


-100 

+ 110 

000 

000 

000 



In this case the equalizing rate is 10 per cent. If the two 
income-sti earns be both discounted at 9 per cent., the for- 
estry use will have the greater present value, $1112, as 
against $1111 for the farming use. If 11 per cent, is used, 
the .'scales are turned and the farming use is the more valu- 
able, being worth $909, as against $908 for the forestry. 
At the intermediate rate of 10 per cent., the two uses are 
equivalent in present value, both being worth e.vactly 
$1000. Since 10 per cent, is the rate which equalizes the 
advantages and disadvantages of the two alternatives in 
present value, it is the rate at which the third coluitm m 
the table will have a present value of zero. Again, it is 
the rate which the $110 yield- on the -$100, or the rate 
"realized" to the investor wtio, by choosing the forestry 
use, relatively sacrifices $100 this year, but obtains a com- 
pensating return of $1 10 next year. Such a rate i.>< therefore 
caUed the raU of return on sacrifice. These terms are ap- 
plied exclusively to the comparative merits of two alter- 
native income-streams. By "sacrifice" is meant the com- 
parative loss from one's income-stream at first. ca\ised by 
.substituting one use of capital for another ; and l)y " return " 
is moant the comparative ga-n which later accrues by rea- 
son of this .«*anie ™l)stitution. 

To return to the original example antl the table in 
i 7, the equalizing rate was 4.2 per cent. Thi.-i was the 



.J. 



li 



i 



I 
I 



■J 



M 



I -4 



■:f- % 



1*1 

i 



154 THE RATE OF INTEREST [Chap. VIII 

rate of return on sacrifice of the forestry use when com- 
pared with the farming use. It is the rate which makes 
the series of future returns. $50, $50, etc., indefinitely, 
equivalent in present value to the first sacrifices, $450 
$450, $150. and $50. It follows • that if the latter series of 
sums were successively deposited at 4.2 per cent, in a sav- 
mgs bank, they would "earn" for the depositor the former 
series of sums. In short. 4.2 per cent, is the rate which an 
mvestor realizes" who in the first four yeans sacrifices suc- 
cessively $450, $450, $150, and $50, and receives as return 
m succeeding years. $50, $50, etc. In general, the rate of 
re urn on .sacrifice is a supposed rate of interest which 
wil make e<iual the present values of the " sacrifices " 
and "return.s" involved in comparing one optional 
income-stream with another. It is not, of courae, to be 
confused with the actual rate of interest. 

Now if the actual rate of interest is 4 per cent while 
th.- rate of return on sacrifice which would be realiml bv 
choosing the forestry rather than the farming use is 4^ 
per cent., it would evidently be profitable to choose forestry 
As the investor might put it, he would l>e getting more than 
the market rate, - getting 4.2 per cent, instead of 4 per 
cent. If, however, the rate of interest in tlic market i. 
4.5 per cent., it would not pay to choose the forestry use 
for to do so would, comparatively to th. farming use, re- 
turn only 4.2 per cent. In this ciuse the prospective 
mvestor would evidently prefer to choose the farming use 
and then lend his money at 4,5 per cent. Hecm-ring to the 
former table, we see that had he chosen the forest use 

T a c ^^'' ^"""'"^ "* ^® ^^"^'' ^*v« sacrificed during 
he first four years successively $450. $450, $150. and $50 
He may. if he likes, put these very sums at interest in 
a savings bank and make 4.5 per cent, upon them, whereas, 
had he chosen the forest use. he woul.l have received only 
4.2 per cent. In other words, when a man can invest at 

' Sep The Nature of Capital ami Income. Qiap XI 11. 




Sbc.81 



SECOND APPROXIMATION 



155 



4.5 per cent, by lending, he will not invest at 4.2 per cent, 
by choosing forestry rather than farming. 

Out of all possible employments of his capital, the 
capitalist will choose that one which, compared with any 
other, has advantages worth the disadvantages, — returns 
worth the sacrifices. This means that the rale of return 
on sacrifice wM exceed the rate of interest. 

In case the advantages precede the disadvantages, as 
when the merits of the mining u.se are compared with those 
of the farming use, the proposition must l;e reversed, as 
follows : The earlier advantage will be chosen only in case 
the rate of later sacrifice on present return is less than the 
rate of interest. In such a case it would be more conven- 
ient, in comparing the two u.ses, to regard them in the 
opposite order, that is from the point of view of the 
advantages, not of the mining use over the farming use, 
but of the farming use over the mining use. This will 
make the sacrifices precede the returns. As long as the 
sacrifices always precede the retvu-ns, we need only to con- 
sider whether or not the rate of return on sacrifice exceeds 
the rate of interest. If it does,' the optional income- 
stream which, compared with another, yields such return 
on sacrifice will be chosen in preference ; otherwise it will 
be rejected.' 

' Of couine it ifl possible to have two alternative uses so related 
that the sacrifices arc not (trouped together in one ma«s and the re- 
turns in another, but are intermingled. Thu-s the first few years 
may offer advantages, the following, disadvantages, those following 
still later, advantages, and so on in alternating succession. In such 
a case, if the market rate of interest i.s 4 per cent, and the rate which 
equaUxes the gains and sacrifices i.-* 4 2 per cent , in order to decide 
which of the optional income-strtam.s ought to be chosen, it would 
be necessary to consider the efTe« I "f a slight variation from the 4.2 
per cent, rate used in discounting the comparative advantages and 
disadvantages. Let the rate change from 4 2 per cent, to 4.1 per 
cut , i.e. toward the actual rate 4 per cent If the effect <if such a 
change is to make the advantages outweigh the di.tadvantages, in 
present value, it is a proof that the income-stream poMt.-ssing thi«e 
advantag»-« and disadvantages is preferable to the on<- Uing com- 
pared with it. In such a caae it is much more convenient not to 



? 



156 



THE RATE OP INTEREST 



[Chap. VIII 



The condition, therefore, determining the choice between 
options may be stated in any one of three ways, namely 
(1) Out of all options that one is selected which has the 
maximum present value, reckoned at the market rate of 
interest ; (2) Out of all options that one is selected of 
which the advantages over any other outweigh, in present 
value, Its disadvantages, when both are discounted at the 
market rate of interest; (3) Out of all options that one is 
selected which, compared with any other option, yields a 
rate of return on sacrifice greater than the rate of interest 



n 



I* i 



i9 

Let us now apply the third mode of statement to the case 
m which the range of choice is not confined to a few options 
but extends to an infinite number. This case is really 
more like the facts of life than the imaginary case of a few 
options such as the farming, mining, or forestry uses of 
land. As a matter of fact, each of these is not a single use 
but a whole group of optional uses. Thus, the farmer may 
cultivate his farm with any degree of intensitv; and for 
each particular degree of intensity he wiU have'a different 
income-stream. He may, for instance, invest $100 worth 
of labor m the present, m order that in six months he 
may have a larger income than otherwise, by $200. If the 
rate of interest is 4 per cent, (reckoned semi-annually) he 
would evidently prefer this option; for it diminishes his 
present income by $100 and increases his income six months 
later by $200, being 100 per cent, in six months, whereas the 
mterest for that time is only 2 per cent. Another course 
would be to mvest, not $100, but $200, in present cultiva- 
tion. The extra $100 would add to his returns in a hti f- 
year's time something less than the $200 yielile^i on his 

^'if^^'f*!^''" *°y ^'^•»»«*"« r"**-. ""••h w 4.2 per cent . but u, rerur 
piexitles wklom or never arise. 



Sic. 9] 



SECOND APPROXIMATION 



157 



first $100, let us say $150. This also would be a good in- 
vestment, yielding him 50 per cent, return when the rate 
of mterest is 2 per cent. And so each successive choice, 
compared with its predecessor, shows a law of decreasing 
returns for additimal sacrifice. Thus, if he invests, not 
$200, but $300, the third $100 thus sacrificed will add to 
his returns in six months, let us say $120. Here is a gain 
of 20 per cent., whereas the rate of interest is only 2 per cent. 
As another option, he may sacrifice a fourth $100 for the 
sake of a return of an additional $110; in like manner he 
may sacrifice a fifth $100 for the return of an additional 
$105; a sixth $100 for an additional $103; a seventh $100 
for $102. Thus far, each successive option is preferred 
to its predecessor ; for, as compared with its predecessor, 
each option yields more than 2 per cent., which is the rate 
of interest for six months. The next option is to sacrifice 
an eighth $100 for an additional $101 in six months. 
Evidently, it will not be to the farmer's interest to take 
this last step; he will stop at the previous step, at which 
he gets a 2 per cent, return on the last sacrifice of $100. 
As we saw in the preceding section, each succes-sive option 
is chosen as long as the rate of return on sacrifice of that 
option, compared with the previous option, is greater than 
the rate of interest, and tliat u.se is rejected at which the 
rate of return on sacrifice becomes less than the rate of in- 
terest. The intensivene.ss of his farming is thus deter- 
mined by the rate of interest, lie chooses that degree of 
inten-siveness which gives hi.s income-stream the maximum 
present value, —which h the same thing as choosing that 
degree at which the rate of return on sacrifice is equal 
to the rate of interest. 

The various possible income-Htreams are represented in 
Figure 17. Income-stream A is large for the first six 
months, and for the second .six months very small. The 
next income-stream B is SKK) smaller than A for the 
first six months, and $2<K) larger for the last six months. 
Tlie other oj.iions are als<j indicated lucoiiic-strcam H h 






% 



r« • 



.i 



158 THE RATE OP INTEREST [Chap. VIII 

the one chosen, because, as compared with its predecessor 
Its disadvajtege is $100 for the first six months and it^ 
advantage $102 for the second six months -just enough 
to "compensate for interest." 

We therefore reach the conclusion that where the options 
are mdefimte m number, the option chosen, compared with a 
neighbormg option with which it was in competition, yields 
a rate of return on sacrifice equal to the rate of interest 




Fro. 17. 

This rate of return, computed on the basis of two altema- 
Uve income-streams closely neighboring upon each other, 
we shall caU the marginal rate of return an sacrifice. It 
foUows that, when there is a contmuous range of choice we 
may substitute for the statement that the choice win'faU 
upon the option of maximum present worth, the better 
sta^ment that the choice will fall on the option whol 
marginal rate of return an sacrifice, reckoned relatively to 
a neighboring option, is equal to the rate of interest. 



Y^ 



Sec. 10] 



SECOND APPROXIMATION 



159 



§ 10 



We have introduced a new magnitude into our discus- 
sion ; namely, the rate of return on sacrifice, and especially 
the particular value of this rate of return called the mar- 
ginal rate of return on sacrifice. This marginal rate of , 
return on sacrifice comes close to being a " natural rate of j 
interest." By means of it we are enabled to admit into 
our theory the elements of truth contained in some of the 
claims of the productivity theories, the cost theories,' and 
Bohm-Bawerk's theory of the technique of production. 

The example just given of the farmer who selects, out of 
a series of ijicome- treams, that for which the return on sac- 
rifice is ecjual to the rate of interest, perfectly exemplifies 
the theory of John Rae.' According to Rae, all instru- 
ments may be arranged in an order depending on the 
rate of return on cost. Some instruments return double 
the cost of their formation in a year; in other words, 
the rate of return on sacrifice is 100 per cent. Others 
return 50 per cent., 20 per cent., and so on in descending 
order. In any community, Rae says, instruments will be 
"vvTought up" to the point at which the rate of return on 
sacrifice corresponds to Rae's equivalent for what we have 
called the "rate of preference," and this, in turn, as we 
have seen, is equal to the rate of interest. It will be evi- 
dent to every student of Rae that the preceding discussion 
accords with Rae's idea that those instruments which 
most promptly yield returns are formetl first, and that ♦he 
less rapidly returning instruments are successively formed 
until the margin is reached which corresponds to the rate 
of interest. The statement of Rae that, for a certain cost 
of formation, an instrument will yield a certain return, is 
merely a form of our statement that a certain decrease of 
present income will he accompanied by a certain increase 

'See Rap, The Soriologieal Theory of Capital, ChapUrt' IV to VI. 
•Of. alsa Landry, L'lnUrit du C'apiW, IWW. Chapter III; Carver, 
Dutr^ution vf Wealth, New York, 1004, p. 230. 



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■' ii 

i 

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160 



THE RATE OF INTEREST 



[Chap. VIII 



in future income. The relation between the immediate 
decrease and the future increase will vary within a wide 
range, wherein the choice will fall at the point corre j)ond- 
ing to the ruling rate of interest. 

The subject is one which may be looked upon from many 
points of view, and it is important that these points of 
view should be thoroughly coordinated. In the example 
above given, the farmer was supposed to invest to-day 
and receive returns six months afterward. Consider now 
a case in which the returns are repeated regularly each 
year. Let us suppose that our farmer possesses some 
swamp land in a primitive state. He has a large range of 
choice as to the method of utilizing this land. He can 
allow it to remain a swamp or, by clearing and draining 
It, convert it into crop-yielding land, the yield bemg in 
proportion to the thoroughness with which the clearing and 
draining are accomplished. Under the first use, let us 
suppose that he derives a perpetual net income of $50 a 
year, and Jet us suppose that, at an immediate cost of $100 
for clearing and draining, he can secure a perpetual net 
mcome from crops of $75 a year. As between these two 
choices, the second involves a decrease of immediate in- 
come of $100, and an increase in annual income thereafter, 
from $50 to $75, or of $25. In other words, the invest- 
ment of $100 will yield him 25 per cent, per annum. Evi- 
dently, if the rate of interest in the market is 5 per cent., 
it will pay him to make such an investment. Next sup^ 
pose that a second $100 invested in improving the swamp 
would cause the crop returns to be $90 instead of $75 a year, 
or $15 more than before. Evidently, the investment of 
the second $100 yields 15 per cent., and is also a lucrative 
one, when we consider that the rate of interest is only 5 per 
cent. A third $100 may increase the annual crop to $100 
mstead of $90, an excess of $10 as compared with the 
previous investment, or a yield of 10 per cent. A fourth 
$100 invested will cause the annual crop to be $105, giving 
an increase of $5 and a yield of 5 per cent. A fifth $100 will 



ill 



Skc. 11] 



SECOND APPROXIMATION 



161 



cause the crop to increase to $108, giving an increase of $3 
and a retimi of 3 per cent. Evidently it will pay the fanner 
to invest in draining and improving his swamp up to the 
fourth $100, but not to the fifth $100. Rather than invest 
this fifth $100 and receive thereon an annual income of $3 
a year, he would prefer to invest $100 in the savings bank 
and receive 5 per cent, a year. 

In other words, the intensity with which he will improve 
and cultivate his land is determined by the current rate of 
interest. Should the rate of interest in the market fall from 
the 5 per cent, just assumed to 2 per cent., it would then 
pay him to invect the fifth $100. For, evidently, if need 
be, he could borrow $100 at 2 per cent, and receive from his 
land a return of 3 per cent. As Rae has so clearly pointed 
out, in communities where the rate of interest is low, 
swamps will be more thoroughly improved, roatls better 
made, dwellings more durably built, and all instruments 
"worked up" to a higher degree of efficiency and a lower 
marginal return than in a community where the rate of 
interest is high. 

The same illustrations which have been given will serve 
to set the present theory in line with that of Adolphe 
Landry in his Thiorie de VIntirit. He states that one of 
the conditions determining the rate of interest is the 
"productivity of capital," in the peculiar sense which he 
gives to this phrase. The process descrilied by Landry 
by which the productivity is assimilated to whatever rate 
of interest happens to rule the market, virtually corre- 
sponds to the successive selection of income-streams as 
outlined in the preceding examples. 

§ 11 
Our next case will serve to show how the element of 
truth already pointed out in the productivity theory of 
Del Mar and George fits into the theory here propounded. 
This theory is that the rate of interest corresponds to the 
rate of growth of animals and plants. In Chapter III we 






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MKIOCOPV lESOUITION TtST CHART 

(ANSI and ISO TEST CHART No. 2) 




A 



/■1PPLIED IM^GE Inc 

1653 Eo>l Mom StrMi 

"ochealSf, N»w rorti 1*609 USA 

('16) »a2 - 0300 Phofi« 

(716) 2M - i9«9 - Fo. 



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162 



THE RATE OF INTEREST 



[Chap, VIII 



saw that the time of cutting a forest will be that at which it 
is growing at a rate equal to the rnte of interest. Thus, if 
n?ne years from the planting of the forest it contains 900 
cords of wood, while in ten years it contains 1000 cords, 
in eleven years, 1050, and in twelve years, 1071, and if the 
rate of interest is 5 per cent., the cutting will occur between 
the tenth and eleventh years. This choice is determined 
by precisely the same principle that has aheady been 
enunciated; namely, that the particular income-stream 
selected will be that which has the maximum present 
value; or, in other words, that which is such that the 
marginal rate of return on sacrifice will be equal to the 
rate of interest. 

To show how this principle applies to the cutting of the 
forest, let us consider as the first option the cutting of the 
forest at the end of nine years, when the income-stream 
consists of the single item, —the production of 900 cords 
of wood.* 

The second option is cutting the forest at the end of ten 
years, and receiving an income item of $1000. The two 
alternatives may be put in the tabular form previously em- 
ployed for the case of forestry and farming, as follows: — 

OPTIONAL INCOMES FROM FOREST 





IO-Ykar 
Plan 


9-Year 
Plan 


DirncRBNcK 
IN Favor op 
10- Yeah Plan 


1st year .... 
2d year .... 


000 
000 

000 
1000 


000 
000 

900 
000 








9th year .... 
10th year .... 


- 900 
+ 1000 



' Ina.smueh as wo amume that the income from the forest is all to 
accrue at one time — the time of cutting — instead of being dis- 
tributed over a long period, the phrase " income-stream " might hero 
faetwr be repliitvd by " income item." 




Ssc. 12] 



SECOND APPROXIBIATION 



163 



The last column shows that the ten-year plan, compared 
with the nine-year plan, involves a sacrifice of $900 in the 
ninth year which might he secured by the nine-year plan, 
but involves a return of $1000 in the tenth year. The rate 
of return on sacrifice would thus be a little over 11 per 
cent. If the rate of interest in the market is 5 per cent., 
it would evidently pay to "wait," or to choose the cutting 
in the tenth year rather than the ninth year. 

The next option would be to cut in the eleventh year, 
which, as compared with the second alternative, would 
involve a sacrifice of $1000 in the tenth year and a return 
of $1050 in the eleventh year — in other words, a rate of 
return on sacrifice of 5 per cent. Evidently, then, it 
would be a raalter of indifference whether the forest was 
cut in the tenth or eleventh year, inasmuch as the rate of 
return on sacrifice in one alternative as compared with the 
other would be exactly equal to the rate of interest. 

Similar reasoning shows that the choice of the next 
option, that of cutting the forest in the twelfth year, 
would yield a return of j^jf, or 2 per cent. Inasmuch as 
2 per cent, is less than the rate of interest, this alternative 
would be rejected. Should, however, the rate of interest 
fall to 2 per cent., or below, it is clear that the time of cutting 
the forest would be postponed until the rate of increase 
in stumpage value was reduced to correspond to the rate 
of interest. 

§ 12 

The same example will serve to show the bearing of 
Bohm-Bawerk's discussion as to the influence of the 
''roundabout process" upon the rate of interest. Accord- 
ing to him, it is at the option of society to invest to-day's 
labor in any one of many different processes bringing re- 
turns in different lengths of time, let us say, nine years, ten 
years, eleven years, etc. : and he premises that the returns 
in these successive years will increase, but at a diminishing 






} 



164 



THE RATE OF INTEREST 



[Chap. VIII 



*•• 



rate, let us say, in the order of the numbers already given : 
$900 for the ninth, $1000 for the tenth, $1050 for the 
eleventh, $1071 for the twelfth, etc. That use will be 
selected, as Bohra-Bawerk has pointed out, which has the 
maximum present value; and also, as he points out, the 
lower the rate of interest, the remoter will be the "produc- 
tion period" on which the choice will fall. If the rate of 
interest is 5 per cent., the choice will fall on the tenth 
or eleventh year; if the rate ia 2 per cent., on the eleventh 
or twelfth year; and the lower the rate of interest the 
more "roundabout" will be the methods of production. 

This is entirely valid under the hypothesis involved; 
namely, that there is a range of optional returns, each 
consisting of a definite return at a definite pomt of time, 
increasing as the production period increases, but at a 
decreasing rate. It is also true, as Bohm-Bawerk has 
pointed out, that not only does a lower rate of interest 
tend to the choice of remoter returns, but that, contra- 
riwise, the choice of remoter returns tends to check the 
fall in the rate of interest; the reason, e^ressed in our 
own terminology, being that the choice W an mcome- 
stream relatively large in the future and small in the 
present tends to increase the relative valuation of present 
as compared with future income. The existence of such 
a range of choice as Bohm-Bawerk assumes, therefore, 
tends to act as a buffer, checking the variations in the 
rate of interest. This effect of the operation of a range of 
choice will be again referred to. 



§ 13 

Thus, the elements of truth which wore found in the pro- 
ductivity theory, in the cost-theory, and in Bohm-Bawerk's 
technique-of-production theory, all find a place under the 
{head of the choice among optional uses of capital. In 
some cases, as in the example illustrating the theories of 
Henry George and Bohm-Bawerk, the selection of one 



Skc. 13] 



SECOND APPROXIMATION 



165 



option rather than another involves, as its effect on the 
income-stream, the mere omission of one item of income 
and the substitution of another. In other cases, as in the 
examples illustrating the theory of John Rae and Adolphe 
Landry, the selection of one option rather than another 
involves the application of labor, or the incurring of cost 
of some other sort, for the sake of a future return. But in 
all cases there is a choice among optional income-streams, 
— a decision how to adjust the income-stream at different 
periods, whether or not to decrease it at one time m order to 
increase it at another. It matters not in what way or at 
what periods of time the flexing of the income-stream 
occurs. It may be, as in the case of the farmer contem- 
plating the planting of a crop, that the income is fle:.3d 
or varied at merely two pomts of time, as seed time and 
harvest; or, as in the case of clearing a swamp, there may 
be a decrease of present income for the sake of an increase 
of the income of all succeeding years; or there may b^ 
any other arrangement of sacrifices and returns. But in 
all cases we have to deal simply with a range of choice 
among income-streams of different conformations. If this 
range of choice were limited to a few options, the best state- 
ment of the principle which governs the selection would be 
that the mcome-stream having the maximum present worth 
would be selected. But if there is a varied or continuous 
range of choice, the preferable method of stating the prin- 
ciple is that the income-stream will be selected which, as 
compared with the neighboring streams, will yield a rate 
of return on sacrifice equal to the rate of interest. 

To a person who has never tried to connect them, many 
of the theories of the authors just compared seem to have 
no vital relation. But they are seen to be connected as 
soon as we look at them in the light of the concept of an 
income-stream. The problems of choosing when to cut a 
forest, of what length to make a production period, to what 
degree of intensiveness to cultivate land, or how far to 
improve a piece of land, are all problems of choosing the 












' I , f 



t 
} * 



166 THE RATE OF INTEREST [Chap. VIII 

best out of innumerable possible mcome-streams. In each 
problem the rival income-streams present differences aa to 
size, shape, composition, or probability, - especiaUy shape 
m respect to shape, they can best be compared by means 



I 
I J 



Fia. 18. 



m 

i I 



I 



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I ' I 



ft '1*1 



Of diagrams. Figures 18 to 21 show typical ways in which 
the mcome-stream may conceivably be subjected to slight 



/^^ 



Fio. 19. 



variation. The unbroken line m each case indicates the 
mcome-stream chosen, and the dotted Ime a neighboring 




Fio. 20. 



possible choice. Figm^ 18 may be taken as applying to the 
planting of a crop; Figm^ 19 to the draining of a swamp; 



Fio. 21. 



Figure 20 to the cutting of a forest; and Figure 21 to a 
f^se of alternating sacrifices and returns. 



Sbc. 141 



SECOND APPROXIMATION 



167 



To students of physics, it will be interesting to obesrve 
that the identity of the principle of maximum present 
value with the principle that the marginal rate of return 
on sacrifice is analogous to the identity between the prin- 
ciple of minimum energy and D'Alemberts principle. A 
suspension bridge assumes the form which will bring its 
center of gravity at the lowest possible point ; this is in 
accordance with the principle of minimum energy. It is 
clear that the various parts of the structure, so to speak, 
compete with each other in the effort each to reach the 
lowest possible point. The result is a compromise; no 
part reaches the lowest point for i*self but is held 
above it by the sagging of other parts. If from the 
position of equilibrium a slight displacement of any de- 
scription is imagined, it requires that the depression of 
some parts is offset by the elevation of others, the work 
being done by the one set being equal to that done upon 
the other set ; this is in accordance with the principle of 
D'Alembert (principle of virtual displacements). The 
income- curve is like the curve of the hanging bridge re- 
versed. The effort is to raise it as high as possible so that 
its present value is a maximum. But its various parts 
compete with each other in the attempt each to reach the 
pomt highest in present value. The result is a compro- 
mise; no part reaches the highest value possible for itself 
but is kept from so domg by the other parts. If from the 
position of equiUbrium a slight displacement of any de- 
scription is imagined, it requires that the elevation of some 
parts is offset by the depression of others, the present 
value of the gains being equal to the present value of the 
losses. This is equivalent to saying that the rate of re- 
turn on sacrifice is equal to the rate of interest. 



a 






■it' 



§ 14 

Up to this point one complication in the problem of 
interest has been carefully kept in the background, not 



fi 



i 

S I -I 



.' f 



I 




168 



THE RATE OP INTEREST 



[Chap. VIII 



because it invalidates any of the principles which have been 
developed, but because it seemed advisable not to distract 
attention from the essential features of the theory by intro- 
ducing prematurely a factor which, after aU, is more intri- 
cate than important. This complication consists m the 
fact that not only, as we have seen, does the choice between 
.different optional mcome-streams depend upon the rate of 
pnterest, but also that even the range of choice depends upon 
that rate. If the rate of interest is changed, a change is 
produced not only in the present values of the income- 
jstreams but in the income-streams themselves. To recur 
to the illustration of the land which may be devoted to one 
of three uses, not only is it true that a change in the rate 
of mterest from 5 per cent, to 4 per cent. wiU change the 
relative present values of the mcome-streams which consist 
of the farming, mining, and forestry uses of tl)e land, but 
this change from 5 per cent, to 4 per cent, may also 
materially affect the three income-streams themselves. 

The net mcome from any mstrument of wealth is the 
difference between the total gross income and the outgo 
But many of the elements, both of income and outgo, are 
matenaUy dependent upon the rate of interest. This is 
true, whether the items of income and outgo are "final" 
or merely "mtermediate." • In the case of intermediate 
income, or "interactions," a change in the rate of interest 
affects the mcome-stream directly, because, as has been 
Bhovm elsewhere,' the valuation of an mteraction involves 
the discount-process and is therefore dependent upon the 
rate of interest. Thus, the service of plantmg apple trees 
wiU be valued m part by discountmg the value of the fu- 
ture apples. Given the value of the apples, it is evident that 
the value of the planting wiU be high or low according as 
the discounting is reckoned at a low or a high rate of in- 
terest. But even "final" mcome -the income secured 
from the apples, for mstance-may bt ' du^ctly affected 

" Bee The Nature of Capital and Income, Chaps Vll-X 
' Ibid., p. 317. * ■ 



Sec. 14] 



SECOND APPROXIMATION 



169 



by a change in the rate of interest, through a redistribu- 
tion in the amounts, combinations, and values of the vari- 
ous items constituting final income, and hence in their 
values. 

It would lead us aside from our topic to follow these lines 
of reasoning to the limit. It will suffice to indicate in brief 
their application in the case of labor. Thf; labor cost 
is one of the commonest elements of outgo in the income- 
account connected with any group of capital. For in- 
stance, whether the land is u.sed for farming, mining, or 
forestrj', it mast be worked by human beings, and the 
cost of the work will materially affect the valuf-n of the three 
income-streams. Now the cost of that work is wages, and, 
to the employer, takes the form of and nomially represents 
the discoimted value of the ultimate enjoyable ser\'ices to 
which the labor leads. Con.sequently, if interest variesij 
wages will var\'. Tlias. if the land is ua&l for farming" 
the wages paid for planting crops will be gauged in the 
estimation of the faniier by discounting the value of the 
expected crops, and will var\' somewhat according as the 
discounting is at 5 per cent, or 4 per cent. In like man- 
ner, the workers engaged in bridge building are paid the 
discounted value of the ultimate benefits which will accrue 
after the bridge is built; the wages of those engaged in 
making locomotives normally represent the discounted value 
of the completed locomotives, and hence ''as the value of 
a completed locomotive is in turn the discounted value of 
its expected services) their wages represent the discounted 
value of the ultimate benefits in the series. In all these 
cases, the rate of wages is the discounte^l value of some 
future product, and therefore tends to decrease as interest 
increases. But the effects in the different lines will be very 
unequal. Workers whose product matures rapidly, as ua 
the case of domestic servants and in the oasf; of those en- 
gage<J in putting the finishing touches on enjoyable goods, 
■wui aave ineir wages CGtiiparatt. ciV littic unt;Cicu dj me 
rate of interest. On the other hand, for lalxjrers who are 



m 



% 



170 



THE RATE OF INTEREST 



[Chap. VIII 



'■It 
l.i 

" l ' 










engaged m work requiring much time, the element of dis- 
count applied to their wages is a much more important 
j factor. If a tree planter is paid $1 because this is the 
discounted value, at 5 per cent., of the $2 which the tree 
will be worth when matured in fifteen yeare, it is clear 
that a change in the rate of interest to 4 per cent will 
tend materially to raise the value of such labor Sup- 
posmg the value of the matured tree still remams at $2 
the value of the services of planting it would be, not $l' 
but $1.15. On the other hand, for laborers engaged in a 
bakery or other industry in which the final satisfactions 
mature early, the wages are almost equal to the value of 
these products. If they produce final services worth %\ 
due, let us say, in one year, their wages, being the dis- 
counted value of this sum at 5 per cent, per annum, would 
. be 95 cents. Evidently m such a case a change in the 
I rate of mterest from 5 per cent, to 4 per cent, would only 
increase the wages from 95 cents to 96 cents. 

But it is clear that such unequal effects coming from a 
reduction in the rate of mterest, as an increase from $1 
to Jl.lo m one industry, and from 95 cents to 96 cents 
m another, could not remam permanently. For the 
laborers engaged in the occupations m which then- work 
matured m a relatively short time, such as the bakers just 
mentioned, finding that then- neighbors engaged m lengthier 
processes were receivmg higher wages, would tend to desert 
their work for this more remunerative employment The 
consequence would be that the amount of labor, and con- 
sequently the amount of final enjoyable mcome, accruing 
from the shorter processes would be reduced, and that 
from the longer processes increased. The consequence of 
this, in turn, would be to raise the value of the earlier 
enjoyable mcome and lower that of the later. Therefore 
in the end, the change m the rate of mterest from 5 per cent' 
to 4 per cent, would effect a redistribution m the values, not 
only of intermediate items of income, but in the valua« of 
the final items themselves. For the various final elements 






Sic. 15] 



SECOND APPROXIMATION 



171 



of income arc bound together, as it were, by means of the 
competition of the preparatory services, such as those of 
the laborers just mentionetl, and the consequent neces- 
sity of equalizing the remuneration for these preparatory 
services. 

In short, a change in the rate of interest will affect all 
income-streams flowing from given instruments of capital 
whether these streams consist of interactions or of final 
services. It will affect (I) the value of interactions, like 
tree-planting or Kroad-baking. becau.se the rate of interest 
enters directly into .0 valuation of all interactions; and 
(2) the value of final income, enjoyments, because many in- 
teractions, as. for instance, the services of laoorers, may 
be used interchangeably in .several different directions. 
The effect of a change in the rate of interest, on the 
value of the interactions, will naturally be the more pro- 
nounced, and will be greater in a countrj' where lengthy 
processes are lisually employed than in one where the 
shorter ones are common. If, for instance, laborers in a 
given country are engaged largely in building elaborate 
works like the Panama Canal, in planting forests, and 
otherwise investing for the sake of remote returns, a fall 
in the rate of interest will produce a considerable r' a in 
wages: whereas, in a country" where such lengthy pro- 
cesses are unknown and workmen are chiefly employe*! 
in tilling the ground and performing personal .services, a 
change in the rate of interest will scarcely affect wag' 
and the values of other preparatorj- services at all. 



J^ 



5 15 



The complete discussion of this subject would lead us 
to a statement of the general theory* of the " price of labor" 
and of prices in general. For present purposes, it is 
only necessary to emphasize the bare fact that the range 
of choice between <lifferent income-streams Ls .somewhat 
dependent upon the rate of interest. If the modification 



i 



: i 



•I 



til 



iil 









4 I 



^1 



172 



THE RATE OF INTEREST 



[Chap. VIII 



due to this fact were introduced into the tables previously 
given for the three different uses of land, we should find 
that the ome-streama from using the land for farming, 
forestry, and mining would differ according to the rate of 
interest. 

Thus, let us suppose, as before, that for a rate of interest 
of 5 per cent, the three optional income-streams are : — 



1st year . 
2d year . 
3d year 
4th year 
5th year . 
6th year 
7th year 
8th }Tar . 
9th year . 
10th year . 
Thereafter . 



Forestry FARiiiNo 



Mining 



000 


450 


000 


450 


300 


450 


400 


450 


500 


450 


500 


450 


500 


450 


500 


450 


500 


450 


500 


450 


500 


450 



2000 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

000 



In our previous discussion, when we changed the rate of 
interest from 5 per cent, to 4 per cent., we supposed the 
figures in this table to remain unchanged. The only change 
we had then to deal with was the change in their present 
values. Now, however, we admit the possibility of a 
change in the table figures themselves. If the rate of 
interest falls to 4 per cent., the product of forest, farm, and 
mine will be more nearly equal to the value of the ultimate 
ser\'ices to which they lead. The value of lumber wUl be 
more nearly equal to the value of the houses it makes, and 
these to the value of the shelter they give; the value of 
wheat from a farm will be nearer the value of the bread it 
will make; and the value of ore from a mine will be nearer 
the value of the steel it wiU become, and this, in turn, more 
nearly equal to the values of those innumerable satisfac- 
tions which come through the use of steel. These shiftings 
forward of the values of the intermediate income of fores°t. 



Skc. 15] 



SECOND APPROXIMATION 



173 



fam, and mine towanl the valuos of the ultimate satis- 
factions to which they lead, combined with possible read- 
justments in the values of these satisfactions themselves 
— the values of house shelter, bread consumption, etxs.— 
will result in a change, say in the figures in the table from 
those just given for 5 per cent, to the following for 4 per 
cent. : — 



Kol(E.«Tr!Y 



Kahmino 



Ist year 
2d year 
3d year 
4th year 
5th year 
6th year 
7th year 
8th year 
9th year 
10th year 
Thereafter 



fXX) 


.500 


OOT) 


.500 


3.50 


.500 


i'A) 


.500 


600 


.5fjO 


600 


.500 


600 


.500 


600 


.5fJ0 


600 


500 


600 


500 


600 


.500 



Mi NINO 
2100 

v.m 

1700 

1.500 

1.300 

1100 

8.50 

6.50 

450 

22.5 

000 



If, then, the rate is 5 per cent., the landowner will choose 
that'use among the three \^hich, computing from the figures 
in the first table, has the greatest present value; while if 
the rate is 4 per cent., he will choose that which, computing 
from the figures in the second table, has the greatest present 
value If, then, the rate i.-3 o per cent., he will choose min- 
ing since, as we saw in § 4. the present values, when we 
compute at 5 per cent. , are : forestrj-, $8820 ; farming, $9000 ; 
mining. $9110 ; but if the rate L^ 4 per cent., he will choose 
the highest from the present values at 4 per cent., computed 
from the second table. These present values now are : 
forestrv, $13,520; fanning, $12,-500; mining, $10,10<». 
Thus the owner will choose forestry. It is true m this 
case that the change in the range of choice does not affect 
the final result. In §4 the choice also fell on the 
forestry use. The only difference U that the particular 



j3 



* , 






174 THE RATE OP INTEREST [Chap. VIII 

figures Of present values in our revised 4 per cent, com- 
putation are different from their values in our original 
4 per cent, computation. The present values at 4 per 
cent, for forestry, farming, mming, respectively:- 

Under our present hypothesis are 13,520 
Under our former hypothesis were ll^SOO 



12,500 
11,250 



10,100 
9,450 



But, whatever, the final outcome of all the readjust- 
ments, It is evident that the introduction of the in- 
fluence of the rate of interest on the range of choice 
does not m any material way affect the reasoning already 
given in regard to the determination of interest. Since the 

Tnn ^ r*"!? 7'" '"^^ ^"^ "^^ ^^g« °f choice, it will 
still be true that, once the range of choice is fixed for a 
given rate of interest, the individual will choose, as before 
that use which has the maximum present value. On the 
basis of this choice he is then led to borrow or lend in oMer 
to modify his mcome-stream .o that his rate of time-prefer- 
ence may harmonize with the rate of mterest. If, upon an 
assumed mte of interest, the borrowing and leading for 
dfferent individuals actually cancel one another, -in 
other words clear the market, -then the mte of mterest 
afismned is clearly the one which solves the problem ; other- 
wise the borrowmg and lending will not be in equilibrium 
and some other rate of interest must be selected. By suc- 

benng that each rate carries with it its own mnge of options 
and ts own set of present values of those options, we finally 
obtain that one which will clear the market 

the fnrll!Tr"' T?!."'^'^ ''^'^^' «"«^"y modified, 
the formuktion of the theoiy stated in §6: (1) Each 
individual has given a specific list of eligible optional 

interest), (2) The rate of preference for each individual 

depends upon the character of his income-stream; (3) All 

It !^^? ™?' ^^ ''"'■'^'' •'^'"' ^^">^g'^ ^he loan or 
sale market, equalized with one another and with the rate 



Sec. 16] 



SECOND APPROXIMATION 



175 



of interest; (4) Each individual selects, out of the range 
of choice of income-streams available at a given rate of 
interest, that particular one which has the maximum present 
value, — in other words, that one whose advantages over 
any other outweigh (in present value) its disadvantages, — 
or, in still other words, that one which compared with 
others makes the rate of return on sacrifice greater than 
the rate of interest, — or, finally (if the options are in- 
finitely nun rous), that one which compared with neigh- 
boring options makes the marginal rate of return on 
sacrifice equal to the rate of interest; (5) The demand 
and supply of loans must balance for each period of time ; 
and (6) The loans returned must equal the loans obtained, 
with interest. 



*, 

If 



,:i 



§16 



t'i 



Having completed the formal statement of the effect of 
the existence of a range of choice ujKjn the rate of interest, 
it remains to point out a practical effect of such a range of. 
choice. This effect is to diminish the fluctuations in the/ 
rate of interest. In a country where there is a large rangef 
of choice l)etween optional income-streatns, the rate of; 
interest is apt to Ix; steadier than in one where the income 
streams are relatively rigid and unalterable. If any 
cause tends to lower the rate of intt^rest, the immediate 
effect will be to put a premium on those income-streams 
the return from which is in the remote future, — for 
instance, to put a premium on forestry uses rather than 
mining uses of land. But the decision to choose such in- 
come-streams tends to prevent the very fall in the rate of 
interest which caused the choice. For, by relatively over- 
supplying the future with income, and undersupplying the 
present, such uses as forestry will tend to raise the relative 
valuation of present over future income, and therefore 
also to raise the rate of interest. Tlie fall, therefore, iu 
the rate of interest which led to the choice of remoter in- 



5* • 



.f^. 



m 

r 



I: ,a 



ll: 



176 



THE RATE OF INTEREST 



! I 





IH' 


M 




w ^ - 




|BI 


Ii 




^H 


1 




I^^Hr 


M 


^B 


H^^HK *' 




^■j^^^Bw 




^H '}i 




^^H ' 




'^^^^^^BB. 




Hlh 




BJMBBfl^ ^ 




^^^^HS: '^ 




n^K - 




■HV' ! 1 



{Chap. VIII 



comes, is checked, and is not so great as it would be if no 
such options were open. 

Conversely, a rise in the rate of mterest will favor those 
options for which the income-streams are relatively im- 
mediate, and will bring its own check; for the choice of 
such an income-stream will relatively impoverish remote 
income and enrich immediate income, and consequently 
tend to diminish the premium on the latter. 

The existence of a large number of available mcome- 
streams, then, acts as a balance wheel which tends to 
check any excessive changes in the rate of mterest. In- 
terest cannot fall or rise unduly; for any such fluctuation 
corrects itself through the choice of appropriate income- 
streams. If interest is high, descending income-streams 
will be chosen which tend to make interest low; while, 
if it is low, the reverse will be true. 

We see here another reason, in addition to those given 
in Chapter VII, for the fact that interest does not suher 
very violent fluctuations. It is not only true, as was then 
pointed out, that natural processes are regular enough to 
prevent sudden and great changes in the income-stream ; 
but it is also true that man constantly aims to prevent such 
changes. Man is not the slave of Nature's income ; to some 
extent he is her master. He has many opiums among 
which he may choose. He possesses, within limits, the 
power to flex his income-stream to suit himself. For 
society the flexibility is due to the aclaptability and ver- 
satility of capital, —especially human capital commonly 
called labor ; for the individual the flexibility is greater still, 
since he possesses a double range of choice. He may 
not only choose among different employments of capital, 
but he may choose among different ways of exchanging 
with other people, —he may borrow or lend, buy or sell, 
invest or spend. This power is virtually the power to 
trade in income; for under whatever form an exchange 
takes place, at bottom it is income, and mcome only, which 
is exchanged. In making his choice among different em- 



j; 



Sxc. 16] 



SECOND APPROXIMATION 



177 



).|.|j| 



m 



ployments of capital, he relies on his power to remetly 
any undesirable time-shape, etc., by recourse to exchange. 
The result of the double range of choice — that between 
optional emplojnnents of capital and between optional 
modes of exchanging income — is that his income is 
flexible and controllable in a high degree. Not only may 
he select the most valuable income, but also the income 
which is most desu-able in re.spect to time-shape. He need 
not even commit himself to a given time-shape for any 
great length of time, for by changing his expenditures and 
investments he can alter that time-shape at will.' 

' For further discussion of the subject of this chapter by means of 
mathematics, see Appendix to Chap. VIII. 



! 






i\i 



I 




t I I 



i 



'1* 

if 

i f 



!3 



CHAPTER IX 

CLASSES OF OPTIONS 
§1 

In order to present a full view of what is meant by 
"optional employments of capital," it will be worth our 
while to pause a moment and examine the different classes 
of options open to the capitalist. 

Options are of three chief kinds: (1) options a mong em - 
p loyments of capital whie hjUfEeiJn kjnd, as, for ins tanc e, 
the options previously cited ^ using land for mining , 
fa rniing, or f orestry ; (2j options among employments of 
capital which differ in the degre e of certainty, as, for in- 
stance, the choice of sailing a ship over several routes 
differing in the constancy of wind and current; and 
(3) options among employments of capital which differ 
i n size and tim e-sha p e. 

Options of the first group do not concern the theory of 
interest so much as the theory of prices, unless, as in the 
example of the mining, farming, and forestry uses of land, 
the optional incomes differ in time-shape as well as in the 
kind of service rendered. Tliis group may \)o designated as 
options of v er5M.tjlitv . They are moat striking in the case 
of tools and human beings. 

Options of the second class may be called options of 
chance. They concern the theory of insurance and spec 
ulation rather than the theory of interest, and, under the 
hypotheris which has thus far been maintainefl, that risk 
is absent, have no need as yet to be considered. This 
group of options is, however, of groat practical importance. 
Under this head, when the options relate to contractual 

178 



Ssc. 1] 



CLASSES OF OPTIONS 



179 



H'- 



services, comes the special case of trade options. It is to 
this class that the term "option" is ordinarily applied 
by business men, and it has been with some hesitation 
that it has been given a broader meaning in this book. 
But no better term seems available; and there is to be 
said, m favor of the broader use of the word, that it cor- 
responds closely to its popular and untechnical meaning. 

The third group of options is the one which specially 
concerns us here, and will alone engage our attention 
through the remainder of this chapter. 

■ When, m Chapter VII, we explicitly excluded optional em- 
ployments of capital, we thereby assumed that the income- 
stream was fixed both m amount and in the times when it 
accrued. We may pass from this case of perfect rigidity 
to the simplest form of option by introducing at first only 
one degree of flexibility. Let us suppose that the income- 
stream from any capital is relatively fixed in amount, and 
that only the time of obtaining it is controllable at will. 
This species of choice occurs in the case of durable goods 
for consumption, which neither improve nor deteriorate 
with time. Wheat and other grains, for instance, may 
be used at almost any time, with little difference in the 
efficiency of the use and little cost except for storage. 
The same is true of coal, cloth, iron, and other durable 
raw materials, as well as, to some extent, of finished prod- 
ucts such as tools and machinery, though usually de- 
terioration from rust or other injury by the elements 
will set in if the \ise is too long deferred. 

\Miere such a range ot choice exists, the possibility of 
obtaining an income from the capital in the future instead 
of in the present will have the effect of preventing the rate 
of interest from sinking as far as it otherwise would ; for if 
the rate of mterest is low, the tendency on the part of the 
investor will be to defer the use of durable goods, —wheat, 
for mstance, — and such a decision, by increasing future 
income and diminishing immediate income, will tend to 
raise the rate of interest, or at least to check its fall. Re- 



*i 



180 



THE HATE OF INTEREST 



[Chap. IX 



versely, the possibility of using such articles at the present 
time instead of later has the effect of preventing the rate 
of interest from rising as far as it otherwise would ; for, 
shouKl interest rise, the tendency on the part of the mvestor 
will be to more immediate employment of such durable 
goods as he had set apart for future use, and this decision, 
by relative)}' increasing present income and diminishing 
future income, will tend to reduce the rate of interest, or, 
at any rate, to check its rise. This is illustrated by wheat 
speculation. A rise in the rate of interest will check 
"bull" operations, suice the speculator will be less will- 
ing to "lose the interest on his money." Reversely, when 
the rate of interest falls, wheat holding will be encouraged. 
Likewise land speculation is relatively easy when interest 
is low and difficult when interest is high. 



», 



se"-' 



iif 



L.'- 



f it , - 

f if, 1 I : 



m ■■ I 



§2 

Under the gi'oup of options applying to durable in- 
struments, there are many special cases. One of the 
most instructive is that which we might suppose if the 
quantity of income obtainable from an instrument or num- 
ber of instruments were definitely fixed, but the time at 
which those services might be obtained were entirely 
optional. To illustrate this, uncomplicated by the pres- 
ence of instruments of different types and the consequent 
necessity to translate the rate of interest into a common 
monetary stanilard, let us imagine a community in which 
the income from all capital is of the character just de- 
scribed. Tins society would then be endowed with a 
quantum of income as fixed as the quantity of money in a 
strong box. It could obtain all the income at once, or 
spread it over any number of years, but could not alter 
its amount either by increase or decrease, just as the owner 
of a strong box could take the contents all out at once, 
or at such times as he pleased, but could not increase or 
diminish the total amount. Every dollar's worth of income 



ilii 



Sic. 2] 



CLASSES OF OPTIONS 



181 



sacrificed from this year's income would eke out next year's 
income by a dollar and no more; and reversely, every 
dollar's worth indulged in this year would reduce by a 
dollar and no more the possibility of future indulgence. 

Let us suppose this case realized on a desert island on 
which some sailors are shipwrecked and left each with 1000 
pounds of hardtack and no prospect of ever improving their 
lot. We will suppose the use of this hardtack to be the 
only "real income" open to these castaways, and that they 
have given up hope of ever atiding to it by accessions from 
outside or by cultivating the island (which, by our hypothe- 
sis, must be barren), the only possible variation of their 
income-stream — consisting of hardtack — being that pro- 
duced by varying the time of its consumption. They have 
the option of consuming their entire store during the first 
year, or of spreading its use over two or more years, 
but in any case they will have the same total income, 
measured in hardtack. A little reflection will show that 
in auch a community the rate of interest in terms of hard- 
tack would necessarily be zero.' For, by hypothesis, the 
sacrifice of one pound of hardtack unconsumcd from this 
year's income can only result in an equal increase in the 
income of future years. Therefore the rate of return on sac- j 
rifice is zero. Since this rate must equal the rates of ^ 
preference and the rate of interest, these rates must all' 
te zero also. 

To illustrate this case by a diagram, we see, as one op- 
tion, that the entire consumption of hardtack may take place 
at an even rate OA within the time OB (Fig. 22). The total 
income will then be represented by the area OACB. An- 
other option is that it shall be spreafl over OB*, double the 
above-mentioned time, and consumed at the rate 0.1', 
half the rate first mentioned, so that the same total 
amount will be represented by the area OA'C'B'. The 
choice of the second use rather than the first implies 

' Cf. Adolphe Landry, L'lnUnt du Capilal, p. 49; Carver, The Du- 
tribiUion of Wealth, p. 232. 



•■^fl 



■Ik 



r} 



t'3 



;> » 



I I 




1^-y 



182 



THE RATE OF INTEREST 



[Chap. IX 



the sacrifice of that part of the immediate income repre- 
sented by the rectangle AD, but the addition of equal 
future income represented by the rectangle DB'. If the 



A' 



-O 

D 



B 

Fia. 22. 



hardtack is not consiuned at a uniform rate, the optional 
income-streams will not be represented by rectangles, but 




Fio. 23. 



by slopbg curved figxires, as ADB and A'DB* (Fig. 23), 
which have the same area. The substitution of .he alter- 



B S 



Sec. 21 



CLASSES OF OPTIONS 



183 



native A'DW for ADB increaaea immerliate income by 
ADA' and decreases subaequent income by the exactly 
equal amount BDff. 

The conclusion that the rate of interest under such con- 
ditions must be zero, is at first startling ; but it Ls easy to 
convince ourselves of its correctness if we reflect that the 
sailors will mofiify the time-shape of their respective income- 
stream until any possible rate of preference for a present 
over a future allowance of hardtack disappears. It would 
be impossible for any would-be lender to obtain interest on 
his loan, for the only way in which a borrower could repay 
a loan would be lo pay it out of his original .stock of hard- 
tack. He would not be fool enough to borrow 100 pounds 
to consume to-<Jay and pay back 105 pounds at the end of 
a year, when he h*l the option to consume the KX) pounds 
of his own hardtack, by sacrificing only IW pounfls out i 
of his own stock kept for next year. Consequently • 
there could be no interest payable in any exchange of ' 
present for future hardtack. It is equally im possible that 
there should be a negative rate of interest. No one would 
lend \0f} pounds of hardtack lo-iiay for 0.5 receivable a 
year later, when he had the option of simply storing away 
his 10<) pounds to-<iay and taking it out un<limirushed a year 
later. Hence, exchanges of present for future hardtack 
coul-i not exist, except at par. There could be no premium 
or iii«?ijunt in such exchange. 

Nor co'ild there be any rate of preference for present 
over fur ^iTc Lanitack. A p<-.»un<i of this year's hardtar:k and 
a poun' i of next year's hardtack would be ef^ually balancc^I 
in present estimation : for. shoulrl a man prefer one rather 
than the other, he would take a po<ind for the preferred 
use away from the unpreferreil. and this process woiild be 
continue<i until the desirability in the present y of a pound 
of immeiiate hardtack and that of a pound of futiire hard- 
tack w^re brought Into e<T;iIihrium. ThiW: if. thro'Jgh 
ins5iJ£cient self-control, he foolishly prefers to Mac. his store 
freely in the preaent and to cut down his reserve for the 






\m 



■i; 



184 



THE RATE OF INTEREST 



[Chap. IX 



future to a minimum, the very scantiness of the provision 
for the future will enhance his appreciation of its claims, 
and the very abimdance of his provision for the present 
will diminish the urgency of his desire to indulge so freely 
in the present. Provided there is some hardtack for both 
uses, the present desire for a pound of each will necessarily be 
the same. Failure of such equilibrium of desire can only 
occur when, as in starvation, the desire for the present use 
is so btense as to outweigh the desire for even the very last 
pound for future use, m which case there will be none 
whatever reserved for the future. But whether the hard- 
tack is at first abundant — for instance, enough to insure 
a long life— or whether starvation will necessarily follow 
after a year or two, the needs of the present and future will 
be adjusted on a basis of par price up to a point of time when 
the income-stream will cease. It is evident that some of 
the sailors, with a keen appreciation of the future, 
would plan to consume their stores sparingly. Others 
would prefer generous rations, even with the full knowl- 
edge that starvation would thereby ensue earlier; but 
none of them would consume all of their stock immediately, 
for to do so would unduly rob the future, already poorly 
provisioned. They would, generally speaking, prefer to 
save, out of such reckless waste, at least something to satisfy 
the more urgent needs of the future. In other words, a 
certain amount of savmg (if such an operation can be called 
saving) would take place without any interest at all. This 
coincides with conclusions expressed by Professor Carver 

I in his Distribviixm of Wealth} It shows also that the 
preference for present over future goods of like kind and 
number is not, as some writers seem to assume, a neces- 
sary attribute of human nature, but that it depends 
always on the relative provisioning of the present and the 
future. 

• p. 232. See also "The Place of Abstinence in the Theory of In- 
terest," Quarterly Journal of Economics, July, 1894, and Fetter's 
Principles of Political Economy, New York (Century), 1904, p. 160. 




Sec. 3] 



CLASSES OF OPTIONS 



185 



§ 3 



The fact that interest was bound to be zero in the case of 
the sailors just discussed, was due to the extreme adjust- 
ability of the time of receiving the given income. To see 
this clearly, let us next consider the case of an income-stream 
which, as before, is of a fixed amount, and the times of 
receiving which, though capable of being postponed as far 
as desired, are not capable of being hastened beyond a cer- 
tain limit; the income, in other wortls, is fixed and sure, 
but comes slowly. Approximately such a case is found in 
mming.' The total yield of a mine is practically fixed by 
the ore deposits which it contains. It is like the chest of 
money; just so much as it contains can be taken from it, 
and no more. But it is unlike the chest of money in that 
its contents cannot be extracted as fast as desired. The 
ore at the top must be r"' -^ed before that beneath can be 
reached. Time for mini) operations is required. Nature 
is slow in yielding up ho/ treasiu-es. This sloumesf^^ ' 
Nature, in view of man's impatience to exploit her, will giv 
rise to a rate of interest. 

It is as though the hardtack of our shijiWTecked sailors 
had in some way been stored in a series of storehouses, each 
provided with a time lock arranged to open at a certain 
date. There is a definite amount of income, but it is only 
available at intervals. Under these circumstances, vmless 
the time locks are timed to open as fast as the castaways 
woukl have chosen of themselves to eat their stores, the 
hardtack of to-day and of next year will no longer exchange 
at par. There will be a premium on present hardtack as 
compared with future hardtack, the amount of the premium 
depending on the relative provisioning of the various 
storehouses, — in short, on the size and time-shape of the 

' Strictly speaking, of course the total product and total expense 
of exploiting a mine will vary somewhat with the rate of extraction. 
An animated discussion of the most profitable rate of extraction was 
carried on in The Engineering and Mining Journal, New York, 1904. 



1^1 



186 



THE RATE OF INTEREST 



[Chap. IX 



1 



mcome-stream as made available by the time locks. The 
case will be practically the same as though the income- 
stream were rigid, as m Chapter VII ; for the only option is 
to postpone the consumption of these provisions, and this 
option would not, under the circumstances, be exercised. 
We see, therefore, that in order thpt a positive rate of 
mterest shall emerge, it is only necessary that mcome shall 
sufficiently hold back its flow. It is not necessary that 
Nature should be reproductive, as Del Mar and George 
m«>intam. Interest would exist even if there were no 
growmg animals and plants, but only a world of minerals 
and other fixed stores to be extracted by man, provided 
only Nature were slower than we could wish m admitting 
us to her stores. In fact, if we were asked to state in a word I 
why there is interest, we should reply, because Nature is | 
slow and keeps man waiting. 



§4 



But while the slowness of Nature is a suflficient cause for 
interest, hftr prnHy/.tiY;fY i,i f" °^Hitioi al ^cause . This 
brmgs us to our next class of options, the class, namely, 
in which, if present income is sacrificed for the sake of future 
income, the amount of the latter secured thereby is greater 
than that of the former sacrificed. The income which we 
can extract from our planet is not, m the aggregate, a 
fixed quantum, as is that part of it which comes from mines, 
but is obtainable in larger amounts for the remote future 
than for the present. Nature is reproductive and tends to 
multiply. Growing crops and animals make it possible to 
endow the future more richly than the present. By waitmg, 
man can obtain from the forest or the farm more than he 
can by premature cuttmg or the exhaustion of the soil. 
In other words, not only the slowness of Nature, but also 
her productivity or growth, has a strong tendency to keep 
1 up the rate of interest. Nature offers man, as one of her 
/ optional income-streams, the possibility of great future 



Ssc.51 



CLASSES OF OPTIONS 



187 



abundance at trifling present sacrifice. This option acts 
as 1 bribe to man to sacrifice present income for future, and 
this tends to make present income scarce and future income 
abundant and hence also to create in his mind a prefer- 
ence for a unit of present over a unit of future income. 



■ ■ (I 



S5 

We next consider the case of an option the exact reverse 
of the preceding, — the case in which, if present income is 
sacrificed, the amount of future income obtain d thereby 
is less than the amount sacrificed to obtain it. This is 
true of the income from perishable goods. 

Suppose our sailors were left, not with a stock of hard- 
tack, but with a stock of figs which deteriorate at the fore- 
known rate of 50 per cent, per annum. In this case the rate 
of interest would be necessarily minus 50 per cent, per 
annum, as may be shown by the same reasoning that es- 
tablished the zero rate in the former case. The possibility 
of such negative interest has been discussed in a previous 
chapter.' When goods are perishable the tendency is to 
preserve them by cold storage, preservatives, etc., so as to 
extend their use into the future. This is an effort to create 
a new optional employment for those goods. 

Some goods, then, like grain for food, and cloth, may be 
indiscriminately applied to the present or future without 
either loss or gain ; others, like grain for seed, breeding 
animals and plants, gain in income power with time ; and 
still others, like meat and fruit, lose. 

The resultant is that, for income as a whole, taking man 
and Nature as they are, it is impossible to sacrifice future in- 
come for present very far without selling one's birthright 
for a mess of pottage, or, to make use of lothor phrase- 
ology, without killing the goose that lays ne golden egg. 
Thus Nature, by her productivity, stimulates man to self- 
denial, and by her slowness she compels it. Were the 

' Chap. V, i 5. 



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I 



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188 



THE RATE OF INTEREST 



[Chap. IX 



world in which we live neither slow nor reproductive, but 
simply an open storehouse of wealth, two things would 
happen which we saw in the case of the shipwrecked 
sailors. One is that the rate of interest would be zero, and 
the other is that man, however frugally he consumed his 
stores, must ultimately perish. 

§ 6 

In the foregoing cases the options consisted of different 
employments of instruments of capital which were assumed 
to retain their physical identities throughout the period 
of those employments. If now we regard an instrument 
or group of instrmnents of capital as retaining its identity 
through renewals or repairs, we introduce another large and 
important class of options ; namely, the options of making 
those renewals and repairs, or not making them, or making 
them in any one of many different degrees. If the repairs 
are just sufficient for the up-keep they may be called re- 
newals; if more than sufficient, they may be called better- 
ments. We shall include all these alterations wrought 
upon an instrument in the same category. They are 
alterations in the form, position, or condition of an 
instrument or group of instruments which affect the stream 
of services which that instrument or group will yield. 
This class of optional employments, when the employment 
of the capital involves sales, merges imperceptibly into the 
special case which we originally called the method of modi- 
fying an income-stream by buying or selling. Thus, 
consider a merchant who buys and sells rugs. Ilis stock 
of rugs is conveniently regarded as retaining its identity, 
although the particular rugs in it are continually changing. 
This stock yields its owner a net income equal to the dif- 
ference between the gross income, consisting of the pro- 
ceeds of stiles, and the outgo, consisting chiefly of the cost 
of purchases, but incluiUng also cost of warehousing, in- 
surance, wages of Sidesmen, etc. If the merch.»nt buys 



Sec. 6] 



CLASSES OF OPTIONS 



189 



and sells equal amounts of rugs and at a unifonn rate, his 
stoca. of rugs will remain constant and its income to be 
credited to that stock will normally be equal to the in- 
terest upon its value. It will be standard mcome.' But 
the owner has many options. He may choose to 
enlarge his business as fast as he makes money from 
it, in which case his net income will be zero for a 
time, but his stock will increase and his ultimate in- 
come will be larger. In this option, therefore, his income- 
stream is not constant, but ascends from zero to some figure 
above the "standard income" of the first option. A third 
option is gradually to go out cf business, by buying less 
rugs than are sold, or none at all. In this case the income 
at first is very large, as it is relieved of the burden of pur- 
chases; but it declines gradually to zero. In the inter- 
stices between these three options there are, of course, 
endless intermediate options. The merchant thus has a 
very flexible income-stream. If the expenses and receipts 
for each rug bought and sold are the same whichever option 
is chosen, and if the time of turnover is also the same, it 
will follow that all of the options possess the same present 
value and differ only in desirability. We should then be 
dealing with that special class of options which we found 
open even in the case of rigid income-streams, — what we 
then called modifications of the income-stream through 
buying and selling. The reason for placing optional 
employments of capital on a different footing is that they 
do not all possess the same present value. In actual fact, 
the rug merchant, and merchants in general, would 
not find that all the optional methods of proportion- 
ing sales and purchases of merchandise possesst^d equal 
present values; for if he attempted to enlarge his business 
too fast he would find that his time of turnover would be 
lengthened, and if he reduced it too fjwt he would find that 

> Tho oanc of evcntv reconstituted capital is cinphftsizcd in J. B. 
Clark's writings. 6 3 TM ni^irU^utinn of Wealth, New York (Mac- 
miUan), 1899; sec The Nature 0/ Capital and Income, Chap XIV, | 4. 



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190 THE RATE OF INTEREST [Chap. K 

his selling expenses per unit of merchandise would be in- 
creased. There is for each merchant, at any time, one 
particular line of business policy which is the best; namely, 
that which will yield him the income-stream having the 
maximum present value. It is his interest to choose this 
policy and to relieve himself of any resulting inconvenience 
in the time-shape of his income-stream by borrowing and 
lending or by buying and selling. Since, therefore, the 
various methods of renewing one's capital usually yield 
income-streams differing in present value, they resemble 
what we have called optional employments of capital and 
may be properly classed as such. 

§ 7 

The propriety of such a classification becomes still more 
evident when, instead of renewals, we consider repairs and 
betterments; for it is clear that the income from a farm 
has a very different present value according as it is tilled 
or untilled, or tilled m different degrees of intensity; that 
the income from a house so neglected that a leak in the 
roof or a broken window pane results in injuring the ul- 
terior is less valuable than the income it would yield if 
properly kept up; and that real estate may be under- 
im^Toved or overimproved as compared with that degree 
of improvement which secures the best results. 

In all cases the best results are secured when that series of 
renewals, repairs, or improvements is chosen which renders 
the present value of the prospective income-stream a maxi- 
mum. This, as we have seen, is tantamount to saying that 
the renewals, repairs, or improvements are carried up to the 
point at which the return which they bring is equal to the 
rate of interest. The owner of a carriage, for instance, will 
replace a broken spoke, because the cost of doing so will pro- 
long the life of his carriage so far as to earn much more than 
the interest upon the trifling ca?t of the spoke. This repair 
may cost him $1 and may save him $20. But so high a 



Skc. 8] 



CLASSES OP OPTIONS 



191 



rate of return as these figures imply cannot be expected 
from every repair, and after the really necessary repairs 
are made, it soon becomes a question to what extent it is 
worth while to keep a carriage in repair. Repainting, re- 
varnishing, and resetting the tires are all costly, and though 
in every case the service of the carriage is increased in quan- 
tity and improved in quality, the return grows less and 
less as the owner strives after increased efficiency. He will 
spend money on his carriage in repairs and renewals up 
to that point where the la.st increment of repairs will secure 
a return which will just cover the cost with interest; 
beyond this he will not go. 

5 8 

.\nother cass of optional income-Htream.s is found in the 
choice between r'"fferent methods of production, es[x;cially 
between different "oes of what has been callfd "capital- 
i.'tic" production, .t is always open to the prf>s[X'Ctive 
housebuilder to build of stone, woo<^l, or brick ; to the pro- 
spective railroad builder to u.se steel or iron rails : to the 
maker of roads to use macailam, a.sphalt, wood, cobble, 
brick, etc., ov to leave the earth unchanged except for a 
little hardening and rolling. The choice will in all ca-ses 
dr-pendon the principles which have Vjeen already exjilainefl. 

For another example, the ser\'ices of a hou.-e which has 
a durability of 60 years will, compared with one which has 
a durability of 30 yea'^s h)e equivalent to the .^Tvices of 
two ho'i«-s, one built to-<lay and ktsting 30 years, and the 
other built at the expiration of that \yfTvA and la.-ting 30 
years more. The 'iifference lj<^-twet>n the one long-lived 
ho'.L*e and the two short-live-l houses is thus not in the 
services, but in the cost of construction. The cost of con- 
structing the 60-year house occurs in the pn-^-nt; that 
of the two successive 30-year houses occurs half in the 
rrr-?ent and half at the end of .30 years. In order that 
the more durable house rnav have the advantage as to 



.■I 



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l4| 



192 



THE RATE OF INTEREST 



[Chap. IX 



i -i 






cost, the excess of its cost over the cost of the first of the 
less durable ones must be less than the present value of 
the cost of the second, deferred 30 years. 

The choice between different instruments for effecting 
the same purpose may, of course, depend on their relative 
efficiency, — the rate of flow of income, or upon their 
lelative durability, — the time of the flow. It is true, 
however, as John Rae has pointed out,' that efficiency 
and durability usually go hand in hand. A house which 
will endure longer than another is usually more comfort- 
able also; a tool which will cut better will wear out more 
slowly; a machine which does the fastest work will gen- 
erally need to be strong and therefore lasting. 

The alternatives constantly presented to most business 
men are between pohcies w .. h may be distinguished as 
temporary and permanent. The temporary involves the 
use of easily constructed mstruments which soon wear out, 
and the permanent policy involves the construction at great 
cost of instruments of great durability. \Vhen one method 
of production requires a greater cost at first and yields a 
greater retu n afterward, it may, conformably to popular 
usage, be called the more "capitalistic" of the two. In 
other words, ''capitalistic" methods of employing capital 
are those which tend toward an ascending income-stream. 
The title "capitalistic" is not a happy one, although it has 
some justification in the fact that an ascending income- 
stream means the accumulation of capital, or "saving," 
and still more in the fact tliat only a capitalist can afford 
to choose a method of production which at first yields Jittlo 
or no income, or even costs some outgo ; for without cap- 
ital no one could subsist, or at any rate subsist with comfort, 
in the interim. It is clear that the capitalist who thus 
subsists on his accumulations does so by posses.sing, or be- 
coming possessed of, a descending income-stream. It is 
therefore as a possessor of income that he is enabled to 
subsist while waiting for the returns froju his new venture. 

' The Sociological Theory of Capital, p. 47. 



Skc. 9] 



CLASSES OF OPTIONS 



193 



He is enabled to invest in an ascending or slowly return- 
ing income-stream by having at command a descenling or 
quickly returning income-stream. We may say, therefore, 
thit a "capitaUstic" method is a method requiring an 
ascending income-stream, and it is so called becaase it is 
open only to those who have command of other and 
descending income-streams, such persona being necessarily 
capitalists. 



8 »-f| 



§ 9 

The best example of the choice between those uses of 
capital affording immediate and those affording remote 
returns is found in the case of human capital, commonly 
called labor. Man is the most versatile of all forms of 
capital, and among the wide range of choices as to the best 
disposition of his energies is the choice between using them 
for immediate or for remote returns. This choice usiially 
carries with it a choice between corresponding uses of 
other instruments than man. To choo:se to plant a tree for 
the sake of fruit ten years hence, rather than to plant com 
for the sake of next year's crop, is to make choice of fliffer- 
ent uses of land as well as of labor. Rut the existence of 
optional emplo\-ment5 of labor, however inextricably boiind 
up with optional emploj-ments of other in.struments, 
desen-es mention both be'-a-xse of its importance and be- 
caase it usually supplies the basi.s for the optional employ- 
ments of other forms of capital. 

It is, in fact, almost exclusively through var>-ine the 
eraploment of labor that the income-stream of .society 
as a whole is capable of chanering its time-shape. The 
indiWdual may modify the time->hape of his particular 
inc-ime-stream through exchange, but in thi.« case the wrson 
who exchange* with him ma«t mo.lify hi* income-«trf^m in 
the ''pposite manner, and the two modifications cancel each 
<jUivt m the total of the wori^i's income. But if an income 
'- ni*>^ifie<i in time--hape thn^ugh a chang*^ in the exertions 



c 

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1 1 



194 



THE RATE OF INTEREST 



[Chap. IX 



of laborers, there is no such offset, since the total social 
income is actually modified also. 

The labor of a community is exerted in numerous ways, 
some of which brbg about enjoyable income quickly, others 
slowly. The labor of domestic servants is of the former 
variety. The cook's and waitress's efforts result in the 
enjoyment of food within a day. Within almost as short 
a time, the chambermaid and the laimdress promote the 
enjoyment of house, furniture, and clothing. The baker, 
the grocer, the tailor, are but one step behind the cook 
and laundress; their efforts mature in enjoyments within 
a few days or weeks. And so we may pass back to labor 
increasingly more remote from enjoyable income, until we 
reach the miner whose work comes to fruition years Later, 
or the laborer on the Panama Canal, whose work is in the 
service of coming generations. 

The proportions in which these various kinds of labor may 
le assorted vary greatly, and it is through this variation 
that the income-stream of the community changes its timo- 
shape. If there are at any time relatively few persons em- 
ployed as cooks, bakers, and tailors, and more as builders, 
miners, and canal diggers, there will tend to be less im- 
mediately enjoyable income and correspondingly more 
enjoyable income several years later. By withdrawing labor 
from one employment to another it is in the power of 
society to determine the character of its income-stream not 
only in time-shape, but also in size, composition, and uncer- 
tainty. This power is exerted through the entrepreneur or 
"enterpriser" ' according to his estimate of what return will 
come from each particular employment taken in connec- 
tion with the sacrifice involved and the ruling rate of 
interest. Upon his judgment depends the future of society's 
income, and — since capital merely represents expected 
income — its future capital. If his judgment is good anil 
he di\ rt^ labor from domestic ser\'ice and the production 

' See Fetter. The PHnciplei of EconomicM, New York (Century). 
1904. Chap XXIX. 



Sic. 10] 



CLASSES OP OPTIONS 



195 



of commodities for immediate service to the conatruction 
of great engineering projects such aa the tunnels to connect 
Manhattan Island with the mainland, he Is increasir-r 
future income at the sacrifice of immediate income, and 
at the same time accumiilating capital. If, on the 
contrary, he makes opposite choice of the employment of 
labor, the opposite results will follow. Should his judg- 
ment be at fault in either ca.se, to that extent wiU the 
results stated faU t ^ be achieveri. Hi^ taak is one of much 
responsibility and great moment for the welfare of the 
world. The great majority whose interests he sup^ 
posedly serves are almost a.s much dependent on his good 
judgment as are the passengers in a railway train de- 
pendent for their safety on the good judgment of the 
engineer. 

§ 10 

Since the choice, for an individioal. among different options 
depends on the rate of interest in the manner dpsrribefi 
m Chapter \in, it is clear that a low rate favors the choice 
of ascending income-streams, but also that the choice of 
such income-fltreams reacts to raLse the rate of mterest. 
If, on the contrary, the rate is high, the oop'wites of both 
these propositions hold true. Thus, apphing these prin- 
ciples to the question of repairs, renewals, and improve- 
ments, it is evident that the lower the rate of interest, the 
better can the owner afford to keep his carriage in re^jair 
and the higher the state of efficieacv in which it and all 
other mstrumenta will be kept. But it is equaUy clf^r that 
the very attempt to keep injtriments up to the highest 
level of efficiency tends, in turn, to increa.^ the rate of in- 
terest; for every repair rr-ins a reduction in present Li- 
come for the sake of future - 1 .hii'trng ^"orward in time 
'X the mcome-stream-and rhi.= will ^aa^ a ri^ in th^- rate 
■■'t interest. Thu-^. any fill in the rate of inrere^t. bv ^rim^i- 
latmg repairs, renewal-, and berrerments. will bring its 



1 ' 
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It 






196 



THE RATE OF INTEREST 



[Chap. IX 




own correction through oversupplying future income at 
the expense of immediate income. 

Again, it is evident that a choice of the more durable 
instruments, as compared with those less durable, will be 
favored by a low rate of interest, and a choice of short-lived 
instruments will he favoretl by a high rate of interest. 
If the rate of interest should fall, there would be a greater 
tendency to build stone houses as compared with wooden. 
The present value of the prospective services and disser- 
vices of stone houses as compared with wooden would be 
increased; for although stone houses are more expensive at 
the start, they endure longer, and their extra future uses, 
which constitute their advantage, will have a higher present 
value if the rate of interest is low than if it is high. We 
find, therefore, as Jolm Rae has so well pointed out, tbit 
where the rate of interest is low, instruments ure substantial 
and durable, and where the rate of interest is high they 
are unsubstantial and perishable. In this case, as in the 
preceding cases, the low rate of interest leads to a choice 
which shifts the income-stream forward in time, and thus 
tends to raise the rate of interest, and vice versa. 

In general, then, a low rate favors the choice of "capit-'- 
istic" methods of production. The construction of a sub- 
stantial bridge which will never wear out is more likely to 
pay if the rate of interest is low than if it is high ; lor the 
lower the rate of interest, the higher will be the present 
value of the remote income which the permanent strjcture 
commands. Reciprocally, the more "capitalistic" the 
production, the greater the tendency to raise the rate of 
interest; so that the existence of numerous options has a 
regulative effect. Beyond the margin of choice there 
always lie untouched options ready to be exploited the in- 
stant the rate of interest f^ lis. Among these, as CasseP has 
pointed out, are watervvorks of various kinds. Not only 
the canals of stupendous size but hundreds of less con- 

' Tht \aliire and Xecetsity of Interett, London (Macmi)lan), 1903, 
p. 122. 



vM 



Sbc. 10] 



CLASaEa OF OPTIONS 



197 



spicuous waterways are suhject.s of poasihlf; investment ; 
among the les.%'r ones are the VA\xt and the Erie canal.s; 
and there might \)e. built numerous others a.s .srx»n a.s the 
rate of interest falls low enough to make the return upon 
cost equal to the rate of interest. TJie same Ls true of the 
improving, dredging, and deepening of harbors and rivers, 
the use of dikes and jetties, and the conatnaction of irri- 
gation works for arid lands. 

There is still room for much improvement in our railway 
systems by making them more efficient and more durable, 
by making the road^ straighter, the roadU.-ds more 
secure, the ro'ling stock heavier, the bridges larger and 
stronger, etc. In a new countr>' where the rate of interr^jt 
is high and the return on sacrifice prf^arioas or small, the 
cheapest and most primitive form of railway Is first con- 
structed. \'er\' often it is a narrow-gaiige road with many 
curves, costing little to construct, but much to ofX;rate. 
Later, when the rate of interest falls, or the traffic so in- 
creases that the rate of return on sacrifice is greater, the 
broad-gauge comes into use and the ciir\-es are eliminated. 
This is the kind of change which has h+ren proceeding in 
this country with great rapidity during recent years. 
There is a transition from relatively srruill first cost and 
large running expenses to precisely the opj-^osite t}-pe of 
plant, m which the cost Ls al.T.o.st all initial and the ex- 
P'ecse of operation relatively in.significanr. 



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iV f. I 



• J : I 




CHAPTER X 



INVENTIOK 



I 



Every range of choice is of necessity a range of choice 
among known options; consequently the range of choice 
will change as human knowledge is enlarged and increased 
through invention and discovery. In the matter of trans- 
portation, man originally had no choice but to walk. 
Afterward, when he learned how to domesticate animals, 
the use of horses for riding purposes opened a new and 
more rapid method of locomotion. Still later, owing chiefly 
to the invention of the wheel, the use of vehicles drawn 
by horses was introduced, then the construction of rails 
on which vehicles should run brought a foiui;h method. 
And now, with modem technical knowledge, each of the 
foregoing options is split up into a ni nber of subordmate 
options; there is the possibility of street transit by sur- 
face, elevated, or subway transportation, and the siorfaee 
transit may be by railway, trolley, automobile, vehicles of 
various kinds, bicycle, or the primeval method of walking. 

When a new invention thus enlarges the range of choice, 
the new options introduced may be effectual or ineffectual, 
— generally the latter. The great majority of patents do 
not pay the cost of procuring them. The reason for this 
is that when it comes to exploiting the new option, the 
rate of expected return on cost is found to be less than the 
rate of interest. Where the opposite is true the invention 
is effectual, and leads not only to a change in the range of 
options, but also to a change in the selection among them. 

When inventions thus result in a new option — in other 
words, when it is profitable to exploit them, — the effect 

198 



Sic. 2] 



INVENTION 



199 



necessarily is, for a time, to reduce the immediate income- 
stream of the community, for the sake of increasing the re- 
moter income-stream. The deferred increase is expected 
to yield a return on the immediate sacrifice at a rate some- 
times far greater than the rate of interest. But this high I 
rate of return on sacrifice to the exploiter of the newly dis-/ 
covered method of utilizing capital does not by itself fix* 
the rate of interest at that level. On the contrary, the 
valuation of the property is immediately re adjusted to 
the new conditions. Those who are first to enter the new 
field, or, in the slang of business, " come in on the ground 
floor," will obtain a return on the*' investment far greater 
than the rate of interest. But they viii immediately val" 
their property in accordance with its expected productiv- 
ity, and the rate of interest on loan contracts will be but 
slightly raised. The effect in raising interest comes merely 
from the shifting forward of the income-stream, which 
leaves the immediate income smaller than before, but 
compensates for this by a still greater iucrease afterwards. 
For, as we have seen, when an income-stream is of ascend- 
mg type, the rate of interest, for contracts connecting 
the periods of scarce income and those of plentiful in- 
come, tends to be high. 



t 



§2 

But, although the effect of the invention is to tilt social 
income into the ascending form, the individual who ex- 
ploits the process may, by the methods of borrowing and 
lending or buying and selling already explained, rectify 
his distorted income curve. He may, if he desires, restore 
his income curve to the very same time-shape that it had 
before his investment in the new enterprise. In this case 
it will be higher than before, all along the line. 

Thus, if his original income curve were ^5 in Figure 24, 
and the exploitation of the new invention required, for a 
certain period, a sacrifice tilting his income curve to the 



J] 



200 



THE RATE OF INTEREST 



[Chap. X 



.h 



ft 



J' 



J 1 * 



position of the dotted line A'CB", he might, by borrowing, 
obtain the income il'JS,' which has the shape of his original 
income curve AB, but exceeds it all along the line. Thus, 
the final effect of the investment is to enlarge the income of 
the investor. Provided he can borrow against the antici- 
pated returns, not only need he not suffer any temporary 




Fri, 24. 



reduction in income from the necessity of investing in his 
new enterprise, but he may even be enabled to enjoy a 
larger income from the outset. 

But if those who exploit the new invention make little 
or no sacrifices in their immediate income, others must; 
and these are they whose savings meet the cost of exploi- 
tation. Since the invention will more than repay this cost 
(whether or not to those who incur it does not matter), 
the effect will be to decrease immediate and increase 
remote income for society as a whole. Borrowing and 
lending merely distribute the pressure upon those most 
willing to bear it; but the effect is necessarily, for society, 
to cause a temporary depression followed by an ascent of 
the mcome-stream, and therefore to increase somewhat the 



•J" 



Sbc. 3] 



INVENTION 



201 



rate of time-preference and the rate of interest. The inven- 
tions of Watt and others, which led to the present railway 
system, are cases in point. Tney caused the income-stream 
of society, from being fairly uniform, to assume a rapidly 
ascending form. The earliest investors were compelled 
. to make great sacrifices, and afterwards, when the fruits 
of their labors began to come in, they were often foregone 
for the sake of yet greater and more remote returns. 
Throughout the period of railroad building, social income 
has been a series of investment, return, and partial re- 
investment, and a curve which would depict the actual 
income enjoyed would show it to be sharply ascending. 
Numerous other inventions have cooperated to this end. 
A whole series of new appliances have followed the dis- 
covery of electricity. The elevator and the steel skeleton 
have revolutionized the art of building. 

In consequence of the ascending time-shape of the in- 
come-stream, the rate of interest has been kept up. It is 
not sufficient, therefore, to suy with Rae, that the high rates 
of return on sacrifice offered by the new inventions have 
directly raised the rate of interest. These very high re- 
turns were secured only by a few. They are out of propor- 
tion to the rates of interest ruling on loans, or the rates 
of interest realized to the ordinary investor. These latter 
are the rates of interest in the true sense of the word, and 
they were raised for the ordinary investor, because he was 
called to the aid of those who were in a position to secure 
the exceptionally high returns, and had, therefore, tempora- 
rily, to .sacrifice income. The result is a general rise in the 
rate of interest, and in consequence a revaluation of invest- 
ment securities, and, in fact, of all capital. The value 
of capital sinks as the rate of interest rises, assuming that 
the value of the income from the capital remains the same. 

This revaluation applies a: o the very capital in which 
the new mvention or discove'^- is embodied. If it is found 



r— 



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202 



THE RATE OF INTEREST 



[Chap. X 




' It ^ 

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I ■ 



that a million dollars invested in a newly discovered gold 
mine will result in a yield of ten millions a year, that mine 
will no longer sell for its cost, but for a sum far above it. 
It is the relation of the income to the new value of the mine, 
and not its relation to the old value, which will reflect the 
true rate of interest. So, also, a new machine may at first 
return an enormous rate of profit on its cost, — far higher 
than the rate of interest; but soon the price of the machine 
in relation to the value of its services will be adjusted to the 
rate of interest. 

The same principle holds of all new enterprises. The 
original investors in The Bell Telephone Company realized 
returns far beyond the interest on their investment; but 
the present investor pays a price for Bell Telephone stock 
commensurate with its dividends. 

The effect of a new invention on the rate of interest is 
therefore registered, not by the original rate of return on 
sacrifice to the lucky "insiders," but by the rate realized 
to tlie investor who comes in later and invests at market 
prices. These prices, in the case of successful inventions, 
w^ill be far in excess of the cost. 

New devices will also cause a revaluation of the older ones 
which they have displaced, Lat in this case the new values 
are lower than before. The buzz saw rendered nearly 
valueless the mill plants equipped in the older methods, 
and the band saw had the same effect with reference to the 
buzz saw. Hand looms and presses became junk or curi- 
osities after the advent of steam looms and presses, and 
the first forms of the latter have in turn been supersede* 1 

The reasons for these reductions in value are simple. 
Each new process produces a larger supply of the particular 
kind of service rendered The price of this service — e.g. 
sawing or printing — is reduced, and consequently the 
capitalizeil value of the given amount of such service which 
can Ix' expected from the older devices is reduced, and often 
so far reducc( » to make the reproduction or even the 
repair of thes' ider instruments wholly unprofitable. 



«4 



Sio. 4] 



INVENTION 



203 



§4 

The subject of the economic effect of invention, and par- 
ticularly of its effect upon the rate of interest, has been 
fully treated by John Rae, and to him the reader of this 
book is referred for extended study.* There is one point, 
however, which Rae apparently did not observe, certainly 
did not emphasize, and that is the temporary nature of the 
1 effect of invention in raising the rate of interest. The 
effect in raising interest lasts only so long as (the result-f 
ing income-stream is sufficiently distorted in time-shapl 
to be of a decidedly ascending type. This period may be 
called the period of investment or exploitation, during which 
society is sacrificing present income, or, as it is inaccurately 
called, "investing capital." Society, instead of confining 
its productive energies to the old channels and obtaining 
a relatively immediate return in enjoyable income, as by 
producing food products, clothing, etc., directs its labor to 
great engineering enterprises such as constructing tunnels, 
subways, water works, and irrigation systems, that is, to 
instruments which cannot begin to contribute a return in 
inenjoyable income for many years. In contemplation, 
future income, during this period, is relatively plentiful, 
and in consequence of these "great expectations," the 
rate of interest will be high. 

Later, however, there will come a time when the income- 
stream ceases to ascend, when all the necessary investment 
has been completed, when no further exploitation is possible, 
and when it is only necessary to keep up the newly con- 
structed capital at a constant level. When this period is 
reached, the after effect of the invention will be felt. 
Society will then have a larger income-stream than before, 
but no longer an ascending one. A mere increase in the! 
Wize of the income-stream, while its shape remains constant, 
wias the effect, as we have .seen, not of increasing, but of 
fomewhat decrpa.'jing the .ato of timc-preference. Con- 

' Tk* Stteiological Thtstry oj Cajnial. 






I 






204 



hr. 



»1 1 ' ^ 



1% 



I . 



THE RATE OF INTEREST 



[Chap. X 



sequently the after effect of all inventions and discove ea 
is not to increase but to decrease the rate of interest. Thus, 
the railway inventions have led to a half century of invest- 
ment in railways, during which the income-stream of society 
has been constantly on the lacrease. To-day, however, 
the limit of steam railway investment has been nearly 
reached in some places, and in others the rapidity of invest- 
ment is perceptibly slackened. Railroads have been an 
outlet for the investment of savings, and have tended to 
supply for them a good return. As the necessity for new 
railroads becomes less, this outlet diminishes, and the 
rate of interest falls. 

But while the after effect of an old invention is to reduce 
the rate of interest, it may, of course, be true that new in- 
ventions will be made rapidly enough to neutralize this 
tendency. It is only when there is a cessation in the world's 
output of new inventions that the rate of interest is thus 
apt to fall back, but whenever invention is active it rises. 
It thus rises and falls according as the introduction or the 
exploitation of inventions is active or inactive. 

The same principles apply not only to invention in the 
narrower mechanical sense, but also to scientific and geo- 
graphical discoveries. The unearthing of a new bed of ore, 
as in Cripple Creek, Alaska, or South Africa, has as its 
immediate effect the necessity for a considerable depression 
in the immediate income-stream of those who desire to 
exploit the new territory, but offers the prospect of very 
great increase in the future; consequently, the rate of in- 
terest in such instances tends to be vciy high. After the 
perioti of exploitation, however, the income curve ceases 
to rise and begins to fall. Thereupon the rate of preference 
for present over future income assumes the opposite ten- 
dency, and the rate of interest declines. 



§5 
It has not been the purpose of this chapter to investigate 
the general effact of inventions, but merely their effect on 




Sec. 5] 



I>rVENTrON 



205 



the rate of interest. Before leaving the siibject, ho^* .,/er, 
it shj- VI at least be state^i that invem-.rjn is the ba.si.s of 
progress in civilization. The invention- of fire, the alpha- 
bet, and the means of utilizing p^jwer — first of animals, 
then of wind and water, then of -team and electricity — 
and their manifold applications, especially to tran.sportation 
and communication, have made it p >.«sible for the earth 
to support its incrpa.-ing population, and deferrc-^l the 
Malthusian pressure up^^^n the means of subsistence; they 
have ma<le possible the stable existence of great political 
units such as the Uuitei .States ; and they have given op- 
portunity for the presentation, diffusion, and increase of 
knowledge in all its f<jrms of art. literature, and science. 
.\nd thus it happens that invention is self-fjerrxituating. 
For not only has science -prune fri.m inventions .such as the 
printing press, the telegraph, and specific scientific instrti- 
ments for observation, like microscopes and telescopes, or 
for measurements, like r hronoeraphs, balances, and microme- 
ters; but mo<Jcrn science is now in tuni yielding new 
inventions. Helmliolz- ^searches in .sound le«i to the 
telephone; Ma.xwell'3 ana Hertz's researches on ethereal 
wa%es led to wireless teleeraphy. Nations like the Unite<i 
.States and Germany w-U lea<i in civilization by taking the 
ereatest advantage >/ this seif-propagafi.ng principle of 
invention: and nations like China, whirh give :t the lea.st 
attention, will lag hehimi. 

The conditions for the most rapid multiplication of in- 
ventions are : I personal efficien-^y. ie[;endent on breeding, 
hygienic habits, and the education both general and tech- 
nical) of the facdties: and for this the Greek motto "a 
"'an^ mini bi a sane t)*>iy" is in p><'jini:: wherefore Galton 
*eeras to show that in Greece geni'is wa.s far more com- 
mon th«n in mo-iem civilization: '2' the f^^ of diffusion 
•f knowle-lge. 3 the -ize of the population within which 
the difftj^ion occurs, —the lanr^r the population the greater 
'f»?uig the r imher of inventive zeni'is*--i. th*^- gr^^arer their 
in'^ntive. and the wider their sphere of inP.uence: '4; the 



« 

5 




•■I ? I ? ^ 



206 



THE RATE OF INTERES:" 



[Chap. X 



encouragement invention through patent protection, 
&nd more especially through the early discovery and ap- 
proval of genius. Inventors are at once the rarest and 
most precious flower of the country. Too often they are 
crushed by the obstacles of poverty, prejudice, or ridicule. 
While this is less so to-day than in the days of Roger Bacon 
or Galileo, it still requires far too much time for the Edisons 
or the Burbanks to get their start. The decades m which 
these rare brains are doing their wonderful work are at 
most few, and it is worth many millions of money for their 
countrymen to set them to work early. As Huxley says, 
it should be the business of any educational system to 
seek out the genius and tram him for the service of his 
fellows; for whether he will or not, the inventor cannot 
keep the benefits of his invention to himself. In fact, it is 
seldom that he can get even a small share of the benefits. 
The citizens of the world at large are the beneficiaries, 
and being themselves not sufficiently clever to mvent, 
they should at least be sufficiently alive to their own in- 
terest to subsidize the one man in a million who can. 



1.^-. 



CHAPTER XI 



third \pproxivla.tiox to the theory op interest 
(assumixo income t;nckrtain) 

§ 1 

Up to this point we have ignored the element of chance, 
by assuming that the entire future income-stream, or at 
any rate, such portions of it as neeri to influence present 
choice, are foreknown and mapped out in advance. In 
the preceding chapter, we have asumed inventions to be 
swrprms,— sudden enlargements of knowledge coming 
upon us without previous anticipation. In other wonis, 
we have assumed that men disregard future inventioas 
and act as though their knowledge of the future were per- 
fect. This assumption, like the aesiamption thiat bodies 
fall in vacuo, in the ordinary presentation of the theory 
of gravitation, has enabled us to complete our formal 
statement of the theorj- more easily, although at the 
expense of e-xaot conformity to artuai historical fact ; for, 
in the concrete world, the most conspiouci.^ characteristic 
of the future is its uncertainty. f:r.r.^fH-|-iently thp '.ntrr^ 
, durtion of th- element of riak will gjvp a=. hy r^j^fs |^^^ 
\ a gggct of p?ality . The general principlea which have 
been stated, however, will stili hold trie when we asmime 
•'incertainty instead of cer.ainty. they merely reqiiire 
to be supplemented by other principles. 

One consequence of chandng o'lr aaeumption as to the 
certainty of future events is trj 'r ompei the aba ndonment of 
the i.VA r,f a aagie rate of mter^^al - In.-ead of a single 
rate of interest representing the rate of exchange between 
:.iJi ytaz i^u next y-ar. ^ -r u-^y urai a gr'att v ari ety of ratea 
* rcoriing ^o the r i^ k involved , the rare m every loan 

2cr 



\ 



r, 
M 



I 






r : 



ft ■ 

I ' I 










1 i I 

t ■ I 

• J 

if 

■|1 






208 



THE RATE OF INTEREST 



[Chap. XI 



contract is adjusted on the basis of the degree of security 
given. Tlius, security may be furnished by sinipie indorse- 
ment of reputable persons, in which case the degree of se- 
curity will be the greater the larger the numFier of 
indorsers and the higher the credit which they possess; 
or it may be by the deposit of collateral securities. The 
necessity of the latter operation will affect a man's abilitj 
to borrow, and limit the extent to which he may modify 
his income-stream by this means. It will not be possible, 
as hitherto assumed, for a man to modify his income-stream 
at will, but only up to the limit of his credit. In conse- 
quence of this limitation upon his borrowing power, he may 
not succeed in modifying his income-stream sufficiently to 
bring the rate of preference between present and future 
income down to the rate of interest ruling in the mar- 
ket ; and for like reasons, he may not succeed in bringing 
the rate of return on sacrifice into conformity with the 
rate of interest. 

One feature of this limitation is the fact that th e ability 
to borrow depends, not so much on the amount of capita l 
whi ch the wou ld-be borrowerl^aessis^as on the form in 
whic h that capital happe ns ia he. Some securities are 
readily accepted as collateral, and accepted for a high per- 
centage of their face value, whereas others will pass with 
difficulty and only for a low percentage. Tlie recent ten- 
dency to change the organization of business to the corpo- 
rate form has had a striking effect in increasing the power 
to borrow. AMiereas formerly many businesses were con- 
ducted rs partnerships and on a small scale, numerous 
stocks and bonds have now been substituted for the old 
rights of partnership and other less negotiable forms of 
security ; hence the possessors of these securities have wider 
opportunities to deposit collateral, and the tendency to 
borrow has received a decided impulse. This explains to a 
large extent the investing and speculative mania which 
followfd the rei-ent widespread consolidation and formatioM 
of trusts. 



Sbc. 1] 



THIRD APPROXIMATION 



209 



Where the security does not oxist in the nonvfinicnt form 
of written certificates, thero i.s oftr;n considorable difficulty 
m negotiating a loan. Tf rnmmr^iiti^u are usf;d ff)r ,s<;curity, 
they must ordinarily be themsfjlves depr^siterj with the 
lender, — in other words, put in pawn. Where the bor- 
rowing takes place in pawn shops, it i.s not h^ecau.sf; of the 
inadequacy of the security, but \jf:om-^o of it.s inoonvcniont 
form, that the rate of interest i.s u.sually vorj- high. Tlie 
pawnbroker will need to charge a hig!^ rate of intere.st, 
partly because he need.s .^^torage room for the security he 
accepts, partly because he need.s .special clerk.s and expert.s 
to appraise the articles deposited, and partly becau.se, in 
many cases, he needs to find a market in which to .sell them 
when not redeemed. He i.s. moreover, able to .secure these 
high rates partly because pawnbroking is in bad odor, and 
those who go mto it therefore find a relative monopoly; 
and partly because of the fact that the cu-stomers aWly 
have, either from poverty or personal peculiarity, a rela- 
tively high valuation of present over future income. The 
effect of their flocking to the pawn shop i.s to rfAnce this 
high valuation; but it will not reduce it to the general 
level in the community, because these person.^ do not have 
access to the loan market m which the ordinarv business 
man deals. To them, undoubtedly, the fact 'that they 
cannof borrow except at high or ti5urioii.s rates is often'a 
great I^ardahlp; but it has. as one beneficent effect, the 
discouragement of getting unwisely into debt. Those' who 
patroniie pawn shops to a larze extent do so h;erau.*} 
they poseess little foresight and self-control, and the im- 
pHiiment which they find in the ^hap^ of a hlzh interest rate 
m a measure takes the place of the =eif-contro! and foresight 
*bch they should possess. Were it pr.spible for thi.s class 
to txMTow at lower rates, many or rhem would sink even 
more deeply mto debt than they act'ialJv do. Thixs, if 
slavery wen? legaliied and ir w-^ p'-x'sibie for a man 'to 
mortgage the income from tl.^ owr: !ar<r. i* ia unforru- 
:i4teiy true that many wo-ild avail r'-f-Tr.pelv^-^ of f hi.s privi- 



\ 



210 



THE RATE OF INTEREST 



[Chap. XI 



•f H 



lege, and would drop to the lowest place in the economic 
scale,— slavery. The fact that such contracts are illegal 
fixes a limit below which the o-dinary ne'er-do-weel can- 
not fall. At this point his ratt of preference for present 
over future is not in harmony with the rate of interest in 
the community. When the market rate of interest is 5 per 
cent., he may feel a rate of preference of 25 per cent. 



* ♦ 



i "11 
• ,■ . I : 



I ? f f ,1 
V 



§ 2 

We find, therefore, that the inhwiuction of the element 
o f chance, and the n ec essity of o vRrcnmipg it by the glvm g 
o f securit yjiagjftfi nne nf its pfyp&tg,the ^spli tting up of th e 
mari^pit inTn a n^ryihAr nf giiK-morV^p Instead of one huge 
market in which there is a single rate of interest, to which 
every individual conforms his own rate of preference, we now 
find a number of separate markets, a number of different 
rates of interest, and a very imperfect adjustment of the 

(individual rates of preference to those rates. 
We need here to emphasize the distinction between a 
commercial rate of interest which includes risk and a pure 
^or..risMfias-Jcate of interest.' The commercial rates vary 
widely, although the range of variation for rates on loans 
easily negotiable is relatively small. In ordinary real estate 
mortgages in the saiie market the range of variation is 
seldom over 1 per cent. 

If we pass from explicit interest, or the rate of interest 
involved in a loan contract, to implicit interest or the rate 
involved in purchases and sales of property of various kinds, 
j?e see again that the greater the risk the higher the "basis" 
bn which a security will sell. A "gilt-edge" security may 
lell on a 3 per cent, basis, when a less known or less salable 
Becurity will be selling on a 6 per cent, basis. The element 
of risk will affect also the value of the coll.'^teral securities. 
Their availability for this purpose will increase tbeir sala- 

' See Glossary under "Btisis" ; also The Nature of Capital and hcumt, 
Chap. XVI. 



? I 



Sic. 3] 



THIRD APPROXIMATION 



211 



bility and pnchance their price. On the other hand, when, as 
in times of crises, the collateral i.s imperatively flemanded, it 
often happens that, for purposes of liquiflation, it is mid 
at a sacrifice. 

In the same way that risk oaa«es the rates of explicit 
interest in a community to diverge from each other, or 
causes rates of preference to separate from rates of interest, 
it will cause the rates of implicit interest to diverge. The 
same individual who would borrow, if he cotild, at 2-5 per 
cent., but who lacks the necessary .aeotarity, mu.st devote 
his energies in-stead to acquiring or prrxlucing instru- 
ments which will have a return on sacrifice at the 2.5 
per cent, level. Although it would \)e more economical, 
if he could only borrow the money, to build durable houses, 
he will build inferior ones. Hence the anomaly, that even 
in countries where the rate of interest i.s low, there will te 
primitive communities in which the instruments possf^siVid, 
in the form of dwellings, tools, implements, etc., are far 
less substantial than is compatible with the low rate of 
bterest. 

§3 

Among other phenomena which follow from the existence 
of risk are t he variations in the d uration of loan.=i. Where 
the futiore is regarded as safe, loan contracts tend to be 
longer in time than otherwise. Railway and government 
seeurities are thus often drawn for half a century- or more. 
On the other hand, to provide for the iincertaintv of the 
imme diate future, the "call loan" is dfe \-i.sefl. This is a 
l<»n which has no specified due date, but can be demanded 
at the option of the lender whenever some cirnimstance 
makes this course advisable. \ loan contract of this kind 
bnngs the burden of risk on the borrower and relativf;|y 
relieves the lender, and In consequence, 'mder such con- 
ditions, the rate on call loans will ii«uaily tend to he low. 

The same prineipies ^u explain the lo'*' rate of implicit 
int«est in many cases. When' a, seciiritv. beraii«ie it i^ well 



\ 



I 

r— 
iB 



212 



THE RATE OF INTEREST 



[Chap. XI 



known, or for any other reason, has a high degree of sala- 
bility, that is, can be sold on short notice without great 
sacrifice, the price will be higher than otherwise, and the 
rate of interest it yields will therefore be low. Hence it is 
that the rate of interest on individual mortgages wiU be 
higher than the rate of interest on more marketable se- 
curities. It is usually considered an advantage to any 
stock to be listed on the stock exchange; for, being thus 
widely known, should the necessity arise to sell it, there will 
be found a more ready market. 

The most salable of all properties is, of course, money; 
and as Karl Menger has pomted out, it is precisely this 
salability which makes it money. The convenience of beingx 
able, without any previous preparation, to dispose of it) 
for any exchange, is itself a sufficient return upon the capital/ 
which a man keeps in this form, and takes the place of anj/ 
rate of interest in the ordinary sense of a money payment. 



if •■ 



i i 

1-3 



«i-' 



§4 

A further consequence of the introduction of the element 
of risk is the wid^divergence_jjetween th e actual rate of 
returarealized b y an investor and the expected rate. \Mien 
risk was regarded as absent, it was assumed that the ex- 
pected always happened; but in the actual world this is 
far from true. Those who invested in some of the mining 
"bonanzas" many years ago have received a rate of return 
of many hundred per cent. ; and far in excess of the rate of 
interest which they would have been willing to take for a 
loan. Reversely, those who invested in the South Sea 
Bubble found an opposite disparity between their expecta- 
tions and theu- realizations. Risk is especially conspicu- 
ous at the time of new inventions or discoveries. Almost 
all prediction is based on a belief in the repetition of past 
experience ; but at these times, past experience is a poor 
guide. When new inventions are made, unwrtaintv 
is introduced, speculation follows, and after that, great 




Sbc. 5] 



THIRD .U»PROXIM-\TION- 



213 



wealth or ruin. The history of ^oM and silver rE^coveries 
and of the invention of ribU;r, Htr^l. and f;lf;r:r,rical appli- 
ances, is fille<i with tales of tho'jsands of wrecked fortunes, 
by the side of which tower the fort'one-i of tr^iay'., ncni- 
veaux richer. 

- V^ rate of inrtrpr'T U Riwq>" ba.yrd upon f-xr^^ctation . 
howeve r^ little thL- may he jiictiSed hv realization . Man 
makes his guess of the future and .--takes hi., action up/jn it. 
Ir his guess he discoiints ever-thing he can foresee or 
e-^timate. even future invention.-? and their effect.^. In a 
recent estimate of the value of a ^^r^pper mine, allowance was 
n-iile for future economies from inventiort^ which might 
rea.s<;.nably be expecte«i. .So. aL^o. the buyer of machinery 
allows not simply for it.? depreciation through phy.--ica'l 
wear, but for its being pos.sibiy i=uperse<ied. N'ew invest- 
ments in steam railroa-ii are t.o-iay marie with due regard 
to the possibility that the ro&i may within a few vears \je 
ran by electricity. It may easily happen tUt in'a coun- 
ty consisting of oversaiig'^ne per^o^ns. or during a perio^i 
when business men are overhop-ef-i. the rate '-.( interest 
wO he higher than the event ••i^tifes. I' i., probable 
'Cat. in ordinary.- comm-mities. realizatl.o.i ju.^ti.^-es the 
average expectation: cc: b, the irjii-i^ ca.^ this is 
not always trie. otherwL^ 



lere "v: ..: ->: .v; 
is due to partial 'sno'^leii^. C".:r '."es*:::t -v 
■•"ontrc'tlei by the :ut;ire, not a.-- [: A.:-t :a^v ; 
icooL? t-: "i; thro'ish the veil :: change 



L.K. Risk 

• mi^t he 

but a.-; it 



> 



J -5 



^n tne precaiinz section ^e 

"-"i oc the p>eud.> 

tne rue on 'insafe 

a' int erest, or t he -^-^ -r .^^ ;r^rr:?^T;r^ 



-^'isseii t.'.e erect of 



i-.^.*..!.- :r :mpi;re ."ate -'.t m'erest;' that L^, 



rmen;.=. 



c--t 



r. '-re .-ate 



cy r^sic The e^ect is iif-^ren" i-v:-:r-llr.? *■- ..- ..-,..,:..,= 
ccDiiuons which may induence tne .-ate '.i creferenc*; for 

" ^** ^** -Vican -If Capuai tiux Ites-mg. i" >a^. XV I, { ^ 



214 



THE RATE OF INTEREST 




»« 



!. 



II 



U 



[Chap. XI 



present over future income. Where the risW rpUf i^^fl | ,p 
human life, the rate of preference for present "^^^ fnty rA 
i ncome is increased .' Consequently the rate of interest, 
even on safe loans, will be raised by the existence of 
such risk. The man who looks forward to a short or 
; precarious existence will be less likely to make permanent 
investments, or, if he makes them, less likely to pay a high 
price for them. Only a low price, that is, a high rate of 
interest, will mduce him to invest. When the risk relates, 
however, not to the duration of life, but to the income- 
stream, the effect upon the rate of interest will depend 
upon which portion of the income-stream is subject to 
risk. If the immediately ensuing income is insecure, 
whereas the remoter income is sure, the rate of preference 
for immediate as compared with remote income will, as was 
shown, be high, and consequently the effect of such a risk 
upon the rate of interest will be to raise it. But if, as is 
ordinarily the case, the risk applies more especially to the 
remoter income than to immediate, the effect is the exact 
opposite ; namely, to lower the rate of interest on a safe 
loan. This is, perhaps, the typical case. If a man regards 
the income for the next few years as sure, but is in doubt as 
to its continuance into the remoter future, he will be more 
keenly alive to the needs of that future, and will consequently 
have a less keen preference for the present. He will then 
be willing, even at a very low rate of interest, to invest, out 
of his present assured income, something n eke out the less 
sure income of the future. The effect of r-sk m this - ise 

therefore, is to lower the rate of interesi la: sme { ans 
hough at the same time, as already explaisas^ s ^ilj rab 
he rate of interest on unsafe loan>. Coi£B»«uentfr is 'irrscs 
of great social unrest and dMic- r. wf» ^nt^^ the i^sHnaious 
combination of high rates wnere irmaemrnxs- wfrmsry is 
given, coexistent with low rai8.s hi arvestmans resBtled 
as perfectly safe. In conimer-asi JsnecatBt wbm a. 
mvestor cannot find many in- estiaeiiif jdeo "^mm. be may 

' Cf. Carver's The Diati-amtiamjn W^mh, z.. 2fi& 



'SS 




Sic. 6] 



THIRD APPROXIMATION 



215 



jput his money without risk of losing it, he will pay a 
high price for the few which are open to him. It has been 
noted in times of revolution that some capitalists have 
preferred to forego the chance of all interest and merely 
hoard their capital in money form, even paying for storage 
charges, which amounts to a negative rate of interest. 

§ 6 

When risk thus operates to lower the rate of interest 
on safe investments and to raise the rate on unsafe in- 
vestments, there immediately arises a tendency to dif- 
ferentiate two classes of securities and two classes of 
investors, — precarious securities and adventurous invest- 
ors on the one hand, and safe securities and conservative 
investors on the other. Risk is inevitable in ever\- business, 
but is regarded by most people as a burden ; hence the few 
who are able and willing to a.ssume this burden become 
a separate class. To-day, when any enterprise is organized 
in corporate form, it is usual to recognize this tendency by 
dividing the securities into stocks and bonds, the stock- 
holder being the person who assumes the risk and, theoreti- 
cally at least, guarantees that the bondholder shall be free 
of all risk. Which persons shall fall into the class of risk 
takers and wliich not, is determined by their relative 
coefficients of caution,' as well as by the relative degree of 
risk which an enterprise would involve for the various in- 
dividuals. Tlie same enterprise may be perilous to one 
and comparatively safe to another, because of superior 
knowledge or other conditions; and the same degree of 
risk may repel one individual more than another, owing 
to differences in temperament, or, most important of all, 
diffprences in amount of capital.' 

This shifting of risk from those on whom it bears heavily 
to those who can best assume it, discloses another mative 

' See The Nature of Capital and Income, Chap. XVI, { 6. 
' Ibid., Appendix to Chap. XVI, p. 409. 



> 






■i 



216 THE RATE OF INTEREST [Chap. XI 

for borrowing and lending besides those which were discussed 
in a previous chapter. Lending, in modem finance, often 
indicates not sunply a difFerence in time-shape as between 
two mcome-streams, but also a difference of risk. The object 
of lending which was emphasized in earlier chapters, before 
the nsk element was introduced mto the discussion, was 
to alter the time-shape of the income-stream, the borrower 
desiring to mcrease his present income and decrease his 
future, and the lender desiring, on the contrary, to decrease 
his present mcome and add to his future. But the stock- 
holder and bondholder do not differ in this way so much 
M in respect tc risk. They are both investors, and 
stand in a very similar po*<ition as to the effect of their 
mvestment on the time-shape of their income. For the 
stockholder, however, there is a risk attached to his income- 
stream from which the bondholder is relatively free. It 
18 this difference in risk which is the primary reason for 
the distinction between stockholders and bondholders 
The bondholder "commutes" > his chance of a high income 
for the certainty of a steady income. 
' The existence of this risk, tendmg, as we have seen, to 
aise the rate of impure interest and lower that of pure 
ater^t, has as its effect the lowpring nf thfLprig e of stock s 
gjhe raising orthejri ce of bonds from whaLffiguld have 
. r^^Siig^Sctivejjuse^ 
aiaeaL On the other hand, the separation of the investore 
into stockholders and bondholders reacts upon the prices 
of stocks and bonds and tends to lessen the disparity 
between them. Were there no bonds, but only stocks, the 
price of the stock would have to be lower than it now is 
in order to induce the timid investor to buy. In other 
words, the effect of the separation between risky and safe 
investments is at once to moderate the lowness of the low 

i. In/" ^"^'^T' '^^'^T""' " "°- '^'»« "*»« «' 'oto^'t, however. 
1« not properly speaking, the rate of commutation; for the r»te of 
commutotion would be the ratio between the avera,; e.rniSiiT th. 

the rate of interert i. the ratio betweca income and capital. 



Sbc. 7] 



THIRD APPROXIMATION 



217 



rate on safe investments and the height of the high rate 
on the unsafe investments. 

The same tendency, to reduce the disparity between the 
rates of mterest on safe and unsafe investments, grows out 
of the practice of insurarux. One effect of insurance > is 
to raise the value of capital subject to risk of fire or other in- 
surable risks, by consolidating those risks and thus virtually 
reducmg them. But this rise m the value of capital implies 
a reduction m the rate of interest which it yields. Agam 
the effect of speculation, by settmg aside a certain clas^ 
of persons to assume the risks of trade, has the effect of 
reducmg these risks by putting them in the hands of those 
who have most knowledge; for, as we have seen, risk varies 
inversely with knowledge. In this way the whole plane 
of busmess is put more neariy on a uniform basis so far as 
the rate of interest is concerned. 









i ) 



§7 

We see, then, that the element of risk introduces dis- 
turbances mto those determining conditions which were 
expressed m previous chapters as explaining the rate of 
mterest. To summarize these disturbances, we may apply 
the nsk factor to each of the six conditions which were 

originally stated as determining mterest. We shall find that 
Its effects are as follows : — 

1. The condition that each individual has a given range 
of choice stiU holds true, but these choices are no longer 
confined to absolutely certain optional income^treams, 
but include options with risk. That is, each individual 
ftnds open to his choice a given set of options which 
differ m size, time-shape, composition, and risk. 

2. Rates of preference for present over future goods are 
of two kmds, according as the goods are comparatively cer- 
tain or uncertam. The marginal rate of preference for a 
certain present over a ctrtain future good, or the pure rate 

• See Ths Natun o/ CajriuU and Inccm*, Chap. XVI. 



r-* 



f -5 



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I 

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218 



THE RATE OP INTEREST 



[Chap. IX 



of time-preference, depends upon the character of the 
total income-stream, — not only its size, shape, and com- 
position, but also and particularly upon the degree of cer- 
tainty attaching to various parts of it and the degree 
of certainty of life of the recipient. Again, the preference 
rate for present certain income as compared with future un- 
certain income, or the impure rate of time-preference, 
will, in normal individuals, be greater than if both in- 
comes were certain, and will be the greater, the higher the 
risk and the higher the caution in assuming it. 

3. Pure rates of time-preference (as among certain goods) 
in different individuals tend toward equality by the prac- 
tice of borrowing and lending, and more generally, buying 
and selling; but this equality is not in all cases attain- 
able, because of limitations on the freedom to modify 
the income-stream at will. These limitations grow out 
of the existence of the element of risk. There are various 
means of reducing or avoidmg risk, — in particular, by 
the devices of collateral security, indorsement, under- 
writing, etc., but all of these processes have more or less 
definite limitations. In consequence, it is not always 
possible to provide security for as large a loan as would 
be necessary to change the income-stream enough to reduce 
the rate of preference of the borrower to the rate of 
interest. If the security is adequate, the rate of preference -) 
will be equalized with the rate of interest ; if not, it will I 
remain above it. Where the security introduces impedi- I 
ments which affect the lender as well as the borrower, it 
will also happen that the rate of interest will be raised, as 
in the case of pawn shops which hold in pledge their motley 
assortment of cumbersome merchandise. Thus, instead 
of one rate for several loans, there will be a number of 
separate rates and a number of wparate markets, accord- 
ing to the nature of the security asked and given. 

At the same time there will be a tendency to ask ami 
receive loans with inadequate security. This introducts 
a pseudo- or impure rate of interest which will be above 



8k. 7] 



THIRD APPROXIMATION 



219 



the pure rate by a margin differing according to risk and 
caution. 

4. When risk was left out of account, it was stated that 
from among a number of different alternatives the indi- 
vidual would select that one which had the maximum pres- 
ent value, — in other words, that one which, compared with 
its nearest neighbors, possessed a rate of return on sacrifice 
equal to the rate of preference, and therefore to the rate 
of interest. When the risk element is introduced, it will 
still be true that the maximum present value is selected; 
but in translating future uncertain income to present 
cash value, use must now be made of the probability and 
caution factors. One consequence is that when we express 
this principle of maximum present value in its alternative 
form in tt.ms of the "marginal rate of return on sacrifice," 
we must qualify this expression as the "marginal rate of 
anticipated return on sacrifice." The rate of return on 
sacrifice which will be actually realized may turn out to 
be widely different from that originally anticipated. 

5. In the former approximations, where the element of 
risk was considered absent, it was shown that the aggre- 
gate modification of the income-streams of individuals for 
every period of time was zero. What was borrowed equaled 
what was lent, or what was added by sale was equal to 
what was subtracted by purchase. The same principle 
still applies; for what one person pays, another person 
must receive. 

6. In the former approximations, the total present value 
of the projected modifications of one's income-stream was 
zero; that is, the present value of the loans equaled the 
present value of the borrowings ; or the present value of 
the additions and subtractions due to buying and selling 
balanced each other. In our present discussion, in which 
future income is recognized as uncertain, this principle still 
holds true, but only in the sense that the present market 
values balance at the moment when the future loars or 
other modifications are planned and decided upon. The 



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220 



THE RATE OP INTEREST 



[Cbap. XI 



fact that risk is present may lead to a wide discrepancy 
between the original expectation and the actual realiza- 
tion. In liquidation there may be default or bankruptcy. 
When the case is not one of a loan contract, but relates 
merely to the diflference in income-streams of two kinds of 
property bought and sold, the discrepancy between what 
was expected and what is actually realized may be 
still wider. But, viewed in the present, the estimated 
value of the future return is still the equivalent of the 
sacrifice. The present value of a future uncertain event is 
equal to its mathematical value multiplied by a caution 
factor,* and the mathematical value is equal to the expected 
value multiplied by a probability factor and .liscounted 
according to the rate of preference for present over future 
income. 

§8 

We thus see that instead of the series of simple equalities 
which we found to hold true in the vacuum where risk was 
absent, we have only a tendency toward equalities, interfered 
with by the limitations of the loan market, and therefore 
resulting m a series of inequalities. Rates of interest, 
rates of preference, and rates of return on sacrifice are only 
ideally, not really, equal. 

We conclude by summarizing in the following table the 
interestKletermining conditions for our three successive 
approximations : — 

» See The Naturt of Capital and Income, Chap. XVI, { 6. 



Sic. 8] 



THIRD APPROXIMATION 



221 




!H 3 * 



lb 



4i 






222 



THE RATE OF INTEREST 



[Chap. XI 



In the first approximation, conditions 1 and 4 are in- 
serted to complete the correspondence with the other two 
approximations; but they are both really the same con- 
dition, and merely reexpress the hypothesis under which 
the first approximation was made. It is the remaining 
four conditions which are of real significance. 

The first two approximations were, of course, merely pre- 
paratory to the third, which alone corresponds to the actual 
world of facts. Yet the other two approximations are of 
equal importance with the third from the point of view of 
analysis. They tell us what woidd happen if future income 
were (1) fixed and certain, and (2) flexible but certain; 
and to know what would happen under these hypothetical 
conditions enables us better to imderstand what does happen 
under actual conditions, just as the knowledge that a pro- 
jectile would follow a parabola if it were in a vacuum, and 
that it would follow a certain other curve if in a still at- 
mosphere of given density, enables the student of practical 
gunnery better to understand the actual behavior of his 
cannon baUs. In fact, no scientific law is a perfect state- 
ment of what does happen, but of what would happen if 
certain conditions existed which do not actually exist.' 
Science consists of the formulation of hypothetical se- 
quences, not of historical facts; though by successive 
approximations the hypotheses may be made nearly to 
comcide with reality.* 

> See the writer's "Economics as a Science," Science, Augtut 31, 
1906. 

* See Appendix to Chap. XI, | 1. 



I 



4*ie^ 



:*-1i^ 



PART IV. CoxVCLUsiONs 



Chapter 
Chapter 
Chapter 
Chapter 
Chapter 



XII. 
XIII. 
XIV. 

XV. 
XVI. 



Chapter XVII. 



Role of Interest in Economic Theory 
Application to Actual Conditions 
Inductive Verification (monetary) 
Inductive Verification (economic) 
Inductive Refutation of "Money 

Theory" 
Summary 



3 



^i>\ 



CHAPTER XII 

BOLE OF INTEREST IN ECONOMIC THEORY 



SI 

Having shown how the rate of interest is determined, 
we have reached the goal which we have set ourselves in the 
present book. But, though this goal marks the end of the 
present mquiry, it is also the starting-point for other fco- 
nomic inquiries of the greatest importance. We cannot 
attempt in this book to explore the fields which would thus 
open out, but in the present chapter we shall inrlicate 
briefly what they are. 

The rate of interest pkys a central rrjie in two great 
branche8_of^Monqmcjcience, — the theory of prices, and 
the theory of distribution. The rdle of the rate of inter- 
est in the theory of prices applies to the determination of the 
price of wealth, property, and services. 

As was shown m The Nature of Capital and Income, the 
price of any article of wealth or property is equal to the 
discounted value of its expected future services. If the 
value of these services remains the same, a ri-^e or fall in 
the rate of mterest will consequently cause a fall or rise 
respectively m the value of all instruments of wealth. The 
extent of this fall or rise will be the greater the further 
into the future the services of wealth extend.' Thus, hgj^. 
from whi(^h aprw-i ^es are expected to accrue un iformly and 

nalvwi, or halved in value if the rate of interest is doubled. 
In^aeMfle of dwgmng ^however, the life of which _ m 
xisit^if jhe rateoi intertttt is doubied, the price "of 

' See Th* Nature of Capital and Income, Chap XIII. 
« 225 



I 



H 



M 






i 






226 



THE RATE OF INTEREST 



[Chap. XII 



will fall less than half, and if the rate of 



interest is halved, the price of dwellings will rise to less 
than double. In the case of furniture the fluctuations in 
value will be even less extensive, andso ^through the list 
of less durable commodities, such as clothings t o t.hn.sft q f 
v ery peri shable_typea^uc.hj^8 food, the value of whi ch wi ll 
not be sensibly affected by a variation in the rate q£ interest. 



* f 




§2 

As to the influence of the rate of interest on the price of 
services, we first observe that services may be intermediate 
or final.' The value of intermediate services or "inter- 
actions" is derived from the succeeding future services 
to which they respectively lead. For instance, the^value 
tqji farmer of the service s of_hi s land in affordin g pastu re 
for sheep will depend upon the discounted value of the serv- 
ices of the flock in produicmg wool. If he rents the land, 
he will calculate what ^e can afford to pay for it on the 
basis of the value of/ the wool which he would expect to 
obtain from his flocX. In like manner, the value of the 
wool-output to th^ woolen manufacturer is in turn in- 
fluenced by the discounted value of the output of woolen 
cloth to which it contributes. In the next stage, the value 
of the production of woolen cloth will depend upon the 
discounted value of the income from the production of 
woolen clothing. Finally, the value of the last named will 
depend upon the expecteil income which the clothing will 
bring to tlyftse who wear it, — in other words, upon the use 
of the clmhes. 

Thus J(ne final services, consisting of the us e of the clothes , 
wjll have an influence on the value oTall the anterior serv- 
ices of tailoring, manufacturing cloth, producing wool, 
and pasturing sheep, while each of these anterior services, 

' See The Nature of Capital and Income, Chap. IX. The .subject 
hfts alrvady been referred to in the present volume, Chap. VIII. 



Sbc. 2] RQLE of interest IN ECONOMIC TffRORY 227 

when discounted, will give the value of the roapective capital 
which yielfia them; namely, the clofhes, cloth, wool, sheep, 
and pasture. We find, therefore, thiit not only all articles 
of wealth, but also all the intermedials .ser\-ices ('"interac- 
tions") which they render, are depf-ndent lipon final enjoy- 
able uses, and are linked to these final uses by the rate of 
in^rest. ILthe rate of int.er egtj;i.iOH or fall.-^_thi.s chain will 
.' hrink or e.-cp anrT The chain haTi^JTIo to li]^^ak7?Jwn fts 
final linkoTenjoyable ser\icf?s, and it.i .shrinkage or ex- 
pansion will therefore be most felt by the Iink.-i mont distant 
from these final sen-ices. A phanoy in the rate^of interest 
will affect but sli^htlv^ jhe price of making clothing, but I 
it will ^ffpct. fnn^jJprQhk- the price of pa.-ituring sheep. 

A study, therefore, of the theorv- of prices involves (I) 
a study of the laws which determine the final a€r\'ices on 
which the prices of anterior interactions depend; (2) a 
study of the prices of these anterior interactions, as de- 
pendent, through the rate of interest, on the final services ; 
3; a study of the price of capital instmrnents and capital 
property as dependent, throiigh the rate of interest, upon I 
the prices of their services. The fir^t -itudy. which seeks 
merely to determine the laws regulating the price of final 
services, is relatively indepen-lent of the rate of interest. 
The second and third, which seek to .-^how the depenrjence 
on final services of the anterior sen-ices and of the capitals 
Trhich betir them, mvolve and <ieperxd upon the rate of 
interest. L'nder this .^cond study tviil fall. a.< a -pecial 
ca.-^. the study of the .letemiina'iur. of econ';rriic rent, 
both the rent of land and the rent of -rher in.-triments of 
wealth. Thus, the rent of the pa.--;;re referred to, con.^ist- 
ins. as it does, of the value of tlie ser\-ices of pa-ituring, 
is depen.ient. throiigh the rat,^ of in'er=--t. upon r'hf di.='- 
counte<i value of the future final -er.-ices ry, Thich the land 
contributes. It is clear, then, 'hat the rent of the land 
L» partly dependent uron the rire of i!i-'•-r'-■^^ an-i rh_-if. the 
•*iime dependence applies to the rent .or anv other instru- 
."nent. 



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228 



THE RATE OP INTEREST 



§3 



fCHAF XII 



Similar considerations apply to the determination of the 
rate of wages. So far as the employer is concerned, the 
payment of wages to a workman repr*»sent8 the value of 
his services. These services are interactions or inter- 
mediate services leading to some future enjoyable service. 
Thus, the shepherd hired by the farmer to tend the sheep 
in the pasture renders services the value of which to the 
farmer is estimated in precisely the same way as the value 
of the services of the land which he hires. It follows that) 
the rate of wages is dependent upon the rate of interest! 
[and, conformably to the previous reasoning, the dependence! 
of wages on the rate of interest is the more pronounced the 
more remote are the ultimate services to which the work 
of the laborer leads. As stated in Chapter IX, in a com- 
munity where the workmen are largely employed in enter- 
prises requiring a long time, such as digging timnels and 
constructing other great engineering works, the rate of 
wages will tend to fall appreciably with a rise in the rate 
of interest, and to rise appreciably with a fall in the rate 
of interest; whereas in a country where the laborers are 
largely engaged in p)ersonal services or in other work which 
is not far distant from the final goal of enjoyable services, 
a change in the rate of interest will affect the rate of wages 
but slightly. 

j W feat has been said, however, applies only to wageaircun 

't he standpoi nt_of the emp loyer. The rate of wages js 

d ependent upon supply as well as dem and ; that is, upon the 

willingness of the workman to cffer his services, as well as 

j upon the desire of the employer to secure them. From the 

1 standpoint of the laborer, wages constitute an incentive to 

exertion or labor. Tnis exertion is, as we have seen, a final 

disservice, and its value is not determined by the rate of 

interest in the manner of services which are intermediate. 

It is a great mistake to treat the subject of wages, as many 

authors do, exclusively from the employer's standpoint. 



Ill 



Sac. 4] RClE op INTEREST IN ECONOMIC THEORY 229 

Our purpose here, however, ia nof. to enter into an extenflerl 
discussion of the therjry of wa£;f;M, but merely to whow at 
what points in that ther^ry the rate of interf«<t enters, anrl 
at what points it dfjfis not enter. 



'II 



The second great branch of ef onornica to which the rate 
of interest applies is the the.;.r/ of rii^tribution. In the 
claa aical political ec onomy, the relation of the rate of in- 
terest to diatributjoirwa.^ entirely misconceivefl. Dis- 
tribution was^ejfoneoualy regarde^i a.^ a sfjfjaration of the 
mcomejjf 'society into "interest, rent, wages, and profits." 
By-^interesLl' of course was meant, not the rate of interest, 
but jhe raff nf intfrg-t^muIti^Jied by the value"of the ca^- 
t al -'vieMing inter est." But we have seen that the value 
of the capital Ls found by taking the income which it yields 
and capitalizing it by mean.-* of the rate of interest. To 
reverse this process, and obtain the income by multiplying 
the capital by the rate of interest, b. prrjoee<ling in a circle. 
The resiiit of multiplying capital by the rate of interest, 
i.«. income, is not really a complex product of two factor-), 
but, on the contrary, is the =ingie original factor. — income. 
^ hir a g ai i^n iTi ..jnia booic that i*. u r.hL- income which 
affords the basis for th e detenniaatioc of tne rate of intere:^t. 
ana, throig^ the rate of inte ref -t. of capi tal value. T\if. 
income-stream <rf society is the ultimate and ba.=iic fact from 
which the whole economic fabric shoiild be constructed. 
Ml of this income springs from capital-wealth, if land and 
aan are incrade«i in that tern, or if not. from capital and 
aian. or capital, land, and man. It .-nay ail be capitalizer-j, 
and hMice. a we follow the iriinition a --.apital viopted in 
tnis b«xiii. i: may ail h« resarie: ±i interesr. :pon the capital- 
viiioe thus found. H^nce • in'erest i.-^ r.ot i cart. b'4t the 
^hote^ f incom e. It Lnciu ie* what w -lilleii rer.t 3x.d nrofiL i. 
j^d ev. wage s: tor tne Income of the worscT^an rfiay 
'« '^apiraiized^iqiiite a^ tr;.- i.^. tne income of land or 



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230 



THE RATE OP INTEREST 



[Chap. XII 



machinery. Thus, sc far from having "interest, rent, 
wages, and profits" as mutually exclusive portions of in- 
come, we see that "interest" includes all four. Thejerror 
of the classical economists and of their modem followers 
in distinguishing between/interest, rent, etc., as separate 
but coordinate incomes, js partly d ue to the failure j o 
p erceive that where as all income springs from capital - 
wealth, vet capital^alue sp rings from income. 

Another oversight closely associated with the last is 
that by which rent and wages were conceived as deter- 
mmed independently of the rate of interest, whereas we have 
just seen that the rate of interest enters as a vital element 
into the determination of both. 

We shall, therefore, in discussing the theory of distribu- 
tion, abandon the "classical" point of view entirely. And 
little regret should be caused by such abandonment, for 
concept of distribution which the classical economists have 
given us is quite incompatible with the ordinary conception 
of the term. Thejihraae-ldiatribution of wealth" implies 
ordinarily, or should Jmply, the problem or~tEe relative 
wpfllth nf inHivi(]iia)j«, — the problem of the rich and the 
poor.' But the separation of the aggregate income into 
four abstract magnitudes has little to do with the question 
of how much income the different mdividuals in socit ty 
receive. Were it true that society consisted of four irde- 
pendent and mutually exclusive groups, — laborers, land- 
lords, entrepreneurs and capitalists, — the fourfold ilefi- 
nition would have some connection with the actual dis- 
tribution of wealth. But, in fact, the entrepreneur is 
almost invariably a "capitalist"; i.e. is the o^ner of other 
capital than land ; the "capitalist" is frequently a landlord, 
or vice versa; and even the laborer is to-day often a small 
capitalist. It is true that a century ago in England the 
lines (>i social classification corres|)onded roughly and to 
some extent, it least, with the abstract divisionB into which 

' Cf. Edwin Cunnan, ' The Division of Incomt-," (Juarttrty Journal 
of Economict, May, 1905. 



Sec. 6] ROLE OF INTEREST IN ECONOMIC THEORY 231 



econombts separated income; but this fact is of interest 
only in explaining historically the origin of the classical 
theory of distribution.* 

§5 

Turning to the true problem of distribution, that of de- 
termining the amounts of capital and income possessed by 
different individuals in society, we find that economists 
have contributed extremely little to its solution. A 
statistical beginning has been made by Professor Pareto 
m his interestmg "curves of distribution of mcome," * 
m which he shows the surprising result that in all cases 
where figures are available, the relative distribution of 
mcomes is fairly uniform in different times and places. 
So far as the philosophical theory of distribution is con- 
cerned, the only writer who seems to have contributed 
materially to the subject is JohiLRae^ He sho wed that 

pp^ynna who hud na^^irnlly^whafwA >».vo /.ollor] jn this book 

a low rate of preference fo r present over future income 
t ended to tyow rich, wherea s lEose who had the opposite 
t rait tended to grow poo r. 

We saw m a previous chapter that the rates of prefer- 
ence among different individuals were equalized by borrow- 
uig and lending or buying and selling. In the case of an 
individual whose rate of preference for present enjoyment 
was unduly high, we found that lie would contrive to modify 
his income-stream by increasing it in the present at the 
expense of the future. We were then intent on studying 
this phenomenon only on the side of income ; but the effect 
on capital can Im? easily seen by a|)plying the principles of 
The Nature of Capital and Income, Chapter XIV. If a 
modification of the income-stream is such as to make the 
present rate of realized income exceed the "standard" 

' Cf. Edwin Cannan, Zoe, eit. 

* Court d'teonomie Politique, Vol. II, Lausanne, 1897, Book III. 

• Th* Sociologiad Theory of Capital, Chi»p. Xlll. 



I 
I 






J 



k 



232 



THE RATE OF INTEREST 



[Chap. XII 



I 



III si 



income, capital must be depleted to the extent of the excess, 
and the individual will grow poor. This may be brought 
about by borrowing immediate income and pa}ring future 
income, or by selling those instruments the income of which 
is far distant, and buying those which have more immediate 
returns. Individuals of the type of Rip Van Winkle, if in 
possession of land and other durable instruments, will either 
sell or mortgage them in order to secure the means for 
obtaining enjoyable se^^•ices more rapidly. The effect will 
be, for society as a whole, that those individuals who have 
an abnormally low appreciation of the future and its needs 
will gradually part with the more durable instruments, 
and that these will tend to gravitate into the hands of those 
who have the opposite trait. By this transfer an in- 
e quality in the distribution of c apital is g raduallyjeffectej, 
and this inequa lity^ _once_ achieved, t^n ds to perpetuate 
itgelL The poorer a man grows the more keen his apprecia- 
tion of present goods is likely to become. When once the 
spendthrift is on the downward road, he is likely to continue 
in the same direction. When he has surcroded in losing 
all his capital except his own person, the process usually 
comes to an end, because society, in self-protection, decrees 
that it shall go no further. But where there is no such 
safeguard, the unfortunate victim may sink into even lower 
stages of debt servitude, as in Java' or Russia. Reversely, 
when the accumulator is well advanced in his accumulations, 
his rate of preference for the present diminishes still further, 
and accumulation becomes still easier. Hence, in some 
countries the rich and poor come to be widely and per- 
manently separated, the former constituting a hereditary 
aristocracy and the latter a helpless and degraded peas- 
antry. 

Fortunately, however, nnnthp|- fflptrir ant^p. which tends 
to counteract these tendencies. This , is >hA offpjp ^ nf \\f}^^J 
It has ab^ady been noted that one's rate of preference for 

' Sec Prof Ciivo Day, Tke Dutch tn Java, New York (lUcmllliui), 
1004, Chap. X. 



Sec. 6] R6lE OF INTEREST IN ECONOMIC THEORY 233 






present over future income, given a certain income-stream, 
will be high or low according to the past habits of the in- 
dividual. If he has been accustomed to simple and inex- 
pensive ways he finds it fairly easy to save and ultimately 
accumulate a little property. The habits of thrift being 
transmitted to the next generation result in still further 
accumulation, until, in the case of some of the descendants, 
affluence or great wealth may result. Reversely, if a man 
has been brought up in the lap of luxury he will have a 
keener desire for present enjoyment than if he had been 
accustomed to the simple living of the poor. The effect of 
this factor is that the children of the rich, who have been 
accustomed to luxurious living and who have inherited only 
a fraction of their parents' means, will, m attempting to 
keep up the former pace, be compelled to check the accumu- 
lation and even to start the opposite process of the dissipa- 
tion of their family fortune. In the next generation this 
reverse movement is likely to gather headway and to 
continue until, with the gradual subdivision of the fortune 
and the increasing reluctance of the successive generations 
to curtail their expenses, in the third or fourth generation 
there comes a return to actual poverty. It thus often 
happens that there is a tendency for the accumulation and 
dissipation of wealth to occur in cy^'leg^ If there is the 
conjunction of favorable circumstances, as thrift, ability, 
and good fortune, a few individuals will rise from the 
lower ranks. They accumulate a few thousand dollars, 
which, imder like favoring circumstances, in the next gen- 
eration or two may become several millions. Then the 
un favorable e ffects of lu xury begi n, and in an equal num- 
bw- oJ generations the majority of the heirs have returned 
to the level at which their ancestors began. An old adage 
liac stait-d this observation in the form, " From slnrt sleg Yga 
Id shirt sleeves in four generations." This cyclical move- 
ment is more apt to occur in countries like the United 
States, where, owing to the rapidly changing conditions, 
there ia a larger number of opportunities either for rising 



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234 



THE RATE OF INTEREST 



[Chap. XII 



or falling in the economic scale. Where, as in the older 
countries of Europe, conditions have become fixed and less 
favorable to changes of any kind, the tendency of the 
distribution of wealth is to remain relatively unchanged. 
This is especially true where, as in England, the customs 
as to the inheritance of property have tended to keep 
large fortunes intact in the hands of the eldest son. 



J. 



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§6 

In tbe^neral causat ion of distribution which has thus 
J been outlined, the centra l role is played by the ind ividual 
I rate of preference forjresent over future inc ome, which , 
a s we h ave seen, is the subjective prototype of the rate of 
ijiterfist. The study of the theory of interest, therefore, 
lays the foundation for a study of the theory of distribution. 
The objective rate of interest represents the norm to which 
the individual adjusts his rate of preference for present 
over future income, and in this adjustment he changes his 
economic status for better or worse. The existence of this 
general market rate of interest to which he adjusts his rate 
of preference supplies an easy highway foi the movement of 
his fortune in one du^ction or the other. If an individual 
has spendthrift tendencies, their indulgence is facilitatcil 
by access to a loan market ; and reversely, if he desires to 
save, he may do so the more easily if there is a market for 
savings. The irregularities in the distribution of capital 
are thus due to the opportunity to effect exchanges of parts 
of the income-stream separated in time. The rate of 
interest is simply the nmrket price for such exchange. 
By means of this market price, both those who wish to 
barter present for future income and those who wish to 
do the reverse, may satisfy their desires. The one will 
gradually increase, and the other decrease, his capital. 
If all individuals were hermits, it would be much more diffi- 
cult eithpr to accumulate or to dissipate fortunes, and the 
distribution of wealth would therefore be much more even. 



■■ti 



Sec. 6] ROLE OF INTEREST IN ECONOMIC THEORY 235 

Inequality arises out of the exchange of income, carrying 
some individuals toward wealth and others toward poverty. 
The inequality of wealth is facilitate<l by the existence of a 
loan market. I n a se nse, then, it is true, as the socialist 
maintains, that inequa lity b due to social arrangements; 
but the arrangements to which it^ Is' due afenot, as he'as- 
sumes, primarily such as take away the opfX)rt)inity to rise 
in the economic scale; tl^ey are the contrary arrangements 
which facilitate both rising and falling,^ accord ing to 
tFf fKnipft nf ^hp individua l. The improvident sink like 
lead to the bottom. Once there, they or their children find 
difficulty in rising. Accumulation is a slow process, and 
especially slow when the great numbers of the f>oor have, 
by competition, reduced the values of their services so low 
that the initial saving becomes almost impossible. 

This is not the place for following out these tendencies 
and their sociological effects, nor neefl we stop to answer 
the many questions which arise in such an inquiry, such as, 
What is the effect of a change in the rate of ititr-rest in 
stimulating or discouraging the accumulation or ili.s."«ipation 
of capital ? ' Or, ^\'hat is the effect on the poor of the luxu- 
rious habits of the rich? Nor are we confeniod with the 
other factors which influence the 'listribution of wealth, 
but which do not involve the rate of iiiterest. We are ut 
present content merely to prepare th»' way for their an.swer 
by indicating the nature of the problems ami the relation 
of the theor.- of interest to them. 

' .Se« E C. K. G'jtiaer, lnler<»t and Savinr;, L^r.-ion 'Macmillari), 
19(W. 



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CHAPTER XIII 



APPUCATION TO ACTUAL CONDITIONS 



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§1 

We have now completed the fonnal statement of our 
theory of interest. It remains to show in what way thb 
theory may be brought into connection with actual experi- 
ence. For this purpose we need first to classify the various 
forms which interest takes. 

We have seen that the rate of mterest discloses itself 
m two ways; namely, as explicit and implicit interest. 
We begin with explicit interest, or the interest in a loan 
contract. From the standpoint of the borrower, loan con- 
tracts may be classified as follows : — 



f 



Loan* 



For private 
purposes 

For public 
purposes 
(municipal, 
etc.) 



For business 
purposes 



To offset misfortune or improvidence. 
To offset fluctuations in income and outgo. 
To anticipate improvement in financial con- 
dition. 

For military purposes. 
To offset fluctuations in revenue and ex- 
penses. 
For public improvements. 
' Crop liens. 
Commercial paper. 
Accommodation paper. 
Call loans. 

Mortgages on farms. 
Mortgages on city real 

estate. 
Mortgage bonds of cor- 

porationa. 
Debentures of corpora- 
tiona. 



Short or 
periodic 
loans 



Long or per- 
manent loans 



23« 



8k:. 1] APPLICATION TO ACTUAL CONDITIONS 



237 



PtivEte jCHUis are loans of individuals for personal purposes 
other than those arising out of business relations. Of these, 
loans contracted becaa<?e of misfortune or improvidence, 
thou^ to-day constituting a very small fraction of total 
indebtedness, represent probably the original type of loan. 
It was against such loans that the biblical, classical, and 
mediaeval prohibitions and regulations -vere rlirecterl, and 
it is only against them to-day that, in enlightened com- 
munities, r^ulations affecting the rate of interest still 
survive. It is such loans that .supply most of the business 
to pawn shops, the patrons of which are usually victims 
of misfortime or improvidence. It is clear that the theory 
of interest which has been propounded applies to this 
species of loan. Sickness or death in one's family, or losses 
from fire, theft, flood, shipwreck, or other causes, make 
temporary inroads upon one's income. It is to tide over 
such a stringency in income that the loan is contracted. 
It ekes out the less adequate income of the present by 
sacrificing something from the more adeqiiate income ex- 
pected in the future. Similar principles apply to the spend- 
thrift, who, though not a victim of accidental mirfortune, 
brings misfortune upon himself. He borrows in order to 
supplement an income inadequate to meet the r- <juire- 
ments which he has set him.seif . while he trx'ts for repay- 
ment to the shadowy resources of a fiistant future. It is 
evident, therefore, that the loan.* j'ist described are made 
for the sake of correcting an income ciirve the time-shape 
of which is incc«ivenient or intolerable. 

The second class of personal loons comprises those grow- 
ing out of such Suctuatiooa in. incocae as are not diie t/) 
mi^OTtune or imprcd'ience. Many peryms receive their 
money-income in very irrnriiar and uneqiial in.«talments, 
while their money outgo may likewise have an irregiilar 
time-schedule. Unless the two *i<ies of the accoimt happen 
to synchroniie. the in<iivid'jai will be alternately "shfirt" 
iu-i "5'jjsa."' Thus, if be receivps hi.* Iarir»Mf. h'. !<!«»< is in 
Jinuary, but has to meet his largest expetwes. let ti^ My 



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THE RATE OP INTEREST 



[Chap. XIII 



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taxes, in September, he is likely to borrow at tax time for 
the ensuing four months, in anticipation of the January 
dividends. That is, he borrows at a time when his inconK^ 
stream would otherwise be low, and repays at a time when 
it would otherwise be high. The effect is to level up the 
fluctuations of his income. 

The third class of personal loans comprises those which 
grow out of large expected additions to income. Heirs 
to a fortune sometimes borrow in anticipation of their 
bequests. A considerable volume of such loans has un- 
doubtedly been contracted, especially in Great Britain. 
The borrower in this case is evidently trying to enjoy in the 
present some of the income which is promised for the future ; 
in other words, to alter the timenshape of his income-stream 
in accordance with his desires. The same motives actuate 
young men preparing for life, and explain the loans which 
are often contracted by them for defraymg the expenses 
of education. It was for such persons that Benjamin 
Franklin left his peculiar bequests to the cities of Phil- 
adelphia and Boston in 1790. To each he bequeathed 
£1000 to be lent out in small sums at 5 per cent, to young 
married "artificers." The sums repaid were to be added 
to the fund and again lent. 

§2 

In the case of public loans, we find the same general 
principles in operation which we have just seen to apply to 
private loans. By a public loan is meant a loan contracted 
by a public corporation or association, such as a state, 
county, municipality, school district, or other administrative 
unit, as well as such quasi-public institutions as churches, 
hospitals, and public libraries. Public loans may be sub- 
divided into three classes : (1) those growing out of military 
exigencies; (2) those prowing out of fluctuations in income; 
(3) those growing out of need for public improvements. 

The first cl.'vw, loivns for war and war preparatiosi, cor- 
responds to the case first considered under private loans, — 



Sfc. 2] APPLICATION TO ACTt'AL (X)NI)ITrON'H 



230 



loans growing out of mlsfijrtuno. Ordinarily the fixixmacH 
of govemi. nt are defrayofl out of taxf^, which con.stituto 
a regular de^iuction from the inoorrif^ of the ta.xf)ayerH; 
but war brings with it extraordinary exf^n.sfis which mii.st 
be met by extraordinary rnean.s. If the ooHt of war wore 
wholly defrayer! by taxea, the taxpayern wouM nuffer large 
and sudden reductions in their incorn"?i for the time being. 
They prefer instead to place .^orne of the burrlen on the 
future, — even upon posterity. Tlii.-i Is accomplished by 
war loans, to be repaid many yearn after the war is ov«;r. 
Thus, so far as the taxpayers are concerned, thf; exfx;n.sft 
of the war is spread over a considerable time, and the im- 
mediate reduction in their income-stream, which would 
otherwise be causes! by the war. is avoide^l. But for the 
world as a whole this is not tnie ; for others than the tax- 
payers, namely, the bonrihoMers, mast l;ear the brunt of 
the re<iuction in the w-orlds income-stream which the war 
had brou^t about. It follows that the Ls-sue of bond^ has 
ad its ultimate effect, not a postponement of the co-t of the 
war, but its shifting from one cla-ss to another. We thu.-i 
see that war loans clearly exemplify the th<<>r\- of k/ans 
which has been elaborateti. The nee.i for «uch loan.- ltowh 
out of an impen'iing depression in the income- trearri of 
the taxpayers. 

The second class of public loans, namely, loans due to 
Suctiiations in public receipts and ■ii.--bursernents, corre- 
spon'is to the secon'l cLa.^s of privj.r.e loafi.-. A zovemment 
receivea its income chiefly in tax'^. an 1 only onoe a year, ' 
whereas its outgo occurs lay by iay and rrionth by month. 
It thus happens that a zovemn^ent Is alterr.ately ar-r-^malat- 
ing a Large siu^liis and ?uf?erinz a larze ijef.oit. The in- 
convenient effects of this hav^ been or ten rnrr.rr^f-ntM upon, 
esp^ecialiy in this counrr.-. where the T.-ea-'ur/ for half a 
cen'ury has h^een n^Iati'/ely in'iepen'ient of ifi-^.titutiona 
of cre<iit.' This inconvenience rriay be Larg^-ly avoide<i by 



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240 



THE RATE OF INTEREST 



[Chap. XIII 



a business relation between the government and some in- 
stitutions of credit, as, for instano-, in England, between 
the government and the Bank ot England. The govern- 
ment may correct the irregularities in its income-stream 
either by borrowing for current expenses in anticipation of 
taxes, or by lending at interest; that is, depositing the taxes 
when first received, in anticipation of the expenses which 
follow. 

The third class of public loans comprises those for public 
improvements, such as the erection of government build- 
ings, the improvement of roads, bridges, and harbors, the 
construction of municipal waterworks or schoolhouses, or 
the prosecution of other government enterprises. In all 
such cases it is usual to finance the enterprise by issuing 
bonds. The reason clearly is that these improvements 
constitute an extraordinary cost, similar to the expense 
of a war, which, without the issue of bonds, would cause 
a temporary depression in income-streams. The taxpayers 
as a whole cannot afford the first heavy drain, even with 
the prospect of substantial benefits to follow. They 
therefore prefer, in place of such a fluctuating income- 
stream, a more uniform one. To secure this uniformity is 
evidently the purpose of the loan. We see, therefore, that 
this class of loans also exemplifies the theory of the re- 
lation of borrowing and lending to the time-shape of an 
income-stream. 

§3 

The third and last general class of loans is that of business 
loans. Business loans are loans growing out of trade. 
They are commonly, though not very felicitously, called 
"productive loans," whereas the loans which have thus far 
been considered would commonly be called "conaumption 
loans." Business loans constitute by far the most impor- 
tant class of present indebtedness. Mr. George K. Holmes 
has estimated that at least nine tenths of the existing m- 



Sic. 31 APPLICATION TO ACTUAL CONDITIONS 241 



debtednem in the United States was incurred for the ac- 
quirement of the more durable kinds of f)roperty, leaving 
not more than one tenth, and probably much less, as a 
"consumption debt," or a debt necessitated by misfortune. 
No theory of interest would therefore Ije complete which 
should fail to apply to business loans. 

At first sight it would seem that the theory which has 
been given, depending as it does on the enjoyable incom.;- 
stream of an individual, can apply only to consumption 
loans. Net income, as was shown eLsewhere,* consists 
of one's personal satisfactions, — nourishment, clothing, 
shelter, and other enjoyable serv-ices. The loans of business 
seem too impersonal to be explained by a theory which 
depends wholly on personal satisfactions. In fact, it has 
often been said by economists, in treating this subject, 
that consumption loans are explained on quite other 
principles than loans contracted in th^ regular course 
of commercial transactions. Even Bohm-Bawerk, in his 
Positive Theory of Capital, states that consumption loans 
are explained by the preference for present enjoyment 
over future, but that the loans of business are chiefly due 
to the "technical superiority of present goods," which 
grows out of the greater productiveness of lengthy pro- 



A little consideration will show, however, that business 
loans are not so different from consumption loaas ; that they 
also are used to tide over lean rimes in anticipation of pros- 
perity; and that they are conu acted to rectify the distor- 
tiwi of the income-stream which would otherwise result 
from busine^ operations. The truth is — and it should 
never be lost sight of - that business men conduct their 
busiaeas with an eye aiwa>-3 to enjoyable income. This 
13 the object of all their operations, though it may be ob- 
scured by the interposition of the many mt*;rmediate steps, 
or "interactions." Buaines. operations are not ends m 
uiemaeivea, but means for ultimate personal enjoyment. 

' n« Xaturt of Capital and Iruome, ChApfl IX, X 



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242 



THE RATE OF INTEREST 



[Chap. XIII 



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[IIP 



A business man not only conducts his business for what 
he can get out of it for fxjrsonal use, but also regulates it so 
that what thus comes out may accrue not in irregular 
spurts, but so far as possible in such a stream as will syn- 
chronize with the exigencies of his home life. In a sense 
we may say, therefore, that it is his home that " runs " his 
business rather than his business that " runs " his home, 

§4 
In order to see how the theory of interest which has 
been explained applies to business loans, let us consider 
the two chief classes; namely, short loans, or those growing 
out of periodic variations, and long loans, or those for rela- 
tively permanent investment. The.jhort_or periodic Jojins 
are those which grow out of the change in the seasons and 
the ebb and flow of business. These loans are^tained 
usuall ^but once a y ear at a specifed time. Th^lTm^ 
cause is the cyclical change in the position of the earth in 
reference to the sun. This gives rise to the cycle of the 
seasons, the effects of which are felt not only in agriculture, 
but in manufacturing, transportation, trade, and banking! 
'Hie alternate congestion and thinning of the freight busi- 
ness, the alternate stocking and depletion of raw ma- 
terial in factories, the fluctuations of trade activity, both 
wholesale and retail, the transfer of bank deposits between 
New York and the West for "moving crops" or for other 
uses, all testify to the seasonal rhythm which is constantly 
felt in the great network of business operations. Without 
some compensflfinpr appnr^tu s 3uch _as that foLborroiong. 
a nd lending, thes e seasonal flu p.tiinfinna wni.| f ^ tr ansmit 
themselves to the"fi^S" &nj^jrabIeJncome:atream.s afjn(]\. 
vidualSj^_and_JhMe_income^ 

ev e n, flflw , wni iid a c fime by fits ^d starta^jLgmnmer of 
lavish enjoyment being foUowed^^by a winter on short 
rations. ^ — ' 

To show how borrowing and lending compensate for 
these fluctuations, we may consider first wliat is perhaps 






Sbc. 4J application TO ACTUAL CONDITIONS 



243 



the moet pcmitive tjpe of the short or periorJic loan; 
namely, t hat contr acted by poor farmers in anticix)ation of 
crops. In the South among the negrr>eH this takfjs the 
form of what is called a "<^rop Ijpn/' the cultivator borrow- 
ing money enough to enable him to livf until cro[> timr; and 
pledging repayment from the crop. Here, evidently, the 
purMse of the loan Is to eke out the meager income of 
tui! ; ijoymeata. Tne loan, in other worrls, is for fu^)- 
si.<* ace. T!.: -ase, therefore, is covered by the theory of 
int«'- 6t ^^hi:.h ':;v been given. 

Vc 'jitK^.^l r /.■ o show that this same theory of interest 
V." •;, J-.t: ") io r.- contracte<l in the commercial world at 
u-c '. .-^ vii-t-- r .V commercial loan is contractwl for the 
-'. • *• C'- '--in goods, with the expectation of repayment 
;. ■ : V/.- .!e. A common form Is what Ls called "com- 
m . !..; pAi^i." A ready-made clothing house may buy 
0-- -^^ m 3u:.;mer in order to sell them in the fall. If 
ik v^rp.fioiiij were conducted on a s'rictlycash basis, 
the tendency would be for the mcome of the clothier to 
suffer great fluctuations. He could realize but little during 
the summer, on account of the enormous e.xpease of stock- 
ing-in for fall trade, whereas in the fall he r ould obtain large 
returns and live on a more elaborate scale. This wo;ld 
mean the alternation of famine and feast ui h'w family, 
f'jne way to avoid such a result would be to keep on hand a 
large supply of cash as a buffer between the money-income 
and personal expenditure. In this ca.-e the fluctuations 
would not reach the stage of personal enjo>7nent, but 
would sp«id tl ir fo* -^ in fluctuati'n.s of the volume of 
cash. A more effect! and less wa.ateful method for the 
merchant, o f takintt thejtinks our^ of ikjncome^ia by 
n^oti ating commercial paper . The clothier, iastead of 
suffermgine large cash e.xpen^*: of 5tocking-in in s-jmmer, 
will make out a note to the manufacturer of overcoats. 
-Vfter the fall trade thi.s note b? f^xtmsr^mh.f-d, h.^vins' 
f'ilfilled ita function of levelimr the Lncome-stre^m of the 
clothier. 



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THE RATE OP INTEREST 



[Chap.XXI: 



Sometimes merchants contract short-time or periodic 
loans, not for some -pecific transaction tuch as the purchase 
of stock in trade, but for general busmess purposes, as, for 
mstance, improvement or enlargement. In this case, the 
extraordinary expense involved may be met by a species 
of loan called " accommodation pape r." Evidently its 
function is precisely the same; na mely, to re ctifythe time- 
shape of tlfft mpnmf^trnam In Wall Street and other 
speculative centers a type of loan known as the "call loan" 
is common, subject to redemption at the pleasure of the 
lender, and used by the speculator for the purchase of se- 
curities. Tlie speculator borrows when he wishes to buy, 
and repays when he has sold; and by adroitly arranging 
his loans prevents the sudden drainmg or flushing of his 
mcome-stream which these purchases and sales would 
otherwise involve. 

In all the cases which have been described, the loan grows 
out of a purchase or group of purchases; and since the 
tendency of every purchase is to decrease one's income, and 
of every sale to mcrease it, it is clear that loans contracted 
for a purchase and extinguished by a sale have as their 
function the obliteration of these decreases and increases 
of the income-stream. It is clear, therefore, that these 
commercial loans fit mto the theory of interest which has 
been propounded. 

55 

The second class of busmess loans is that of long-time 
loans or "permanent" mvestments. In this class are placed 
mortgages, whether on farms or on urban real estate. As 
shown by Mr. George K, Holmes of the United States Census, 
more than two thirds of farm mortgages are contracted for 
the purchase of the property, and the remainder principally 
I for improving it, or for the purchase of farm implements 
and other durable wealth or property. These purchases 
or improvements, involving as they do large expenditures, 
would be difiicult or iin|)088ible without l(Mins. If the attempt 



8m. 6] APPLICATION TO ACTUAL CONDITIONS 



245 



were made to enter into them without recourse to a loan mar- 
ket, they would cause temporary depressions in the income- 
streams of the farmers. The farmer who attempted to buy 
his farm without a loan would have to cut down his current 
expenses to a minimum and suffer a correspondmg reduction 
in his enjoyable mcome-stream, unless he avoided this result 
by some other of the methods which have been explamed, 
such as " the method of buying and selling." For instance, 
he may sell some other capital in order to buy his farm. 

Mortgages on city lots are usually for the purpose of im- 
proving the property by erecting buildings upon it. Here, 
again, the expense mvolved would, if taken out of income, 
reduce the mcome of the owner temporarily to very small pro- 
portions. He naturally prefers to compensate for such extra- 
ordinary inroads by a mortgage which defers this expense to 
the future, when his receipts will be more adequate to meet it. 

We come next to the loans of business corporations and 
finns,8uch, for instance, as raih-oad bondsand debentures, the 
securities of street railroads, telegraph, and telephone com- 
panies, and other "industrials." These loans are usually 
issued for construction purposes, as in cases in which a rail- 
road wbhes to extend its lines, replace iron rails with steel 
ones, or a curved route by a straighter one. The borrowers 
in this case are the stockholders. Tliey may be said 
to contract the loan in order not to have the expenses 
of the improvement taken outof their dividends. Sometimes, 
where the dividends are large and the stockholders few, divi- 
dends are applied, in part or wholly, to the making of im- 
provements, BiiJLordinaalx^tliereductionmllieatockhQkkr's 
income-stre am is avo ided by the device of invitingt he bond - 
holders to cancel the_outgaes connccti!dwith thn impro yp- 
nic nt, m consideratio n of receiving a part of thft iucreaafii^ 
inco mewhich will later ToUow from these improve atcnte! ] 

We sec, therefore, that business loans, or loans growing 
out of a purchase and sale, are as truly for the purpose of 









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246 



THE RATE OP INTEREST 



[Chaf. XIII 



il 



reshaping the income-streams as are private and public 
loans. The reasons that business loans are usually re- 
garded by economists as on a different footmg from private 
and public loans appear to be three : — 
I 1. The proceeds of business loans are usually spent, not 
for the borrower's bread and butter, but for durable 
capital; consequently the loan seems not to be connected 
with mcome, but rather with capital. A spendthrift 
who borrows $1000 in order to pay for wmes is certainly 
to be distinguished from a merchant who borrows the same 
sum m order to pay for new stock in trade. Yet in either 
case the loan adds $1000 to immediate income beyond what 
the income would have been wUhout the loan hut wiih the 
expense for the wines or the stock in trade. 

To make the comparison as simple as possible, let us sup- 
pose that the two men were each enjoying an incow^ 
$10,000 a year. This represents the value of their nou.i. . 
ment, clothing, shelter, etc., which constitute true income. 
In the year (say 1901) of the proposed loan, each man has 
two courses open to him : (1) he may meet the expenditure 
for wines or stock in trade by sacrificing one-tenth of his 
$10,000 worth of nourishment, clothmg, shelter, etc., or (2) 
he m y meet it by borrowing. If the spendthrift follows the 
first course and meets the ex{)enditure by skimping out of 
his $10,000 income, he will not suffer any change in the 
value of his income, hut will obtaui $1000 worth of wine 
drinking, at a sacrifice of $1000 worth of other pleasures. 
His income for the year 1901 will still be $10,000. Nor will 
there be any necesrory change in the income of subsequent 
years. He merely changes the composition of this year's 
enjoyable mcom > partly into wine-drinking, but his income 
remains $10,000 a year. Tlie merchant, however, who 
skimps out of lus $10,000 income in 1901 in onier to pay for 
stock in trade, will actually reduce his enjoyed incotiie of 
1901 by $10(K); for this ^twk in trade, unlike wine, will 
not give any innnetlisite satisfaction. It wrve-t only as :i 
means of .necuring futun' satisfaction.^, .so that, let ms «av. 




sk.o] application to actual conditions 247 



$1100 may be enjoyed in 1902. The income of the mer- 
chant will thus be, not $10,000 each year, as was that of 
the spendthrift, but $9u00 in 1901 and $11,100 in 1902. 

Having seen what efTect the expenditures would have in 
the two cases viUhout recourse to borrowing, we next ask 
what will be the effect in the two ca.ses of borrowing $1000 
in 1901 and repaying, let us say, $1050 in 1902. Tlie spend- 
thrift who borrows to get his $1000 worth of wine will have, 
in 1901, that much more of enjoyed income, making i total 
enjoyed income in that year of $11,000, and in 1902, when 
called upon to pay his debt of $1050, he will have to sacrifice 
just 80 much out of his mcome of $10,000 for 1902. His 
resulting enjoyed mcome will therefore be in 1902 only 
$8950. As to the merchant, he will be able to buy his 
stock in trade m 1901 without the neces.sity of any sacrifice 
out of his $10,000 for that year, so that his income in 1901 
will be $10,000. In the following year he will pay the 
$1050 for his loan out of the $11,100 for 1902. ((Jf the 
$11,100, $10,000 was the original income, and $1100 what 
we have assumed to be the returri.s from \m .stwk in 
trade.) He will thus have $10,0.t() left as his real income 
for that year. 

Comparisons are .shown in the following tables : ~ 

INCOME OF SPENDTHRIFT 
WHO BUYS $1000 WORTH OF WINE 



f^'^ 

•^ii> 



IMl 


IMt 


Without loan $10rif»O 


$1M,0(K) 


With loan . 1 1 mtit 






INCOME OF MERCHANT 
WHO BUYS $1000 WORTH OF STr»C'K IN 


TRADE 


IMI 


IMS 


\\iih.>ut loan $ o.OOi) 

With loan uunH} 


$11, KM) 

lo.aio 





#" 



"I 



ii 



248 



THE RATE OP INTEREST 



[Chap. XIII 




It is clear that in each case the effect of the loan is to add 
11000 to the income of 1901 and subtract $1050 from that 
of 1902. There is absolutely no difference between the 
two men in this respect. The difference between them b 
chiefly that the spendthrift is making a foolish and the 
merchant a wise addition to his income of 1901 at the 
expense of that of the year foUowmg, and this difference is 
only one of degree, due to the fact that the final satis- 
factions by means of the wine come earlier than the 
satisfactions obtained by means of the stock in trade. 

2. But the example given of the "consumption "-loan is 
not the only one possible, and no doubt it will still seem to 
some readers that there must be another difference between 
production- and consumption-loans. Suppose the case of a 
victim of misfortune, such as illness. To tide him over his 
emergencies he is compelled to borrow, using the proceeds 
of his loan merely to meet his grocer's and butcher's bills. 
Here is indeed a case of a " consumption "-loan which is not 
foolish, and yet is surely different from the loan of the mer- 
chant to buy stock in trade. 

The effect of business loans is to enable a merchant to 
embark on an enterprise, while personal loans merely relieve 
noed.s. Let us examine this difference. It is not a dif- 
ference which invalidates the principle that both loans are 
additions to present income at the expense of future income. 
The unfortunate, with his misfortune, but vnthout his loan, 
would have, let us say, an income of $9,000 in 1901 and 
$11,100 in 1902, which are the same figures we assumed 
for the merchant irith his investment but ivithout his loan. 
With the loan, thereforo, the unfortunate and the merchant 
would be in the same situation. Both would have $10,000 
in 1901 and $10,050 in 1902. The effect of the loan in the 
two cases is thus identical so far as their income-streams 
are concerned. The difference is that the unfortunate, 
if deprived of his loan, coukl not escu|)e from hia income- 
stream of $9,000 in 1<K)1 and $11,100 in 1902, whereas the 
merchant, if deprived of hia loan, could, if he rhose, giv. 



^^ 



iiiii.. 



8bc. 6] APPLICATION TO ACTUAL C50NDITI0NS 



249 



up the mvestment in new stock altogether. If the merchant 
did not have this option, the two cases would be so similar 
that not even a stickler for the distinction between con- 
sumption-loan and productive-loan would assert any es- 
sential difference. For, suppose the merchant has ah^ady 
been committed, sometime previously, to buy the goods for 
his stock in trade, not, perhaps, reaUzing that he would be 
unable to pay for them without borrowing or skimping. 
When the time arrives that he must of necessity buy the 
goods and pay for them, he finria that a loan is badly needed 
to avoid pinching himself in income. He will now think 
of the loan, not as enabling him to buy stock in trade, for 
that must be done anyway, but as enabling him to buy his 
bread and butter. In short, his loan , like the unfortunate;8 J 
ja ^necessity-loan . It is because ordinarily the merchant 
is not thus constramed to buy the good.s that the loan is 
connected, in his mind, with their purcha.se rather than 
with his private necessities. It still serves to relieve 
that mcome, but he has another method of relief, — not 
to buy the goods at all. The contrast, t hen, between 
him s^nc\ tho iinf^rtiiryy^^ jg "slmply that JifiIEik8-A_third 
pcfSsih U rrniin a whioh the tm^r finp« pnf [ ^«vp This is 
shown in the following tables : ~ 

INCOME OF MERCHANT 



1901 



IMM 



.4 Without loan am' without inventment 
B Without loan but with ir.\estmf-nt . 
' W ith loan and with investment . . 



$10,000 tlO.OfK) 

9,(XJ0 ll.HJfJ 

10,000 10,0.50 



I 
} 



'If 

» it 



ih 



I', 



I i. 



,1 

^ IS 






INCOME «JF IXFORTUNATE 



1*01 



1308 



B Without loan $ 9.fjrX) $11,100 

'^ With loan 



lu.tXK) 



10,050 



- If 



250 



THE RATE OF INTEREST [Cbap.XIII 



"St 



' » 







We see here that the unfortunate has two options, B and 
C, and the merchant three possible options, A, B, and C. 

^It is the existence of this third option A which nuikes the 
chief real difference between the merchant borrower and the 
borrower in misfortune. So far as the other two options are 
concerned, the two men are similarly situated. That this 
fact is overlooked is due to the unconscious substitution, 
in considering the case of the merchant, of the third option, 
A, for the second, B. That is to say, when the effect of 
a merchant's loan is considered, this effect is measured 
with reference to his situation without the loan and 
toithout the purchase of the goods, instead of with reference 
to his situation without the loan but vrith the purchase. 
The latter method measures the effect of the loan in the 
sense that it shows the difference produced by its pres- 
ence or absence, other things being equal. It treats the 
merchant's loan in the same way that the imfortunate's 
loan is treated, and thus puts the two on the same 
basis. The true sequence of thmight then is: Of the 
two options A and B, the merchant selects B (buying 
the goods) because it has the greater present value (or, what 
amounts to the same thing, because the rate, 10 per cent., 
of the return of $1100 on the sacrifice of SICXX) is greater 
than the rate of interest, 5 per cent.) ; then he selects C 
(borrowing money), which has the same present value 
as B, but a more desirable time-shape. This description 
takes account of the whole series of operations, and cor- 
responds to the principles propounded in Chapter VIII. 

3. It is the third option A which gives rise to the con- 
tention that the loan produces a profit not possible or easy 
without it, and that it is, therefore, " productive." We have 
just seen that the loan phenomena are resolved into two 
separate steps, the rejection of il in favor of B, and the 
rejection of B in favor of C. Yet since it may often happen, 
as shown in Chapter VIII, that the first step (choice of 
options) would not be taken unless the second step (loan) 
'*'ere already in contemplation, it is true that, in a sense, 



Bao. 7] APPLICATION TO ACTUAL CONDITIONS 251 



Til 



the choice of the loan includes the choice between the 
options A and B. Looked at in this way, the effect of 
the loan is measurable by comparing C with A, such com- 
parison including both the steps stated. In this sense, 
and in this sense alone, is the loan "productive." It is 
productive in that it enables the merchant to buy the 
goods. He thxis chooses an option (B) which has an 
advantage (over A) in present value, or yields a rate of 
return on sacrifice (10 per cent.) greater than the rate 
of interest. The reason that the loan is regarded as 
"productive," then, is that it gives the merchant the op- 
portunity to make 10 per cent, instead oi 5 per cent. But 
obviously it ia not the loan (choice of C rather than B) 
which yields the 10 per cent., but the choice of options with- 
out the loan (B rather than A). The profit is the advantage 
of B over A ; but the loan merely substitutes C as a more 
desirable equivalent of B. It does not add to the profit, 
though it changes the form in which it appears. After the 
loan, the profit appears in the accounts for 1902 in the 
form of $50 more mcome for C than for A. 

If, after all has been said and understood, any one still 
prefers to call such a loan "productive," no objection is 
offered, provided always that it is made wholly clear 
what is meant by the term " productive." The essential 
point is that our theory of interest is not restricted in 
its application to personal and public loans, but includes 
the loans of bxisiness. These business loans come into 
the same theory as the other loans, and differ only in 
the existence of a wider range of choice in income- 
streams. 

§7 

We have seen that the theor>- of interest which has been 
propounded is adequate to exj^in the motives which lead 
to Ijorrowing and lending in the sictual businesss world. 
The purpoee of loans in all cajses may Ix? said to be to modify 
the shape of income-streams so as to suit the particular 



^'fj 



M 






H. 




252 



THE RATE OF INTEREST 



[Chap. XIII 



P 



9 ^ -» 3 



requirements of the case, — to increase present income at 
the sacrifice of future, and to eke out present scarcity 
in anticipation of future abundance. As Jevons statecl, 
capital is required to enable one to support himself while 
engaged in undertakings which require time. 

The foregoing classification is made from the standpoint 
of the borrower. From the standp>oint of the lender, loans 
do not need to be so minutely classified. The lender is 
usually either one who wishes to invest permanently, or one 
who wishes to invest temporarily. The former may lend 
on mortgage, or he may buy the securities of companies, 
governments, or municipalities, or he maybe a depositor in a 
savings bank. In all cases the lender is evidently sacrificing 
what he might enjoy in present income, in order that he may 
have a still larger income in the future. In other words, he 
is modifying the time-shape of his income curve in a manner 
opposite to that which the borrower pursues. When he 
invests for short times, this course is generally due to a 
periodic fluctuation in his incomenstream, the large present 
flow being precedent to a shortage in the not far distant 
future. Business men and institutions are in this way 
constantly investing for short periods funds which otherwise 
would exist in the form of idle cash. The government 
or individual which we supposed to have borrowed at the 
time of deficit in anticipation of surplus may, instead, fol- 
low the reverse policy of investing the surplus at interest, 
in order to provide better for the payment of expenses at the 
time of anticipated deficit. 

5 8 

The same person may be alternately borrower and lender, 
according to the exigencies of his income-stream. When the 
same person is simuUaneotisly borrower and lender, he be- 
comes a broker for managing credit operations for other 
persons. This is usually the function of institutions such 
as banks of discount and deposit, savings banks, trust com- 
panies, exchange brokerage firms, and mortgage companies. 




-, JU U' 



ir 



Sw:. 8] APPLICATION TO ACTUAL CONDITIONS 



253 



It is through 8uch firms that borrowers and lenders usually 
reach each other, rather than directly ; but whether directly 
or by means of such intermediaries, the borrowers and 
lenders are constantly playing into each other's hands. 
This is particularly evident in the case of periodic fluctua- 
tions; for it usually happens that the same cycle of opera- 
tions which makes one man's income alternately large and 
small will make another man's alternately small and large. 
Thus, when the clothing manufacturer sells to the retailer 
of ready-made clothing, not only does this operation tend 
to make inroads in the income-stream of the latter, but it 
also tends to bring to the former an accession of income 
mconveniently concentrated. For this reason the manu- 
facturer may decide to keep the commercial note which the 
clothier makes to him, rather than to discount it at a bank. 
The manner in which fluctuations in income-streams 
mutually compensate among borrowers and lenders is well 
seen in the South, where cotton planters have long been 
accustomed to borrow of the banks in springtime, to repay 
m the fall after the cotton is sold. Until recently the banks 
which supplied these loans found difficulty in leveling the 
consequent irregularities produced in their own income- 
streams. They were forced to do so largely by keeping an 
idle stock of cash, or investing it at low rates in Northern 
banks. But recently cotton mills have settled in the South, 
with a cycle of income exactly the reverse of that of the 
planters. They buy their crops in the fall, manufacture 
throu^ the winter, and sell in the spring. The conse- 
quence is that they come to the banks for loans in the fall, 
which is just the time when the banks are receiving their 
pay from the planters, and liquidate these loans in the 
spring, at just the time when the banks are in need of 
funds to lend to the planters. In this way the irregularities 
in the income-strt'ank- of both planters and manufacturers 
are leveled, virtually by mutual cancellation, but actually 
through the intermediation of the bank*. 



1 1 



'J 






'J;:. 






..^a 



254 



THE RATE OF INTEREST 



[Chap. XIII 



■ I. i 



Hitherto we have considered loans only with reference to 
the time of issue and repayment. But it frequently happens 
that loans are transferred at points intermediate between 
these two dates. In that case they pass by sale like other 
property, and affect the income-streams of those who buy and 
sell in precisely the same way as if they lent and borrowed. 
The buyer of a security is in the same position as a lender, 
— he parts with present income for the sake of future. 
The seller of a loan security is in the same position as a 
borrower, — he is securing present income and foregoing 
the future interest he would otherwise receive. The price 
at which such loan securities are sold will determine the 
rate of interest realized and borne by the buyer and seller 
respectively. The effects caused by the tranrfer of loans 
may be negatived by later transactions. ITie seller of a 
bond may not really use the proceeds to swell a large income, 
but may reinvest in some other seciuity, and the buyer may 
not hold the security until maturity, but may sell again 
at the next turn of the market. 

What has been said of loan securities applies also to every 
form of property which may be regarded in the same light. 
The buyer of rwlway stock is not very different from the 
buyer of railway bonds, or the lender. He also is sacri- 
ficing present income for future, so far as this particular 
purchase is concerned, even though, as just shown, 
the effect may be negatived by some other transaction. 
Likewise the seller of railroad stock is similar to the seller of 
bonds, or the borrower. The only distinction is that in 
the case of buying and selling stock the rate of interest 
is implicit rather than explicit. 



Ills I! 



§10 

Explicit and implicit interest really differ, however, 
in degree rather than in kind. An income bond, while 



Sbc. lOJ APPLICATION TO ACTUAL CONDITIONS 



255 



nominally yielding explicit interest, raay actually, if the 
income is inadequate, yield quite a different interest, and 
the price of sale takes into account the latter contingency 
quite as much as the former. Preferred stock, likewise, 
while nominally involving the risk of non-payment, often 
represents a case more nearly like that of explicit interest. 
It is quite as possible, on the basis of the purchase price 
and the practical certainty of a definite fixed income, to 
calculate the rate of mterest to be realized to the investor, 
as in the case of the bond buyer. In the case of ordinary 
stock, however, in order to calculate the interest to be 
realized, it becomes necessary to make a forecast of the 
probable dividends. It is where the element of chance thus 
enters that implicit interest really differs from explicit. 
Where the ownership of an article of wealth is total instead 
of partial, the element of chance is always present. In fact, 
bonds, so far as they escape from the universal reign of 
chance, do so only by carving out of the fluctuating income 
arismgfromamass of capital-wealth a certain definite part, 
small enough not to absorb the whole even at its lowest 
ebb. But while the rate of interest is somewhat difficult 
to calculate in advance in the case of other property than 
loan securities, it may be approximately estimated, and 
from the rate which has been actually realized in the past 
it may sometimes even be exactly calculated. In the case 
of land, it is not imcommon to reckon the value of so many 
years' piirchase of the crop returns, on the assumption that 
the same value of the crop returns will continue indefinitely. 
The element of risk, which is so dominant in actual 
busmess relations, has also been considered in the theory of 
this book. The buying and selling of property serve to 
modify not only the time-shape of the income-stream, but 
also the degree of certainty. The investor who wishes lo 
take chances may invest in stock, and he who does not, 
in bonds. Risk constitutes the real difference between 
them, and the reason for the existence of the two types 
of securities. Both are investors, and both sacrifice present 



i 



is* 












u. 




I -^'"riiTWiinrnrr'iimr" r — ¥af«Firry^ 



Micioconr rcsoiution test chart 

(ANSI and ISO TEST CHART No. 2) 




A 



/^^PPLIED IM/1GE I 

1653 toil Md.n Stree' 

Rochest.r, N«i* rorh U609 USA 

(?16) ♦82 - 0300 - Phon. 

("6) iW - 5989 - Fo< 



■li 



; »! 



256 



THE RATE OP INTEREST 



[Chap. XIII 



income for future ; but one assumes a future income with 
risk and the other receives one without risk, or at any 
rate, with no large degree of risk. That stockholders and 
bondholders are both investors is not inconsistent with the 
fact already emphasized that the stockholder is a borrower 
of the bondholder as a lender. In dealing with each other 
they are on opposite sides of the market, the bondholder 
being a buyer or investor and the stockholder a seller or 
borrower. But in dealing with " the company," they are 
on the same side of the market ; both are buyers of 
securities, or^investors. 

Thus by borrowing and lending, or by buying and selling, 
an individual regulates the character of his income-stream 
to suit his individual needs and idiosyncrasies. This ad- 
justment involves comparisons of risk and of futurity, 
and in the latter case involves a rate of interest, implicit 
or explicit. This rate is utilized by individuals to enable 
them to increase or decrease the flow of their income at 
different periods of time, and it is throu^ their efforts to 
do so, by bargaining with each other, that the rate of 
interest is itself determined. The theory of its determina- 
tion applies to the actual loans of business, loans of neces- 
sity, improvidence, or purchase, loans of persons, corpora- 
tions, and loan brokers, and applies also to cases in which 
there are no contract loans at all, but only the buying, 
selling, and valuing of property, in which transactions the 
rate of interest is always implicitly contained. 



Tw 



t« 



'U 



CHAPTER XIV 



,;i 



INDUCTIVE VERIFICATION (MONETARY) 
§ 1 

No study of the principles governing the rate of interest 
would be complete without verification by facts. In this 
chapter those facts will be presented which bear on the 
problem discussed in Chapter V, the problem of apjrrecia- 
tion and interest. The object will be to ascertain the 
extent to which, in the actual world, the appreciation or 
depreciation of the monetary standard is foreseen by bor- 
rowers and lenders, and provided for in the rates of interest 
upon which they agree. 

At the outset the question arises. How can a merchant 
be said to foresee the appreciation of money ? Appreciation 
is a subtle concept. Few business men have any clear 
ideas about it. Economists disagree as to its definition, 
and statisticians as to its measurement. If we ask a 
merchant whether or not he takes account of appreciation, 
he will say that he never thinks of it, that he always 
"regards a dollar as a dollar." In his mind, other 
things may change in terras of money, but money itself 
does not change. Yet it may be true that he does 
take account of a change in the purchasing power of 
money, under guise of a change in the prices of other 
things. In our daily life we seldom think of the earth 
as moving; nevertheless we take account of its rotation 
whenever we speak of "sunrise" or "sunset." During 
a period of paper-money inflation the ordinary man 
conceives the premium on gold as a rise of gold bullion, 
not a fall of the paper money; but he arrives at the 
same practical results. Appreciation of money, whether 
b reference to gold bullion, commodities, or labor, is in 
effect taken account of in the practical man'u forecaat of 
■ 2fi7 



vf: 



"^1' 



'-'J 
-5, 



'it 



'I 



!^^ 



m 






258 



THE RATE OF INTEREST 



[Chap, XIV 




I * 



'Hill 



l# 



all the economic elements which concern him, — the prices 
of his product, the cost of his living, the wages of his work- 
men, and so forth. Moreover, he takes account of the 
relatiij importance of these factors as affecting himself, 
and not of their relative importance in the elaborate aver- 
ages of the statistician, — averages which may emphasize 
some particular commodity or labor whose fluctuations 
have no interest for him. His own aim is not to predict 
the in dex numbers of Sauerbeck of jf'Che United States 
bureau of L abo r, but to foresee those price changes which 
affect his ow^ n e conomic future. To foresee a rise or fall of 
a particular price is to that extent to foresee a change in 
the purchasing power of money. Such forecasts enable a 
man to make reasonably correct decisions, and in particu- 
lar to contract a loan with intelligence. If gold appreciates 
in such a way or in such a sense that he expects for himsolf 
a shrinking margin of profit, he will be cautious about bor- 
rowing unless interest falls ; and this v ery unwillingness to 
borrow, lessening the demand in the " money market," will 
brin g inter ggt_dQSiL. On the other hand, it intlation is 
going on, he will see rising prices and rising profits, and 
will be stimulated to borrow capital unless interest rises ; 
moreover, this willi n gngsf to bor row will its elf raise interes t. 
Foresight is clearer and more prevalent to-day than 
ever before. Multitudes of trade journals and investors' 
reviews have their chief reason for existence in supplying 
data on which to base prediction. Every chance for gain 
is eagerly watched for. An active and keen speculation is 
constantly going on which, so far as it does not consist 
of fictitious and gambling transactions, performs a well- 
known and provident function for society. Is it reasonable 
to believe that foresight, which is the general rule, has an 
exception as applied to falling or rising prices ? 

§ 2 
Appreciation and depreciation in this book are used in 
a purely relative sense. If jold appreciates relatively to 



Sue. 2] INDUCTIVE VERIFICATION (MONETARY) 259 



silver, then necessarily silver depreciates relatively to gold. 
Any standard appreciates 1 per cent, relatively to another 
standard if a certain amount of it now commands 101 
imits in this other standard, when previously it commanded 
only 100 units. 

General evidence that an expected appreciation or de- 
preciation of money has an effect on the rate of interest in 
that money can be obtained from several sources. During 
the free-silver agitation of 1895-6, it was observed that 
mimicipalities could often sell gold bonds at better terms 
than "currency" or "coin" bonds. There was a strong 
desire on the part of lenders to insert a gold clause in 
their contracts, and they were willing to yield something 
in their interest to secure it. The same tendency was 
strikingly shown in California ' during the infiation period 
of the Civil War. For a time, gold contracts could not be 
enforced, and in consequence interest rates were excep- 
tionally high. 

During a period of progressive paper inflation the rate 
of interest in contracts drawn on a paper basis is high. 
This was true during the Civil War, and also during the 
currency troubles in the thirties. Raguet wrote:* "In 
the six months before the suspension of '37, although the 
amoimt of the currency was greater than it had ever been 
before in the United States, yet the scarcity of money was 
so great that it commanded from 1 per cent, to 3 per cent, 
per month." It would be unsafe to found much inference 
on these facts ; their significance may be partly or wholly 
different. But they raise a presumption that anticipation 
of further depreciation of currency tends to increase the 
rate of interest. 

A.definite te st must be sought wh ere two standards ar e 
dinidtanepusiy^ used. An excellent case of this kind is 

' Bernard Moses, "Legal Tender Notes in California," QuarUrly 
Journal of Economic; October, 1892, p. 15. 

' Currency and Banking (18.39). p. 139; also Sumner, History of 
Banking, New York (1896), p. 264. 



• J 






. i\ 




260 



THE RATE OF INTEREST 



[Chap. XIV 



supplied by two kinds of United States bonds, one payable 
in coin and the other in currency. Froir. the prices which 
these bonds have fetched in the market it is possible to 
calculate the interest realized to the investor. The cur- 
rency bonds were known as currency sixes and matured in 
1898 and 1899. The coin bonds selected for comparison 
were the fours of 1907. The following table gives the rates 
of interest realized in the two standards, together with the 
premium on gold. 

RATES OF INTEREST REALIZED FROM DATES MEN- 
TIONED TO MATURITY' 





Coin 


CUB- 
RENCY 


Price of Gold 




Coin 


CUB- 
BKNCT 


Jan., 1870 


6.4 


5.4 


119.9 


Jan., 1879 


3.7 


4.5 


July, 1870 


5.8 


5.1 


112.2 


Jan., 1880 


3.8 


4.0 


Jan., 1871 


6.0 


5.3 


110.8 


Jan., 1881 


3.3 


3.4 


July, 1871 


5.8 


5.0 


113.2 


Jan., 1882 


3.0 


3.5 


Jan., 1872 


5.3 


4.9 


109.5 


Jan., 1883 


2.9 


3.3 


July, 1872 


5.6 


5.0 


113.9 


Jan., 1884 


2.6 


2.9 


Jan., 1873 


5.7 


5.1 


111.9 


May, 1885 


2.7 


2.7 


July, 1873 


5.4 


5.0 


115.3 


Jan., 1886 


2.6 


2.6 


Jan., 1874 


5.0 


5.0 


110.3 


Jan., 1887 


2.3 


2.6 


July, 1874 


5.1 


4.9 


110.7 


Mar., 1888 


2.3 


2.9 


Jan., 1875 


5.0 


4.7 


112.6 


Jan., 1889 


2.2 


2.6 


July, 1875 


5.1 


4.4 


117.0 


May, 1890 


2.1 


2.6 


Jan., 1876 


4.7 


4.4 


112.9 


July, 1891 


2.4 


3.0 


Julv, 1876 


4.5 


4.2 


112.3 


Jan., 1892 


2.6 


3.1 


Jan., 1877 


4.5 


4.4 


107.0 


Mar., 1893 


2.8 


3.1 


July, 1877 


4.4 


4.3 


105.4 


Nov., 1894 


2.7 


3.5 


Jan., 1878 


5.0 


4.6 


102.8 


Aug., 1895 


2.8 


3.6 


July, 1878 


3.9 


4.4 


100.7 


Aug., 1896 


3.2 


4.3 



> This table haa b«en obtained by the aid of the usual broken' 
bond tables. In the case of currency bonds, it was only necessary 
to deduct accrued interest (if any) from the quoted price and look 
in the table for the interest which corresponds to the price so found 
and the number of years to maturity. In the case of coin bonds, 




Sec. 3] INDUCTIVE VERIFICATION (MONETARY) 261 

Several points in this table deservo notice. In 1870 
the investor made 6.4 per cent, in gold but was willmg to 
accept a return of only 5.4 per cent, m currency. This fact 
becomes intelligible in the light of the theory which has been 
explained. It meant the hope of resumption. Because 
paper was so depreciated there was a prospect of a great 
i rise in its value. It was not until 1878, when the prospect 
of a further rise disappeared, that the relative position of 
the two rates of interest was reversed. After resumption 
in 1879 the two remained very nearly equal for several years, 
until fears of inflation again produced a divergence. The 
quotations for 1894, 1895, and 1896 show a considerably 
higher rate of interest in the currency standard than in the 
coin standard, as well as a higher rate in both standards 
than in previous years. The difference is between 2.7 
per cent, and 3.5 per cent, in 1894, and between 3.2 per cent, 
and 4.3 per cent, in 1896. Both the increase and the wedg- 
ing apart of the two rates are explainable as effects of the 
free-silver proposal and its incorporation (July, 1896) in 
the platform of the Democratic party. 



*. r- 



§3 

We see, therefore, that the facts agree with the theory 
previously laid down. But it is necessary further to inquire 
how close is this agreement. For this purpose the figures 
just given are of little value. They represent the rates of 
interest realized for the periods between the dates named 
and the times at which the bonds matured ; but as these 

since the quotations are given in currency, it is necessary to divide 
the quoted price by the price of gold in order to obtain their price 
in gold (t.« "coin"), and then proceed as above indicated. The 
quotations of prices of bonds and gold are the "opening" prices for 
the months named, and are taken from the Financial Review (Annual 
Summary of the Commercial and Financial Chronicle), 1895, The 
Commercial and Financial ChronicU, the (Nev York) Bankers' Maga- 
nnf, and the Banker*' Almanac. Aft«r 1884. January quotations 
were not always available. 






• it- 






xJkk 



262 



THE RATE OF INTEREST 



[Chap. XIV 



*l 



imm 



periods are not the same for the two bonds, the two cor- 
responding series of interest rates are not entirely com- 
parable. Such a rate of interest is a sort of average of the 
rates of interest for the individual years of the periods in 
question.' Thus, in the foregoing table, the rate of interest 
in currency placed opposite January, 1870, is 5.4 per cent. 
This is the rate realized between 1870 and 1899. It is a 
sort of average of, say, the rate of interest for the period 

RATES OF INTEREST REALIZED FROM DATES MEN- 
TIONED TO JANUARY 1, 1879 (DATE OF RESUMPTION) ' 









Appreciation or Currxnct 








IN Gold 




Coin 


CURRENCT 






"Expected" 


Actual 




J 


t 


a 




Jan., 1870 . . 


7.1 


6.3 


.8 


2.1 


July, 1870 . . 


6.2 


6.7 


.5 


1.4 


Jan., 1871 . . 


6.7 


6.3 


.4 


1.3 


July, 1871 . . 


6.4 


5.7 


.7 


1.8 


Jan., 1872 . . 


5.9 


5.7 


.2 


1.3 


July, 1872 . . 


6.2 


5.7 


.5 


2.1 


Jan., 1873 . . 


6.5 


6.2 


.3 


2.0 


July, 1873 . . 


6.2 


6.0 


.2 


2.8 


Jan., 1874 . . 


5.6 


6.1 


-.5 


2.1 


July, 1874 . . 


5.7 


5.8 


-.1 


2.4 


Jan., 1875 . . 


6.0 


5.4 


.6 


3.1 


July, 1875 . . 


6.1 


4.2 


1.9 


4.9 


Jan., 1876 . . 


5.4 


4.1 


1.3 


4.3 


July, 1876 . . 


5.2 


2.4 


2.8 


4.9 


Jan., 1877 . . 


5.5 


4.0 


1.5 


3.5 


July, 1877 . . 


5.7 


3.1 


2.6 


3.6 


Jan., 1878 . . 


8.2 


6.0 


2.2 


2.8 


July, 1878 . . 


4.8 


2.6 


2.2 


1.4 



' Fo- t» e nature of this average, see The Nature of Capital and 
Income, . .pendix to Chap. XII, { 5. 

' Since the figures in this table represent the rates of interest 
which will render the "present value," at the date of purchase, of 
all the future benefits up to January, 1879, equal to the purchase price, 
they can be calculated by Homer's method as indicated in | 9 



I 4 ' • 

f 



Sec. 3] INDUCTIVE VERIFICATION (MONETARY) 263 



between 1870 and 1879 (which, as we shall see, was 6.3 
per cent.) and that for the period between 1879 and 1899 
(which was 4.5 percent.). For a true comparison between 
coin and currency rates, we must seek rates relating to the 
same period in each case. This is the method in the fol- 
lowing table. In it, the periods selected all terminate on 
January 1, 1879, the date of resumption of specie payments. 
The rates of interest in this table are the rates which 
would Ije realized by investors who should buy the bonds 
at the dates mentioned and sell them on January 1, 1879. 

of the Appendix to Chap. V. But the method which has been adopted 
is less laborious, as it enables ua to use the bond tables. It can best 
be explained by an example. The opening price, January, 1870, of 
currency sixes was 109|, and in January, 1879, the price was I19i. 
These prices require no correction for accrued interest. Our problem 
is, if a man spends $109 J in 1870 and receives $119^ in 1879 with 
Sd per annum (semiannually) in the meantime, what rate of interest 
does he realize? Now it is clear that the answer is the same if all 
the benefits and sacrifices involved are doubled or halved or increased 
or decreased in any common ratio. Let us then divide them all by 
1.19i. Then we would have $91.3 paid in 1870 for $100 due in 1879, 
and $5.02 per annum in the meantime. That is, the rate of interest 
realized is exactly as if the bond were a 5.02 per cent, bond maturing 
in 1879 and bought at 91 .3 in 1870. This rate can readily be obtained 
from the bond tables by interpolating between the figures for a 5 
per cent, and a 5 J per cent, bond purchased at 91 .3 with 9 years to run. 
For a 5 per cent, bond we obtain 6.28 per cent, and for a 5i per cent, 
bond, 6.81 per cent. Hence for a 5.02 per cent, bond the result is 
6.30 per cent. 

The third column gives what may be called the expected rate of 
appreciation of currency in terms of gold ; that is, that rate of appre- 
ciation which would have made the two interest rates equally profit- 
able. It is therefore the difference between tht> two rates of interest. 

Finally, the last column gives the actual rate of appreciation be- 
tween the dates mentioned and January 1, 1879. This is calculated 
from the quoted prices of gold. Thus the opening price of gold 
January, 1870, was 119.9, and January, 1879, 100. Hence currency 
appreciated in nine years in the ratio of 100 to 119.9, which is at the 
rate of 2.1 per cent, per annum. If the appreciation proceeded uni- 
formly, this method would be strictly correct. As it is, a more elabo- 
rate method would be required, in accordance with the principles 
<>xp!asncd in J 9 of the Appendbc to Chap. V, to take account 
fully of the fluctuations of the annual appreciation. But for our 
present purposes, and for results worked out to but one decimal 
place, the simpler method here adopted is sufficiently correct. 



■y,}tl 




•if 



?l' 






*,v 



\\ lift \ 



264 



THE RATE OF INTEREST 



[Chap. XIV 



From this table we see that the rates of interest realized 
for the period, January, 1870 to January, 1879, were in 
coin, 7.1 per cent., and in currency, 6.3 per cent., the dif- 
ference ' between which is .8 per cent., the rate of apprecia- 
tion which would equalize the investments in the two bonds- 
Tliis may Ix; called the "expected appreciation." The 
actual rate of appreciation was 2.1 per cent. Tiiat is, 
the estimated appreciation was about two-fifths of the ap- 
preciation as it really turned out. Those who held currency 
sixes therefore had the 'setter investment during 1870- 
1875). In fact, it is well known chat many speculators 
grew rich by exchanging gold bonds for currency bonds 
about this time. Tlie table shows that there was the 
same underestimate of future anpreciation in July, 1870, 
Januarj-, 1871, and July, 1871. From that time to July, 
1874, the table shows that the outlook for resumption 
grew gloomy, due no doubt to the strong greenback senti- 
ment. The inflation bill of 1874 actually produced a 
prospect of negative appreciation; i.e. depreciation. This 
bill was vetoed by President Grant, and in December 
of that year the bill for resumption was passed by the 
Senate. Accordingly, January, 1875, opened with a more 
hopeful estimate. The bill became a law on the 14th of 
January, and there was an immediate rise in the "expected 
appreciation" which from that time forward averaged 
2 per cent. But during the same period the actual ap- 

' The formula used is therefore simply / = t + o. ( j represents the 
rate of interest in coin, i the rate of interest in currency, a the expected 
rate of appreciation — that is, the rate of appreciation of the cur- 
rency standard with respect to the coin standard). As shown in Ap- 
pendix to Chap. V, S 3, this formula applies strictly only when the 
rates of interopt and of appreciation are "reckoned continuously." 
But practically it applies to all cases with which we have to deal, 
as the interest periods are seldom over half a year. Even when the 
interest is payable only annually, and, in consequence, the correct 
formula is 1 + j = (1 -f t) (l -l- a), (see Appendi.x to Chap. V, § 2), 
the value of a calculated by thi.s formula will seldom differ perceptibly 
from its value calculated by the simpler formula ; = i -I- o, here 
emoloyed. 




Sbc. 4] INDUCTIVE VERIFICATION (MONETAKY) 265 

preciation from thf, dates named to January, 1879, averaged 
3.6. per cent., .so that even after the government promised 
resumption, inve.storn and sfK;culators did not put implicit 
confidence in that promi.se, the "exfKjcted appreciation" 
being only a little more than half the actual apfjreciation. 
This corre.sfxjnd.s to the Wf;!l-know n fact that the resump- 
tion act was looked upon a.s a fiolitical maneuver, likely 
to be repealed.* 

§ 4 

Ha\nng comp«ired the rates of interest in paf)er and 
coin, we may next compare them in gold and .silver. The 
comparison, to be of value, mii.st l^f: l>f;tween gold and silver 
contracts in the same market and with the same security. 
Such contracts are fortunately available in the London 
market of government securities. The loans of India 

' It should be observed that the mftthod employed to detrTrnine 
the rate of interest realized u open to one d.ineer. It norreotly Tiprc- 
sent* the rate of interest actually rf-alized bet^-een two dates, but, 
unless the later of the two date?! Is maturity, it does not nerea.^arily 
represent the rate of interest expected at the fir-t date. The in.-estor 
could not know in Januar 18T0, what the price of bondrf would be 
in January, 1879, unless the bond.J matured at that time. To aecu- 
rately compare, in 1S70. the rf^lative advantages of noin and currency 
bond: for the period lS7f>-187!< i ' -"cast would have been necea.sary, 
aot only of the relation of curr'T.- ■ -n g. !. but al.-o of the price-' of 
the two bonds in 1S79 Th--* ■ - in ■ 
catst made in 1S79. It foi; wj ■.- i 
and embodied in the pnc:es ijf •..at y- 
terest realized between 1S70 and !■'"'» 
t.ike of the opposite kind :n tho :' - 

But in most cases the metn^.-d z\ 
althouirh in 1S70 it wo'ill have b<^t-: 
the prices of the two b<jnd.s in 1879 
^ipon that any irreat change in pr.i>- . 
thus eliminates itself for the m.j-it par* .; 
•hat the "mrs in nredictinii wh.it "h- 
he -.n 1879 are nearly equal l^ that -r> 
proximately of the same term. Th'' 
the currency bonds in 1898 and I8'.>') 

•hat the coin bonds of 1907 wer-? '-h': 
1881. 



depend on a new fore- 

. • .'. thw foreca.-it of 1879 

'iid affect the rate of in- 

e .J.arae manner a.a a mia- 

h70 

-*i'';en" f-i.v-r. For, 

t. .jfed. • f-xactly 

-i.ly be d> pended 

• both ahxe. and 

ir..-rr,n. The T--iV)X\ 

•■ ".-.': "X-, bond.-i wo'ild 

!^d-' reiected w^^re ap- 

:.- ....itured m 1907, 

• .- 'a.-.e year* be- 

"'iCi- "h>"..s* of 



-Hi' 



f ig 



266 



THE RATE OF INTEREST 



[Chap. XIV 



have been made partly in gold and partly in silver, and 
both forms of securities are bought and sold in London.' 
The interest on the silver, or rather rupee, bonds is paid 
by draft on India. Tlie sums actually received in English 
money dep<nid on the state of the exchanges. The rate 
of interest in the silver standard is calculated in the same 
way as was shown * for coin bonds in § 3. Tlie results are 
contained in the following table : — 

RATES OF INTEREST REALIZED FROM DATES NAMED 
TO MATURITY OR IN PERPETUITY* 






II- ^ 






Rupee 


Gold 


DlFFEH- 
ENCE 


excranoe on 

India 

Pence per Rt7pek 


1865 


4.3 


4.1 


.2 


23.2 


186S 


4.3 


4.0 


.3 


23.0 


1870 
1871 


4.3 
4.1 


4.0 
3.8 


.3 

.3 


23.6 
23.2 


1872 


3.9 


3.7 


.2 


22.6 


1873 


3.9 


3.7 


.2 


22.4 


1874 


3.9 


3.8 


.1 


22.2 



• The silver bonds or "rupee paper" were issued to raise loans in 
India, but they have also been enfaced for payment in England, and 
in 1893-1894 some Rs. 25,000,000 were on the London books. — Bur- 
dett's 0§.cial Intelligencer (1894), p. 75. 

' Thus in 1880 the average price paid in London for "rupee paper" 
of face value Rs. 1,000 yielding 4 per cent., or Rs. 40 per annum, was 
£79. In order to find the rate of interest realized by the investor, 
we must translate £79 into sUver. The average rate of exchange 
in 1880 was 20d. per rupee. Hence £79 were equivalent to 948 
rupees. That is, speaking in tenns of silver (or, more exactly, in 
terms of exchange on India), the price of a 4 per cent, bond was 94.8, 
which, if the oond be treated as a perpetual annuity, yields the in- 
vestor 4.3 per cent. In the same year, an India gold bond yielded 
3.6 per cent. 

' This table is formed from averages of (usually ten) quotations 
distributed through each year, taken from the Economiat, the In- 
vestor's Monthly Manual, and the (London) Bankers' Magazine. The 
fourth column is founded on the table in the Report of the Indian Cur- 
rency Committee (1893), p. 27, but is corrected to apply to calendar 
instead of official years. 




•I 'M 



SK.i] INDUCTIVE VERIFICATION (MONETARY) 267 

RATES OF INTEREST REALIZED FROM DATES NAMFD 
TO MATURITY OR IN PERPETUITY— Continued 





Rupee » 


Gold" 


DlFTEB- 
ENCE 


Exchange on 

India 

Pence per Rupee 


1875 


4.0 


3.6 


.4 


21.9 


1876 


4.1 


3.7 


,4 


20.5 


1877 


4.1 


3.7 


.4 


20.9 


1878 


4.2 


3.9 


.3 


20.2 


1879 


4.4 


3.7 


.7 


19.7 


1880 


4.3 


3.6 


.7 


20.0 


1881 


4.0 


3.4 


.6 


19.9 


1882 


3.9 


3.5 


.4 


19.5 


1883 


4.1 


3.4 


.7 


19.5 


1884 


4.1 


3.3 


.8 


19.5 


1885 


4.1 


3.5 


.6 


18.5 


1886 


4.1 


3.5 


.6 


17.5 


1887 


4.1 


3.4 


.7 


17.2 


1888 


4.1 


3.1 


1.0 


16.5 


1889 


4.1 


3.0 


1.1 


16.5 


1890, Ist half 


4.0 


3.0 


1.0 


17.6 


1890, 2d half 


3.9 


3.1 


.8 


19.3 


1891 


3.8 


3.1 


.7 


17.1 


1892 


3.9 


3.1 


.8 


15.3 


1893 


3.9 


3.0 


.9 


15.0 


1894 


3.9 


3.0 


.9 


13.5 



' The quotation from which the interest was computed for 1895 
and succeeding years is for 3i per cent, rupee paper. All previous 
quotations are for 4 per cent.'s. The 4 per cent's were repayable on 
thre*^ months' notice; this notice was given in 1894, and the bonds 
redeemed or converted into 3^ per cent.'s before the close of the year. 
To obtain the rate of interest realized, the London quotations in 
pounds sterling are first converted into rupees at the current rates of 
exchange, and then the bonds are treated as perpetual annuities. 
The results differ from those given in the Investor's Monthly Manual, 
because the rupee is there converted at a conventional value, not the 
market value. , 

' From 1865 to 1880 inclusive the figures refer to 4 per cent, s, 
repayable October, 1888, or later; those of 1881-1884 are for 3i per 
cent.'s maturing in 1931, and those for 1885-1906 are for 3 per 
cent.'s maturing in 1948. 



M' 






:M 



268 



THE RATE OF INTEREST 



[Chap. XIV 



RATES OF INTEREST REALIZED FROM DATES NAMED 
TO MATURITY OR IN PERPETUI.'Y— Conduded 



I 







Rupee 


Gold 


Differ- 
ence 


EXCRANOE ON 

India 
Pence per Rupee 


1895 


3.4 


2.8 


.6 


13.4 


1896 


3.3 


3.1 


.2 


14.3 


1897 
1898 


3.5 
3.7 


3.1 
3.2 


.4 
.5 


15.1 
16.0 


1899 


3.6 


3.2 


.4 


16.1 


1900 


3.7 


3.4 


.3 


16.0 


1901 


3.7 


3.5 


.2 


16.0 


1902 


3.6 


3.5 


.1 


16.0 


1903 


3.5 


3.5 


.0 


16.0 


1904 


3.6 


3.7 


-.1 


16.1 


1905 


3.6 


3.6 


.0 


16.1 


1906 


3.6 


3.2 


.4 


16.0 



From this table it will be seen that the rates realized 
to investors in bonds of the two standards differed but 
slightly until 1875, when the fall of Indian exchange began. 
The average difference previously to 1875 was .2 per cent., 
while the average difference from 1875 to 1892 inclusive 
was .7 per cent., or more than three times as much. Within 
this period, from 1884 exchange fell much more rapidly 
than before, and the difference in the two rates of interest 
rose accordingly, amounting in one year to 1.1 per cent. 
Inasmuch as the two bonds were issued by the same gov- 
ernment, possess the same degree of security, are quoted 
side by side in the same market, and are similar in all other 
respects except in the standard in which they are expressed, 
the results afford substantial proof that the fall of exchange 
(after it once began) was discounted in advance and af- 
fected the rates of interest in those standards. Of course 
investors did not form perfectly definite estimates of the 
iwtnvp fall, hut thft fe.ar nf a fall predominated in varying 
degrees over the hope of a rise. 



w- 



liim 



Sbo. 41 INDUCTIVE VERIFICATION (MONETARY) 269 

The year 1890 was one of great disturbance in exchanges, 
the average for the first six months being 17.6 and for the 
last six months 19.3. The gold price of the silver bonds 
rose from an average for the first six months of 73.8 to 83.5 
for the last six months, but the rise in their silver price 
was only from 100.6 to 103.7, showing that the increase of 
confidence in the "future of silver" was not great, and in 
fact only reduced the disparity in the interest from 1.0 
to .8 per cent. 

This great rise in exchange and the slight revival in silver 
securities occurred simultaneously with the passage of 
the Sherman Act of July, 1890, by which the United States 
was to purchase four and a half million ounces of silver per 
month. There can be little doubt that the disturbance 
was due in some measure to the operation or expected 
operation of that law. 

This is not the only case in which the relative prices of 
rupee paper and gold bonds were probably affected by 
political action. One of the smallest differences in the two 
rates occurs in 1878, which was the year of the Bland Act 
and the first international monetary conference. 

After the closure of the Indian mints on June 26, 1893, 
exchange rose from 14.7 to 15.9, the gold price of rupee 
paper from 62 to 70, and consequently its rupee price from 
101.2 to 105.7. From this point the exchange again 
dropped, much to the mystification of those who had pre- 
dicted an established parity between gold and silver at the 
new legal rate of 16d. per rupee. There was much dis- 
cussion as to the reasons for the failure of the legal rate 
to become operative. The reason seems to have been that 
the closure of the mints to silver attracted into the cir- 
culation silver from other channels, especially old Native 
hoards. Within a few years, however, this source of supply 
was dried up so that the legal par was reached in 1898 and 
has been maintained ever since, subject only to the slight 
variations of exchange due to the eo.st of shipping specie. 
But until the par was proved actually stable by two or 



t 



ci 



.-r 



Li- 









■ -t-^a- - tJ Sri"! 






l^lf^r 



270 



THE RATE OF INTEREST 



[Chap. XIV 



three years' experience, the public refused to have confi- 
dence that gold and the rupee were once more to run 
parallel. Their lack of confidence was shown in the dif- 
ference in the rates of interest in gold and rupee securi- 
ties during the transition period, 1893-1898, and the two 
or three succeeding years. From 1893 to 1900 inclusive 
the two rates averaged .5 per cent, apart. From 1901 to 
1906 inclusive, the average difference was only .1 per cent.' 

§ 5 

We shall next attempt to apply the theory of appreciation 
and interest to periods of rising and falling prices. We 
are met, however, by the diflficulty that comparison can 
only be made between successive periods. We can learn 
what the rate of interest has been during a price movement, 
but we cannot know what it wovld have been if that price 
movement had not taken place. Without this missing 
term of comparison, it is difficult to measure the influence 
of the rise or fall in price level. No two periods are so alike 
industrially that wo can say they differ only in the state 
of the monetary standard. Other influences innumerable 
affect the "value of money." In spite of these difficulties, 
however, certain general conclusions can be established. 

It must be borne in mind that we are studying the effects 
of rising, not high, prices, and of falling, not low, prices. 
Falling prices are as different from low prices as a waterfall 
is from sea level. Our study is not of price levels, but of the 
slopes between price levels.' 

' The preceding comparisona serve only to establish the influence 
of the divergence between the standard.^ on the rates of interest, 
but afford no mea.sure of that influence. In order to measure the 
extent to which the fall of silver was allowed for by investors, it would 
be neeesfcary to examine the rates realized during specific periods, 
as in the case of coin and currency bonds consid.-^red in { 3. A some- 
what unsatisfactory attempt to do this was made in "Appreciation 
and Interr-Mt," but is not reproduced here. The caae ia unlike that 
of the United States coin and currency bonds, since in the caae now 
under dLsrussinn, the two kinds of bonds, rupee and gold, did not 
have approximately the same date of maturity. 

' De Haas appears to have fallen into the confusion between high 




Sec. 5 ] INDUCTIVE VERIFICATION (MONETARY) 271 

It was once predicted by Mr, H. H. Gibbs,' formerly a 
director of the Bank of England, that the progressive 
scarcity of gold would raise the rate of interest. He 
reasoned that such scarcity would make a stringency in 
the money market, and that the banks, each struggling to 
attract reserves from the others, would raise their rates. 
This prophecy, however, was not fulfilled. The theory that 
appreciation raises interest has been frequently affirmed, 
and has even received the stamp of approval of Mr. Robert 
Giffen. But it is utterly at variance with facts.* 

When prices are rising or falling, money is depreciating 
or appreciating relatively to cf/mmodities. Our theory would 
therefore require high or low interest according as prices 
are rising or falling, provided we assume that the rate of 
interest in the commodity standard does not vary. This 
assumption would be thoroughly justified only in case the 
two periods were alike in all respects except in the expan.sion 
or contraction of credit and currency. 

In the following table for London the perials are selected 
to correspond with the main movements of prices. Thus, 
the period 1826-1829 was a period of falling prices, so that 
money appreciateti in terms of coinmo«lities at thf average 
rate of 4.2 per cent, per annum. This is indicaterl in the 
third column by the figure + 4.2. In the period I8.'}6-1839 
prices rose so that money fell at the rate of 2.3 per cent, per 
annum, indicated by— 2.3. The fourth and last column 
indicates the rate of interest which is virtually paid in com- 
modities. It is the rate of commo<lity-intercst equivalent 
to the market rate of money-interest actually paid, and 
therefore is, in each case, the sum of the two items of the 
two preceding colunm-j, 

and rising; priws, both in hw criticism of Jevons and in hi.s trpatment 
of stati.>tics. See "A Third Element in the Rate of Interest," Jour- 
nal of the Royal Statistical Society, March, 18-^9. 

> The BimetaUic Controveriy London (Wilson), 1886, pp. 19, 231 
245-249, 373. 

'See "Appreciation and Interest," p 57. 



■* 



h 



If 



,^|: 









.^7 





Ill 5 5 Ik 



272 



THE RATE OF INTEREST 



[Chap. XIV 



LONDON R.\TES OF INTEREST IN RELATION TO RISING 
AND FALLING PRICES' 











Virtual 








Appreciation 


Interest in 




Bank 


Market 


OP Money in 


Commodities 






t 


Commodities 
a 


(Market) 
7 


1S26-1S29 


4.4 


3.5 


+ 4.2 


7.7 


lS30-lS,^-) 


4.0 


3.2 


0.0 


3.2 


is;ifl-is;«) 


4.7 


4.2 


- 2.3 


1.9 


1S40-1S44 


4.2 


3.5 


+ 5.9 


9.4 


1845-1847 


3.7 


4.2 


- 3.0 


1.2 


1848-18.')2 


2.9 


2.5 


+ 1.2 


3.7 


1853-18.17 


4.1 


5.3 


-2.4 


2.9 


1858-1864 


4.4 


4.2 


-3.0 


1.2 


1865-1870 


3.8 


3.6 


+ 1.1 


4.7 


1871-1873 


3.9 


3.7 


-6.2 


- 2.5 


1874-1879 


3.2 


2.7 


+ 4.3 


7.0 


1880-1887 


3.3 


2.6 


+ 3.8 


6.4 


1888-1890 


3.8 


2.9 


-1.4 


1.5 


1891-1S9G 


2.5 


1.5 


+ 3.4 


4.9 


1897-1900 


3.2 


2.6 


-6.6 


-4.0 


1901-1906 


3.6 


3.1 


-1.5 


1.6 



* This table is constructed from the data given in the Appendix 
to this chapter. The third column is based on index numbers (Jevons' 
for 1826-1852, and Sauerbeck's for the remaining years). The index 
numbers for two dates, as 1826 and 1829, being given, their inverse 
ratio gives the relative value of money (in commodities) at those 
two dates. From these it is easy to calculate the average annual 
change in its value. The method is the :iame as that employed for 
finding the rate of interest by which $1, by compounding, will 
amount to a given sum in a given time. Theoretically, since the 
loans here included run usually perhaps thirty to ninety day.s, the 
quotations of rates of interest averaged should begin at the first of 
the two dates, and cease, say, sixty days before the second. But the 
it:dex numbers are not always for definite points of time, nor cun 
the interest quotations be subjected to such minute corrections witli- 
out an iinmen.se expenditure of labor. Hence, the method adopted 
has been to average the rate^ for all the years of a period; e.g. for 
the four years, 1826-1829. 1 he " appreciation " is reckoned between 
those dates. If the index numbers represent the price levels at the 
middle of 1826 and 1829, then the average interest rates ought in 
theory to include only the last six months of 1826, and the first 
four months of 1829. But it seems better to include too much at 
both ends than to omit the averages for 1S26 and 1829 altogether, 
for the reason that an average is the more valuable the greater the 
number of terras included. 



8«c. 6] INDUCTIVE VERIFICATION (MONETARY) 273 

If this table \)e exaniinftd, it will \xi found that if, in 
comparing one period with the next, the rate of interest 
falls, the " appreciation " usually ri^en, or if the rate rises, 
the " appreciation " falls. Tlie cornpari.son of each period 
with the one following may he denignatefi as a "se- 
quence." In twelve out of fiftcf^n sf^quences for hank rates 
and in eleven out of fifteen for market rates, interest 
is high or low according to the degree in which prices are 
rising or falling. Attention is called particularly to the 
period 185.1-18o7, during which prices row; very fa.st simul- 
taneously with, and presumably .>f;cause of, the great gold 
production. The market rate of interest avf^ragcd 5.3 
per cent., which was far higher, not only than in any siil>- 
sequent, but al.so than in any previous fKfrivl. 

§ f> 

The following table for Iif;rlin displa},^ the same connec- 
tion Ijetween price movements and intere.-;t : — 

BERLIN RATE.S OF I.\"TERF.-T I.V RELATION TO FlI.iINf; 
AND FALLINO PRICE.S ' 



' 4^ 



Ba.vi 



Mabezt 



lNil-lv-,2 


4.0 





- 1..V 


l*.-3-lH." 


4.7 


— 


- 3.3 


IH.>-V-1V>4 


4.3 


3.7* 


_ •■> ■-) 


lvi.--l>70 


4.7 


4.0 


0.0 


I'i71'-i^73 


4.5 


4.1 


-4.1 


1 '74-1 ^7') 


4.3 


T •-> 


-3.1 


IvSo-lv^} 


4.3 


3.4 


-0.1 


I'i.'^-t-lvsS 


3.*^ 


2. .5 


- ■;.o 


I <■*•>- iH'.n 


4.0 


3.1 


- 1.4 


i^Vi-l'iai 


3.4 


1 •> 


- .5.2 


1V:«^IV>'> 


4.2 


3.6 


-»5..S 


:-,»,<.,_i%o 


4.2 


3.2 


5.4 


1%3-1'>\5 


3.0 


3.0 


- 1.4 



APPRtCIA- VlF-.TfAt. 

TIO.V or I.VTEREAT I N 

Mo.VET IX CoMHCDrTIEil 

CoJiMODiTiE.^ .'P.arik, 



\A 



Virtu A I, 

I.VTKKEST IS 

(.oMMODiTira 
^Market) 

; 



1..') 

4.0 

0.0 

♦;.3 

3.3 

5.4 
l.S 
7.4 
3.2 
'.6 
1.6 



■ Tlud table is cotLStr-icwd fr-.^n *,ht> ijita s. thi* .\pp»»E(lLx, The 
iv^rw? in the secuad colmnn aiArkeii * ij f.r ".iie year> l^'n-lV54, 



.11 

t1 



it 



274 



THE RATE OF INTEREST 



[Chap. XIV 



In the foregoing table the relation between appreciation 
and interest is observed in seven out of twelve sequences 
for braik rates (two bemg neutral) and in eight out of ten, 
for markst rates. 

For France, index numbers covering a wide range of 
articles are not available. Using those given in the " Aid- 
rich Report" for sixteen articles, we have : — 

PARIS RATES OF INTEREST IN RELATION TO RISING 
AND FALLING PRICES' 









Appreciation 




Bank 


Market 


OF Money in 
Commodities 


1861-1864 


5.1 




-8.1 


1865-1870 


3.2 




+ 3.6 


1871-1873 


5.3 


4.6* 


-4.5 


1874-1879 


3.1 


2.6 


+ 4.3 


1880-1886 


3.2 


2.8 


+ '-'.3 


1887-1890 


3.1 


2.6 


-5.1 


1891-1895 


2.6 


2.0 





Here the same connection is observed in five out of six 
sequences for bank rates and three out of four for market 
rates.' 

It will be noted that the course of prices and interest 
has been very much the same in England, Gennany, and 
France. 

For New York we have the following table : — 




not 1858-1864. The "appreciation" to 1891 is calculated from the 
figures of Soetbeer and Hoinz, as given in the "Aldrich Report" 
of 1893 of the U. S. Senate on Wholesale Prices. The figures for the 
later years are taken from The London Economist and from A. Soet- 
beer's tables in the Journal of the Royal Statistical Society, Vol. 
LXVII, Part I, pp. 85, 89. 

' This table is constructed from the data in the Appendix. The 
average in ihe second ooJumn marked (*) is for the years 1S72-1S73, 
not 1871-1873. 

* Assuming that prices fell, 1891-1895. 



8«c. 6] INDUCTIVE VERIFICATION (MONETARY) 275 

NEW YORK RATES OF INTEREKT I.V RELATION TO 
RISING AND FALLING PRICES* 








Caix 


no 

Dath 


Pkimk 
Two 
, .Vamr 
♦JO Ijath 


A»Pii«ciA- 

rirtS r,r 
MONBT IS 

f>,MMOrj- 

iTie*! 


VinTrAi, 
I.«miiE«T I.V 

CoMMOI>lTirjl 


VlRTCAL 
I.vnCREflT IN 

Commod- 
ities 
r Prime) 






i 


t 


a 


] 


; 


1849-1S57 


6.2 


9.2 





-.3.8 


.5.4 




18.58-1860 


.5.0 


7.4 


— 


-6.4 


13.8 , 




1861-186.5 


.5.9 


8.4 


dA 


-20.2 


-ll.>, ' 


- 13.4 


1S66-1874 


.5.4 


8.4 


7-5 


-h 4.7 


13.1 


12.2 


187.>-1879 


— 


— 


.5.1 


+ 7.9 




13.0 


1880-1884 


— 


— 


.5.4 


-^0.6 


1 


6.0 


188.5-1891 


— 


— 


0.1 


-0.2 


-- 


4.9 


1892-1897 


— 


— 


4.6 


^.5.6 


1 

1 


10.2 


1898-1906 


— 


— 


4.6 


-3-5 




1.1 



^e find here the same a.sfiooiation of appreciation and 
interest in all of the three sefiuences for call loan.«, in two 
of the three cases for 60-day paper (^the third being neutral), 
and in three of the six c&ses for "prime" paper c^ne F.;eing 
neutral). 

Perhaps the most remarkable featiire of thL« table Ls the 
e-Ttremely low rate for 1S7.S-1S70. The "xtraordinar^' change 
in interest rate.* beeinnina in 1S7.5 ha-? bee.i observed hj^tfore ; 
bu: i'..? connection with the re.-nimption act sl.~ it 5!eern.« to the 
writer ha.« been rrii.:»oon«tnie»i.* 

• Piia table is rijnatnr.ztai f.'fjtn im 'ia^.i in '.h(^ .^ppTidix. Th»» 
r%:.vs A appr^H-iaticn ar«? oaic'iliit*^! fr:ra Fi.iciitrr * £irir'» for prices 
4£il Taa-s in the ".\idrioh R«p«:r 

' TTius Wiluara Br^'izh. t»femn« T*t that a«:*. 4.ava ''The mpn? 
laiicuxiwniecr '.f oar int*'cr,ioa to put o'lr nsf^aev on a v^unil m«^tal- 
.ic 'ttirfis had hr.'izht "^apitii t.; tij in jiich iC'i:i-'Lin''e thit '.Yj- r'^ump- 
t;< t TM not •}cly made *?^/ biit th<» n'ma^ ~i'(^ of intT«^?'.t wm 
r^i'jc^l. . This ffTiAriLibie r»ii'ii:tii,c. l? 'xpuinablft only 

■.a th^ ir-Airid r,f a larr» reflits of f>r»Ld :apitAi ' .ViiuroZ Law 

»•! ■•oiild »:tp»»ct; a still iow<?r nt« of Ji:«?r^t i/t<;r r^imption h*d 

c«r«;n i«!':i:cipiiihed; but the facts are tiw )pp<-.sit« 



.'|i 






1^ 






276 



THE RATE OF INTEREST 



[Chap. XIV 



§ 7 

The preceding statistics apply to gold standard countries. 
The following table gives the rates of interest and appre- 
ciation for silver standard countries — India, Japan, and 
China : — 

RATES OF INTEREST IN RELATION TO RISING AND 
FALLING PRICES IN CALCUTTA, TOKYO, AND 
SHANGHAI » 



.611 



n 1 



iffiii' 





Bank 


Mabket 


Appreciation in 
Commodities 


Calcutta, 1873-1875 


5.3 




+ 2.6 


1876-1878 


6.8 




-11.0 


1879-1885 


5.9 




+ 3.8 


1888-1889 


6.0 




-2.6 


1890-1893 


4.3 




-4.7 


Tokyo, 1873-1877 


14.0 


12.0 


-0.2 


1878-1881 


16.3 


12.2 


-13.3 


1882-1886 


12.8 


10.3 


+ 10.4 


1887-1893 


9.3 


9.4 


-2.8 


1894-1899 


9.7 


11.2 


-5.8 


1900-1902 


11.0 


12.4 


0.0 


Shanghai, 1874-1881 


9.1 




-1.4 


1882-1888 


7.5 


5.8* 


+ 1.3 


1889-1893 


7.0 


5.8 


-0.9 



Here we find the theory confirmed in three out of four 
cases for India, three out of five for bank rates in Japan, 
and three out of five for market rates ; one out of two for 
bank rates in China, while the one case for market rates 
is neutral.' 

' This table is constructed from the data given in the Appendix 
The entry marked (*) is for 188.5-1888, not 1882-1888. 

•See also "Price Movements and Interest in India," by the 
writer, in Yale Review, May, 1897, p. 80. 



8bc. 81 INDUCTIVE VERIFICATION (MONETARY) 277 

Summarizing the cases for the seven countries examined 
we find 64 favorable and 22 unfavorable to the theory, dis- 
tributed as follows : — 



Favorable 
Unfavorable 



I I France .. ! India Japa China 

LAND MANT i 'nTATES ! 



23 

7 



15 
5 



8 
2 



8 
2 



3 
1 



6 
4 



Total 



64 
22 



TTie favorable cases are about three times as numerous 
as the unfavorable cases. This is a large preponderance, 
especially when we consider that there are so many causes 
affecting the rate of interest besides the mere appreciation 
or depreciation of the monetary standard. We therefore 
conciude with great confidence that, "other things being 
equal," the rate of interest vi relatively high when prices are 
rvnng and relatively low when prices are falling. 

§ 8 

The question now arises whether, on the average, the 
rate of interest ftdly adjusts itself to price-movements. 
This question cannot be answered with perfect certainty in 
any individual case, for the reason that we have no means 
of knowing what the rate in commodities would have been 
had it been possible to have contracts drawn in "com- 
modities" or in a monetary standard which wa^ stationary 
with respect to commodities. We have, however, computed 
the "virtual" interest in commodities by adding to the rate 
of interest in money the rate of a[jpreciation of money in 
commodities. Thus in London for 182^1829 the rate of 
mterest in money was 3.5 per cent., but money was appre- 
ciating relatively to commodities 4.2 per cent., so that the 
"virtual Interest." or intere-st actually pai«i, tran.slated in 
terms of commodities (the forty commoflities averaged 
by Jevons) . was 7.7 per cent. It will be seen from the tables 
that the virtual rate of interest reckoned in commodities 



,/ 



. 'S' • 



I 'm 






Mitf* 




m 



1$-^ 




278 



THE RATE OP INTEREST 



[Chap. XIV 



usually varies inversely with the rate reckoned in money. 
For 1853-1857, money mterest was 5.3 per cent., and for 
1874-1879, 2.7 per cent. ; but commodity-interest for 1853- 
1857 was 2.9 per cent, and for 1874-1879, 7 per cent. There 
are two possible explanations for this inverse relation. One 
is that when prices are rising the cause may not be monetary 
but may lie in a progressive scarcity of commodities pro- 
duced and exchanged ; and, reversely, when prices are falling, 
the cause may he in progressive abundance. From the 
theory of interest maintained throughout this book it 
follows that a progressive scarcity of commodities, implying 
as it does a progressive descending income curve, tends to 
make the rate of interest low ; and reversely, progressive 
abundance, implying an ascending income curve, tends to 
make interest hi^. When, therefore, general price-move- 
ments represent changes in the income-stream of enjoyable 
services, the rate of "commodity interest" would naturally 
be high when prices were falling and low when prices were 
rising, whatever might be true of " money-interest." 
The second possible reason that commodity-interest and 
\ I money-interest vary inversely during price-movements is 
"^ I that these movements are often imperfectly foreseen. The 
high or low rate in commodities is then an abnormal 
phenomenon. It is, as it were, a trick played by money 
on those who put too much faith in its stability. Thus, 
during 1898-1905 the increase of prices in the United 
States is known to have been due lai^ely to the in- 
crease of gold production. There is no evidence that 
commodities were getting scarce and incomes decreasing, 
but rather the reverse. There seems, therefore, no reason 
which would justify the low commodity-rate of interest 
of 1.8 per cent, which we found to have been virtually paid 
during that period. This low rate must, in all probability, 
have been due to inadvertence. The inrushing streams of 
gold caught merchants napping. They should have stemmed 
the tide by putting up interest, not only to 4.6 per cent., as 
they did, but two or three per cent, higher. 



Sk. 8] INDUCTIVE VERIFICATION (MONETARY) 279 



Doubtless both of the cauaes p\&y a part in the explanation 
of particular cases. Sometimes commodity-interest is low 
during rising prices because it is foreseen that the real in- 
come-stream is then drying up, sometimes liecaus^; it is not 
foreseen that monetary inflation is taking place, and some- 
times for both reasons ; and rever--ely, corrinio<lity-interest is 
high during falling prices, sometimes hncause of a foreseen 
increase of the income-stream, sometimes becaase of unfore- 
seen contraction of the currency, and .sometimes both. 

It is impossible to decide what part these two f — 

foreset^n changes in real income and unforeseen ri ji 

their monetar\" mea-ure — may play in each indivii a«. 

We are too ignorant of the actual conditions be 'le 

scenes. Nevertheless there Is internal evidence i ow 
that in general the latter factor — unfore.seen r: *ry 

change — is the more important. This evidente ..iist* 
in the fact that commodity-interest fluctuates ■« «idely 
in some cases even becoming negative. The foU'jv- .a^ tabl 
shows that xhe mear variability or '"standard i-viati'-a 
from the mean, whii... '^•est meas^lre of the :: K-*uanori 

of any variable, Ls far gre<- .r the calculate<i 'jt vir »a.l 
rate of ' aterest than for the actual money rate of .terf--t 







j 


V.tH. 


rr 










■"•tandafi 


-T*tion, 






No. 


PXKIOD*.— 

i 

i 


Market 

I-VTSaEST 


ViRTT 

Inter; 




LocdoQ .... 




1 ", ! 


.S.S 


.■i.U 




Beriin .... 




; \ 


.56 


2.^'} 




New York . 




1 


l.i>i 


S.43 





The virtual interest in comm'>iities is from four to eight 
times as variable as the maricet mterest in noney. 

AH these facts sugj^est — indeeii. practically demon- 
strate — that monev-interest w.a.> not a<le<iuatply &<■! justed 
to the changes in porch-^ing power of rr.oney. It i.-^, of 
course, not to be assumeii that comrriO«iity-interest ought 



H 













280 



THE RATE OF INTEREST 



[Chap. XIV 



to be absolutely invariable ; but it is practically certain that 
its variations could not be three and a half times the 
variations in money-interest, xmless the price-movements 
were inadequately predicted. If any doubts were possible 
on this point they must disappear when we find that for 
1871-18.3 commodity-interest in London was minus 2.5 
per cent. This shows that money lenders would have been 
better off had they simply bought commodities in 1871 and 
held them until 1873. As it was, they actually lost some- 
thing, measured in commodities, as a consequence of 
lending money. Such losses are especially apt to appear 
in short periods. Thus if we take the period 1824^1825, 
we find that the market rate was 3.7 per cent., the rate of 
appreciation was minus 14.5 per cent., and the virtual rate 
of interest in commodities, minus IP S oer cent. ! 

In New York during the inflati. period, 1861-1865, 
commodity-interest sank to the ridiculously low figiu-e of 
minus 13.4 per cent. This shows in a striking way how 
thoroughly the greenback inflation upset all business cal- 
culations, and how little the investing public realized in 
advance tho serious rise in prices of those fateful years. 
That foresight was actually misguided at this time is amply 
confirmed if we examine the predictions as to the termi- 
nation of the war and the reduction of the gold premium, 
which were recorded from month to month in the " Notes 
on the Money Market" in the (New York) Bankers' Maga- 
zine. In all probability such errors of prediction are 
common in periods of paper money inflation. Our tables 
in § 7 show it for the Japanese inflation of 1878-1881. 

§ 9 

We can now imderstand why a high rate of interest need 
not retard trade nor a low rate stimulate it. These facts 
have puzzled many writers. For instance, Robert Baxter 
wrote : ' — 

' Journal of the Royal Statistical Society, June, 1876. 




,4f 



■■:L-li 



m 



Sec. 9] INDUCTIVE VERIFICATION (MONETARY) 



281 



" Public inquiry has been of late strongly directed to the reasons 
for the very low rate of interest upon loanable capital in the year 
1875, the more especially as ten years ago the very high rates then 
prevailing created equal surprise." 

And Jevons wrote : ' — 

"The effect of such and many more changes effected during 
the last twenty years or so is seen in a general increase in wealth 
and of mercantile industry and profits. Thus only can be explained 
the extraordinary high rate at which the interest of money has 
in the last ten years often stood. During 1854-18.57 *he rate of 
interest was only for a few months below 5 per cent., but for many 
months above it. For more f^an half a year it stood at 6 and 7 
per cent., and in .he end of 1857 it remained for nearly two months 
at 10 percent. Again, in 1861, interest rose to 6 and 8 per cent., 
and all this, to the surprise of the elder generation, without the general 
stoppage of trade, the breach of credit, and the flood of bankruptcy, 
which has hitherto attended such rates of interest. It is certainly not to 
increasing scarcity of capital we should attribute such rates, but 
rather to a greatly extended field for its profitable employment." 

But were these rates high ? If we turn to our table for 
London rates, we find that the average market rate for 
1853-1857 does appear to be the highest in the table; but, 
unmasking it of the money element, we find it is equiva- 
lent to a commodity-interest of 2.9 per cent. This is a very 
low rate. Merchants with increasing prices and money 
profits would find it easy to repay loans on such a basis. 

Professor Bonamy Price,' writing at a time of very low 
interest rates, says : — 

" Every one remembers the agitations associated with 7 per cent., 
the trepidation of merchants, the apprehension of losses in busi- 
ness. ... If only a moderate rate could be reckoned on as steady, 
how happy would every one have been ! . . . Yet what are the 
facts and feelings to-day? Is every merchant, every manufac- 
turer rejoicing in the pleasant terms on which he obtains the ac- 
commodation so necessary for his business ? . . . Alas ! no such 
sounds mee our tars. . . . Commercial depression is the uni- 
versal cry, t -pression probably unprecedented in duration in the 
annals of trade, except under the disturbing action of a prolonged 

' Investigations in Currency, p. 95. (The italics are the present 
writer's.) 

' "One percent," Contemporary Review, April, 1877. (The italics 
are the present writer's.) 



■;''il 

1 ' 



. 'V 



hi 



u 



M 
+! 







j£ • 






282 



THE RATE OF INTEREST 



[Chap. XIV 



*/ 



war. ... In the export figures, the writer still f: " to see any 
signs of the long-looked-for revival of trade. Both quantities 
and values continue to shrink in all save a few cases. . . . What, 
then, is the cause 7 The explanation will certainly not be found in 
gold nor in any form of currency whatever . . . nor has any one said 
anything so ridiculous. . . . That cause is one and only one: 
overspending." 

If we turn back to the London table we find, however, 
that for 1874r-1879 the commodity-rate of mterest, so far from 
being low, was 7 per cent. ! It would be astonishing if trade 
did not shrink under such a burden. 

All these writers mistook high or low nominal interest for 
high or low real interest. Tooke apparently did the same. 
In his History of Prices, Vol. II, p. 349, he names as the 
last of six reasons for the fall of prices for 1814-1837, "a 
reduction in the general rate of interest." Tliis is probably 
not only an inversion of cause and effect, but also, when the 
veil of money is thrown off, a misstatement of fact. The 
commodity-interest for 1826-1829 was 7.7 per cent. Tooke, 
Price, and Jevons all overlooked the fact that interest, 
unlike prices, is not an instantaneous but essentially a time 
phenomenon. 

§ 10 

When long periods of price-movements are taken, the 
influence of appreciation on interest is more certain. The 
following table shows this for England. It consists of 
four periods, of 10, 12, 22, and 11 years respectively: — 

LONDON MARKET RATES OF INTEREST IN RELATION 
TO RISING AND FALLING PRICES 





Maiikbt 
Intlrcst 


Appmeciation 
OP Monet in 

CoMliOOITIKS 


ViRTtTAL 

Interest in 

CoMMODITlEa 




t 


a 


1 


1826-1835 


3.4 


+ 1.2 


4.6 


1853-1864 


4.6 


-0.9 


3.7 


1S74-1S95 


2.4 


+ 2.4 


4.8 


1896-1906 


2.9 


-2.9 


0.0 




■'■SaBiWIKT 



=J-'*WW 



S«c. 10] INDUCTIVE VERIFICATION (MONETARY) 283 



In averages covering so many years we may be sure that 
accidental causes are almost wholly eliminated. We find 
that diu"ing the period of falling prices, 1826-1835, the aver- 
age rate of interest was only 3.4 ; that during the following 
period of rising prices, 1853-1864, it was higher (4.6 per cent.) ; 
that during the next period, 1874-1895, when prices were 
again falling, the rate was a^ain low (2.4 per cent.) ; and 
finally that in 1896-1906, with prices rising, interest again 
recovered. In every case interest is high when prices are 
rising and low when they are falling. For these long periods, 
therefore, we find the facts in agreement with the theory 
in every case. It is also a notoeworthy fact that the com- 
modity-interest in this table of long periods is far less 
variable than for short periods. The variability, as shown 
by the " standard deviation " of the four figures in the above 
table is, for London, .82 for the market rate, and 1.94 for 
the virtual rate. The adjvstment of {money) interest to long \ 
price-movements is more perfect than to short price-ma.ements. i 

The following table gives the long time averages for New 
York. The war period is omitted : — 

NEW YORK RATES OF INTEREST IN RELATION TO 
RISING AND FALLING PRICES 



1849-1857 
1875-1896 
1897-1906 



Interest Prime 

Two Name 

60 Oats 

i 



8.2' 

5.1 

4.5 



Appreciation or 

Money in 

Commodities 

a' 



-3.8 
+ 2.6 
-3.4 



Virtual Interest 
IN Commodities 



4.4 

7.7 
1.1 



We find that the money rate in the second period, 
when money was appreciating, was, as our theory requires, 

' The average of Elliott's figures (which are not for " prime " paper) 
ia 9.2, but 1 .0 has been deducted from this average in order that it may 
be properly compared with the average of Robbins's figures for 1875- 
1891. This correction is based on the fsct that 1.0 wai= the a erage 
excess of Elliott's figures over Robbing's during the fifteen years, 
1860-1874. See Appendix to Chap. XIV, | 1. 



1 
1 



I? 



1 ir 



'M 





284 



THE RATE OP INTEREST 



[Chap. XIV 



lower than that in the first, when money was depreciating, 
but that the rate in the third period, when money was 
again depreciating, was, unfavorably to our theory, lower 
than that in the second when money was appreciating. 
Here we also see that the variability of the virtual interest 
in t«rms of commodities is less than for short periods, find 
more nearly like the variability for the market rate of 
interest in terms of money. The variability, as measured 
by the " standard deviation," of the rates of interest for 
the three periods in the above table are for market rate 
of interest in terms of money, 1.6; for virtual interest in 
terms of comm dities, 2.3. 

§ 11 

Three general facts have now been established : (1) Ris- 
ing and falling prices and wages are directly correlated with 
high and low rates of interest ; (2) The adjustment of interest 
to price-movements is inadequate; (3) This adjustment 
is more nearly adequate for long than for short periods. 

These facts arc capable of a common explanation ex- 
pressing the manner in which the adjustment referred to 
takes place. Suppose an upward movement of prices l)e- 
gins. Business profits (measured in money) will rise; for 
profits are the difference between gross income and expense, 
and if both these rise, their difference will also rise. Bor- 
rowers can now afford to pay higher "money-interest." 
If, however, only a few persons at first see this, the interest 
will not be fully adjusted,' and borrowers will realize an 

' It seems scarcely necessary to add as an independent cause of 
maladjustment the accumulation (or in the opposite case, depletion) 
of bank reserves, for this is but another symptom of maladjustment 
due to imperfect foresight. An increase of gold supply, as in 1852- 
1853 (see Tooke and Newmarch, Hulory of Prices, Vol V, p. 345), 
may first find its way into the loan market instead of into circulation. 
But if foresight were perfect, this would not happen, or if it did hap- 
pen, borrowers would immediately take it out (or increase the liabili- 
ties against it) to f vail themselves of the double advantage of low 
intei-est and high prospective profits from the rise of prices ubout t<.> 
follow. 



Sic. 12] INDUCTIVE VERIFICATION (MONETARY) 285 



extra margin of profit after deducting interest charges. 
This raises an expectation of a similar profit in the future 
and this expectation, acting on the demand for loans, will 
raise the rate of interest. If the rise is still inadequate, the 
process is repeated, and thus by continual trial and error 
the rate approaches the true adjustment. 

When a fall of prices begins, the reverse effects appear. 
Money profits fall. Borrowers cannot afford to pay the 
old rates of interest. If, through miscalculation, they still 
attempt to do this, it will cut into their real profits. Dis- 
couraged thus for the future, they will then bid lo-'-er rates. 

Since at the beginning of an upward price-movement the 
rate of interest is too low, and at the beginning of a down- 
ward movement it is too high, we can understand not only 
that the averages for the whole periods are imperfectly 
adjusted, but that the delay in the adjustment leaves a 
relatively low interest at the beginning of an ascent of 
prices, and a relatively high interest at the beginning of a 
descent. And this is what we find to be true. That the 
adjustment is more perfect for long periods than for short 
seems to be because, in short periods, the j'cars of non-atl- 
justment at the beginning occupy a larger relative part of 
the whole period. 






I 



§ 12 



WTiat has been said bears directly on the theory of " credit 
cycles." In the view here presented, {periods of sjHiculation 
and depression are the result of inequality of foresight. 
If all persons underestimated a rise of price in the same 
degree, the non-adjustment of interest would merely pro- 
duce a transfer of wealth from lender to borrower. It would 
not influence the volume of loans (except so far as the diver- 
sion of income from one person to another would itself 
have indirect effects, such as bankruptcy). Under such 
circumBtances the rate of interest would be below the nor- 
mal, but as no one would know it, no borrower would 











286 



THE RATE OF INTEREST 



[Chap. XIV 



borrow more and no lender lend less because of it. In the 
actual world however, foresight is very unequally distrib- 
uted. Only a few persons have the faculty of always 
"coming out where they look." Now it is precisely these 
persons who largely make up the borrowing class. Just 
because of their superior foresight, there is delegated to 
them the management of capital ; the y become " captains 
of industry." It therefore happens that when prices are 
rising, borrowers are more apt to see it than lenders. 
Hence, while the borrower is willing to pay a higher 
interest than before for the same loan, lenders are willing 
to loan for the same interest as before. This disparity has 
as its effect that the rate of interest will not rise as high 
«»s if both sides saw the conditions equally well. It will 
also cause an increase of loans and investments.* This con- 
stitutes part of the stimulus to business which takes place 
in times of rising prices. 

When prices fall, on the other hand, borrowers see that 
they cannot employ "money" productively except on 
easier terms, but lenders do not see why the terms should 
be made easier. In consequence, "enterprisers" borrow 
less, trade languishes, and, though interest falls in conse- 
quence of decrease in demand, it does not fall enough to 
keep the demand from decreasing.* 

We see, therefore, that while imperfection of foresigat 
transfers wealth from creditor to debtor or the reverse, 
inequality of foresight produces overinvestment during 
rising prices and relative stagnation during falling prices. 




' That this and the corresponding statement in the next paragraph 
are borne ' it by facts appears to be confirmed, so far as bank loans 
and discounts are concerned, by Sumner, History of Banking in the 
United States (New York, 1896). and Juglar, Crises Commerriales 
(Paris, 1889). 

• President Andrews, in An Honest Dollar, p. 3, writes: "Interest 
is low . . . not because money is abundant as before, but because 
it ia not, !•-= scarcity hax'ina; induced fa!! of pricps, and sn paralysis 
in industry." But, it should be added, the cause of the fall of interest 
is primarily the expectation of small profits. 




Sic. 13] INDUCTIVE VERIFICATION (MONETARY) 287 

In the former case society is trapped into devoting too 
much investment of productive energies for future return, 
while in the contrary case, underinvestment is the rule. 
It does not seem possible to decide the question which of 
the two evils is the greater.' 

§ 13 

The facts which have been shown in this chapter are im- 
portant in two respects. They prove, first, that men do 
actually, even if unaware of so doing, contrive to offset the 
effects of changes in the monetary standard by adjusting 
the rate of interest ; and, secondly, that this adjustment is 
far from adequate. In consequence of the inadequacy 
of the interest-adjustment, a large amount of wealth is 
continually and unintentionally transferred from the cred- 
itor- to the debtor-class, and vice versa. The bimetal- 
lists were partially right in their claim that the creditor- 
class were gainers during the period of falling prices in 
the two decades 1875-1895. The situation has been the 
exact opposite during the decade 1896-1906. We must 
not make the mistake, however, of assuming that the en- 
richment of the debtor-class during the last decade atones 
for the impoverishment of that class during the previous 
two decades; for the personnel of social classes changes 

• For arguments on both sides, see Professor Marshall'.s evidence, 
Report on Depreasion of Trade (1886), p. 422. See also his Principlea 
of Economics, Vol. I (3d ed., 1895), p. 674: "When we come to dis- 
cuss the causes of alternHting periods of inflation and depression 
of commercial activity, we shall find that they are intimately con- 
nected with those variations in the real rate of interest which are caused 
by changes in the purchasing power of money. For when prices are 
likely to rise, people rush to borrow money and buy good.s, and thus 
help prices to rise; business is inflated, and is managed rerklcssly and 
WB.stefully; those working on borrowed capital pay back less real 
value than they borrowed, and enrich themselves at the expense 
of the community. When afterwards credit is shaken and prices 
begin to fall, every one wants to get rid of commodities and get hold 
of rrjf.npy which != rapidly ri?ing in va!-i«; thi? mako; pri'!'« fa!! all 
the faster, and the further fall mak"8 credit shrink even more, and 
thus for a long time prices fall because prices have fallen," 






>-ji 






rf i 



288 



THE RATE OP INTEREST 



[Chap. XIV 



rapidly. Nor must we make the mistake of assuming that 
the debtor-class consists of the poor. Tlie typical debtor 
to-day is the stockholder, and the typical creditor, the 
bondholder. What is actually going on to-day in conse- 
quence of a steadily cheapening dollar is a vast transfer 
of advantage from bondholders to stockholder3. It is tliis 
transfer which has produced many of our latest million- 
aires. Their millions have been silently abstracte<l from 
the pockets of the unsuspecting "safe" investors in bonds, 
depositors in savings banks, and the salaried classes. Tlie 
fault, however, is not of those who thus profit, but of the 
monetary conditions which permit the ceaseless ebb ami 
flow of price-levels. Tlie problem of a stable monetary 
standard is of vital importance. We are apt to forget its 
importance during a period of "prosperity," and we are 
apt also to forget that much of what is called prosperity 
is delusive. It is delusive for two reasons: First, it is 
often not general prosperity, but prosperity of the debtor 
or stockholding or entrepreneur classes, who are always 
much in evidence, at the expense of the creditor, bond- 
holding, salaried classes, who bear their losses silently 
behind the scenes; secondly, so-called prosperity is often 
another name for reckless wastefulness, for which there must 
be a day of reckoning in the forn. of a commercial crisis.' 

» See The Gold Supply and Prosperity, edited by Byron W. Holt 
(The Moody Corporation), New York, 1907. 




!f . 




CHAITER XV 



INDUCTIVE VERIFICATION (ECONOMIC) 
§ 1 

In the last chapter we found statistical evidence of the 
influence of changes in the monetary standard upon the 
rate of interest. We now proceed to a similar inductive 
study of the economic —as distinct from the monetary — 
mfluences upon the rate of interest. 

Ip a study so broarJ, it would be aseless to attempt 
any exhaastive verification by statistics; the facts at hand 
are too meager, and not such as to enable us to isolate the 
separate causes at work. It will usually happen in any 
given ca.se that some of the economic causes tending to 
make interest high are combine<l with others which tend 
to make it low. The fact, therefore, that interest is either 
high or low in such a case will not, of itself, be deci.sive 
m favor of any theory. The best that we can expect is to 
show that the facts as we find them are at any rate consist- 
ent with the theory maintained. For practical purposes, 
such a .showing is enough, both because the theory should 
stand on its own merits as an analysis, without the bol.ster- 
ing of statistical verification : and becau.se, if the analysis 
were really incorrect, a ver>' cursor\- examination of the 
facts would probably suffice to refute it. 

In our study of facts it is well to remember that the causes 
tending to make interest high or low sometimes work out 
their effects, partly or wholly, in other way.s. For instance, 
the economic causes wh'ch, in the United .States, have 
tended to make interest high, have also tended to bring in 
loans from oiner countries, such as Great Britain, where the 
rate of interest was low. The introduction of the loans 
preventeij interest from being as high as it otherwise would. 






290 



THE RATE OF INTEREST 



[Chap. XV 



Ft 



If' 



kS^ 

3 J 






i! 



4tt 



In genoral it is tnie that a cause which woul d tend t o 
ma ke iiitg restjhighjii- a iioiiimunitjjnaylirmply result m 
increasing the loans contra cted by that jomin unity, pro - 
vided there exists anothe r cnmrniinity la. wh^ the rate 
of interest is lower - If recourse to borrowing is not prac- 
ticable, other methmls of adding to present at the ex- 
pense of future income —of "tipping forward" the income 
curve —may be found. If this " tipping forward " goes far 
enough it will show itself in a dissipation of capital; if not, 
in a slower accumulation. Contrariwise, the causes which 
work toward lending may, if lending is impracticable, result 
in some other form of " tipping back" the income curve and 
may show itself in a more rapid accumulation of capital or 
a less rapid dissipation. Finally, the same economic causesi 
which tend to make interest high will tend also to encouragej 
the production of the less substantial and durable instruJ 
ments, whereas those causes which tend to make interest 
low will favor the production of instruments of the more 
durable and substantial types. 

In short, in our collection of facts we should ascribe 
very similar significance to the four sets of phenomena — 
high interest, bo rrowi ng, d.joi^alim_ol_ca2ital, and peri'^h- 
aJSfifUy of instruments; any causes back of these phenomena, 
wKTch, according to our theory, should produce any one of 
the four, will tend also to produce the other three. Like- 
wise we should ascribe similar significance to the four op- 
posing phenomena — louiiiiJerest, lending, accumuUition, and 
durability[ of instrjiments. 

§ 2 
Briefly stated, the theory we are testing is that t he rate 
of mterest exjiresses human preference for p resent o ver 
{uture Igoods, asJhaLpr^grence works Itself o ut from tK e 
n^re of_ the individual and the characte r of his incom e- 
stiream. We shall begin by considering the manner in 
which the nature of the individual influences the rate of 
interest. 



^!ll| 



8«c. 2] IN'Dr;CTIVE VERIFICATION (ECONOMIC) 291 

In a previous chapU;r we enumf;rat/;fl the cau.sf;H which, in 
the nature of man, tend to make interest high or low. It 
was there maintairif.-d that foresigfit, .Hf;lf-conf.rol, and regard 
for posterity tend to ma kf^ ^terf^ T^vv T ~\^'e may there- 
fore expect to find, in a community poH-sfissing these fjuali- 
ties, one or more of the four interfrquivalent phenomena 
already mentioned — low: intere-t, lending to other com- 
munities, accumulation of capital, and oon.Htnifttion of sub- 
stantial instruraent.s ; and to find, in a community lacking 
the.-?e qualities, one or more of the four opfKj.-iite conditions. 

No extender! stufly i.-: nf^le«i to .-:how that preci-sely these 
oppoaing sets of phenomena an- ar-tuaily found in the two 
opposite conditions mentions]. Thie communities and 
nationalities which are most, notf^l for the qiialities men- 
tione<i — foresight, self-control, and r^-gard for [x>sterity — 
are probably Holland. .Scotland. Plri^anrl. Fruncc% and the 
Jews, and among these peoples inferf-st ha.s U-en low. More- 
over, they have been money lender-i, they have the habit 
01 thrift or accumulation, and their instruments of wealth 
are in genei-al of the siibstantial variety. The durability 
of their instruments is especiaiiy of^A-ions in their buildings, 
tiioth public and private, and in their ways of transpxjrtation 
— carriage roadi. tramways, and raiiroa^is. Thas in I>.g- 
land the railways have e-xpende-i an average of $16.5,W) 
p»rr mile, which is from two to three ti.Ties the r-orresp<-inding 
e.xpen-iiture in m^st co'intries.- The liff^ren'^e, though 
parJy explainal.>le by a .lifferen';-e in method.-! of account- 
ing, seems largely due to the lower rute of time-preference 
in F.ngland. 
•John Rae observes of Holland : — 

"The Dutch snem. of ill Eoropeir. .i-s,';;,-,.-..^. h.-.herto to have been 
LTLouiieii to oarnr LTi-strimen'..* to th«^ m^j^t •»iowlv rptiirr.mg orders. 
The diinbility pven to ili the irL-?tr_iii^r.-.-> -or..'trjnt»^l by them, 

aee Dorsey, En.jiuk and Am^TrCnn R.i^-ni.U C->monT»A., Sew 



ii 



.V}ntt>f. Vvi LXII 
V:i. LXXIV, p. 1224 








-m 




292 



THE RATE OF INTEREST 



[Chap. XV 



the care with which they are finished, and the attention paid to 
preserving and repairing them, have been often noticed by travel- 
ers. In the days when their industry and frugality were most 
remarkable, interest was very low, government borrowing at 2 
per cent., and private people at 3." ' 

On the other hand, among communities and peoples noted 
for lack of foresight and for negligence with respect to the 
future are China, India, Java^' the negro communities in 
the Southern states, the peasant communities of Jlussia,^ 
and the North and South American Indi ans, both befo re 
and after they had been pusu'ied to the wall by the white 
man. In all of these communities we find that i nterest is 
hj ghr that there is a tendency to run into debt and to dissi- 
pate rather than accumulate capital, and that their dwell- 
ings and other instruments are of a very flimsy and perish- 
able character. 

It may well be that there are other causes at work to 
produce these results. We are here merely noting the fact 
that lack of foresight is one factor present. 

Of China, Rae states : — 

"The te-itimony of travelers ascribes to the instruments formed 
by the Chi .se a durability very inferior to similar instruments con- 
structed by Europeans. The walls of houses, we are told, unless 
of the higher ranks, are in general of unbumt bricks of clay, or of 
hurdles plastereil with earth ; the roofs, of reeds faster^ to laths. 
We can scarcely conceive more unsubstantial, or temporary fabrics. 
Their partitions are of paper, requiring to be renewed every year. 

A similar observation may be made concerning their imple- 
mento of husbandry and other utensils. They are almost entirely 

' The Sociological Theory of Capital, pp. 128-129. 

' My colleague, Professor Clive Day, informs me that the rate 
of interest in Java is often 40 per cent. 

' See Blooh, The Future of War, p. 205. It appears that the peas- 
rjxt will sell a promise to labor a short time in the future at one 
third the current wages! See also E. B. Lanin (pseud.), "Russian 
Finance, " Fortnightly Review, February, 1891, Vol. LV, pp. 188. 190, 
196, for typical and extreme cases Inostranietz, " L'Usure en Russia," 
Journal des Economiite, 1893, Ser. 5, Vol. XVI, pp. 233-245, states 
that the rates paid by poor peasants to well-to-do peasants are fre- 
quently 5 per cent, per week! 



SBC. 2] INDrCTTVE VERIFICATION' 'ECO.VOM f,;, 



203 



of wood, the metals <>n1>..^^^ but very ipar.naiv inno 'hfrir '^onstric- 
ooa: TOtideq'ieritly they *5on ■wear ou',. ar.d .'•';•, i;.''; fre'rifrit re- 
newals.' 

■■ European traveler! are ^lirpnaefl it meeting . . . httie float- 
ing farms, bj the wie of iwimps ■w!i;':h. oalv requ.re cirair.ir.g to 
render them tillable. It «enia •■-, '.heci *trir.«e that lab^^^r -ihoiiid 
act rather be best^iwed -.n the *rA:(i earth, ifhere .t.a frjit.'i .Tuitht 
end'ire. than on strifrf.ires that m'lst :ft<:a./ nr.ii pen.rh ..'-. i. few 
years. The people they ire unocx :r^.T.A. :.•.'. n, Tiirh of fiitiire 
years as of the preaent time. " ■ 

"The Father Pirean-n. Jiiiee<i. i.i.T<tr~,.r. "hat .*. .a the..- zr-^fat 'ie- 
Mieney m. foretho'iaht md -TiaaL;-/ .- -.r...-^ r'r~p«-oT, ■»-;;. rh i.'^ the 
cause )f the scar-^ities am: facnes that :re',';ftr.tiy occiir. I hje- 
jr- ■ 'ae ja3r?. -hat. nctw.thstaii'iinz -.•• zrear - ^T.her of ..-.hahit- 
ui. 'TLina would rirrush ■■- .i^gh zr'i.n f-.r i.l. hut that "here -i 
i";t nuficient economy .c^r-e': .- .*.•! :or..-»ii2r.::-:..r.. i.iri '.r.at they 
empioy an litoo-shii:!! .'iant.— r :t .-, _z ".-t- ~a.-. .:' i!-:t.j-e of the xo.ie 
of tne 'oimtry. ind :f ra<;!:;e. ' ' 

"Iz 'Thina. we are to id ■- B.i.— ow -ha: 



ie -pza. ri-.r 



cer ?er.*.. out tnar 



^anea : 



-•-rr- r. 



J*-; 



:?L:n -OX writes :c CI:: 
■ The leaal mai:m 



i^i : :u<:w-: 



a J per ;er.-. per r.er..-ien:. i.-ji -.cj: ^riiai 
ntr. is iiready menticcei:. ]lj per :ect.. cer ic-t .rr.. ' 

Etrec :c. the ieit?ra.-Tt wiiert Fr-r'- r-^' iav^t -*^'.'.!e<i. 
•j:jt n.:e :f ir."er»rft !:? ^i.uri. iC': :*- t^:\<:'..'.c. -uf;r. a.- ha.-- 
'.'".•"^TT'r'i. IS rnly "»r''i-i.-f*r .f T.e ^•. .i^ile.-.t ecr r.or.-.ic 
zc.eD:cieH':c. ■ tvr-i :?-:r:: ir.r.a*:. Thir-*: r'i.*.- ir^ -*:*:.'■- .:, the 
Azc^ntirs;.' wher^ ".le rar-tr? :c i::"-.'--* .- '.hir„i i.*^ zivcrn. 
*t IS iu'er^stm:! "■: .r.ser^^ I'.-r -/_r- -< --.niv:.'..--; ■';r.r..:;'ior..-« 
ir <rLziJ. wiut;h i: IrrT p r:*: .oe.: 
Lei jri«: ^7 : ■: Ir.a;:.-: rr-..- 

wii 1.-. ir-fT l^>r. I; r»tr ^er 




«f»,' 






5^^_ 



•V p -^s 



>:- .* cn^-inn; - . rhan .C 



) - 



294 



THE RATE OF INTEREST 



(Chap. XV 



l#<v 




Of the North Ameripan Indians, line observed: — 

"Upon the banks of the St. Lawrrncp, there are several Httle 
Indian villages. They are surrounded, in general, by a good deal 
of land from which the wo(h1 seems to have lieen long extirpated 
and have, besides, attached to them, extensive tracts of forest. 
The clcnri-d land is rarely, I may almost say never, cultivated, nor 
are any inroads made in the forest for such a purpose. The soil 
is, nevertheless, fertile, and were it not, manure lies in heaps by 
their houses. Were every family to inclose half an acre of ground, 
till it, and plant in it potatoes and maize, it would yield a sufficiency 
to support them one half the year. They suffer too, every now and 
then, extreme want, insomuch that, joined to occasional intem- 
perance, it is rapidly reducing their numbers. This, to us, so strange 
apathy proceeds not, in any great degree, from repugnance to labor ; 
on the contrary, they apply very diligently to it, when its reward 
is immediate." ' 

Of the South American Indians in Paraguay Ra») tells 
of the difficulties which the Jesuits found in persuading 
the natives to provide for the future: — 

" ... if these [the Jesuits] gave up to them the care of the oxen 
with which they plowed, their indolent thoughtlessness would 
probably leave them at evening still yoked to the implement. 
Worse than this, instances occurred where they cut them uj) for 
supper, thinking, when reprehended, that they dufScieutly excu^ia 
themselves by saying they were hungry." ' 

In regard to the negro and the Russian we may cite the 
statistics of George K. Holmes ' and the observations of 
N. T. Bacon.* 

§3 

In many if not all of the case's which have been cited 
there are, of course, other elements which would tenil 
to explain the facts besides mere mental characteristics. 
Thus, th e high r ate of interest among the negroes and th e 
Russian peasants is un doubtedly due in gart to thei r poy - 

' The Sociological Theory of Capital, pp. 71-72. 

' Loc. cit., p. 76. ' Census of 1890. 

* Yak Review, Vol. XII, pp. 141, 239; Vol. XIII, p. 51. 



8kc. 3] INDUCTIVE VERIFICATION (ECONOMIC) 



•f?,} 



erty, jhough t hfjr^ijoyf^rty ia in turn largflyluf in tlif; men-' 
X a] cnaracter j .-tic- !. Thcrf; i:-- \\<:r>- in of^-ratir.ri thf; virious 
circle which has Fx;f!n noU;'l in ('])iipu-r XII. U'lurro tluTc 
is too little appreciation of the hh-Aa of the future, capital 
tenfl3 to disapf^iaj ; and the iiri-r-.-nrc of poverty tends to 
enhance still further the dfrnand- of thf: [jre-^-nt and to 
pre.ss down its victims from had to wf^r.-*-. 

But there are not v.antinj^ chs*s in which even fxrr.-ons who 
have wealth, but who neverrhek:.-..-! laek foresight and sfilf- 
control. exhibit the .-:ame fact.-. e.-'{K;ciaIIy by running into 
debt. This is charac:teri.-;tic of a con.'-idfrrable nurr,lx;r of 
the spoiled sons of rich Engli.sh noblemen. Tlie tyjx; is well 
described in some of .Steven.ion's novels. Thfsic pf^rsons 
are found living in Aastralia and el.-^^where in virtual 
exile on a .stif^end provide<l by their farr;iiies at stated 
intervals. This .stif.iend is sometimes provifled on '-ondition 
that they remain away fro.m their original environrnciit with 
its temptations to extravagance. One .■■uch individual 
known to the writer had inherited a large fortune. The 
precaution hail Ijeen taken to leave it in tru.st -/> that he 
could riraw only the income. Yet this man contrived to 
contract larse debts on chattel mortgages at high rates of 
interest, and was noted for his wa.-T.eful. short-sighted 
erection of temporary- dwelling- in the various coriimunitiea 
anions which he contin'oally fti'ted. TTie :-ame character- 
istics are often found among we althy iLtudents at univer- 
sities, who have ac':[uire<l. through ir:.pror.<-r hori:f- training, 
an exaggerate'! Mea of the nee-is of the moment and little 
appre'^iation of those of the future. Tnerre t:.f-:^ Ijecome 
the victims of money lenders, and are frequent piatrons of 
the pawn shops. 

N'ljt only do we find examoles oi 3. high rate of prefe renc e 
f'-.r Dresent_qv'er^utuTe_g>>is_amon£ the £ro<ii£a[;y_ruLh. 
but we often fi n<i the opr.'".)site exarr.ple of a low rate o f 
" reference for pr esent over_f:.;t;ure 2 0«>is among the thrifty 
'CQL Examples are espeoiaily ireiiuent among the Jews, 



wr 



•la 



prop'ensity to aocumuiate 



fionev f, ;n 




296 



THE RATE OF INTEREST 



[Chap. XV 



,%*■■ 



in the face of misfortune and social ostracism, is too well 
known to recjuire extended comment. 

§ 4 

The factor wliich has been ( Mgiiated as ' ■. gard for pos- 
terity" deserves special attend • )n Perhaj); *,he most con- 
spicuous example of extremt (psngard f.^r posterity is 
found in Rome during the time of its decline and fall. The 
following quotations from Rae contain important testi- 
mony : — 

"It were needless," he says, "to enlarge on a subject so well 
known as that of the general corruption of Roman manners, from 
the time of the first Ca?8ar. Venality and licentiousness may be 
said to have been universal. I shall confine myself to one particu- 
lar, as mr.king sufficiently the declension of those principles on 
which the strength of the effective desire of accumulation mainly 
dejM'nds. I allude to the decay of the family afte'-i.ons, of which 
evidence everywhere meets us. The men did not wish to be fathers, 
scarcely did the women wish to be mothers. . . . They lived, not 
in others, or for others, but for themselves, and sought their good 
in enjoyments altogether selfish. It was their aim to expend on 
their own {)ersonal pleasures whatever they possibly could. It 
would seem a.s if the majority, could they have forekimwn the 
exact limits of their lives, would have made their fortunes and 
them terminate together. As they could not do so, the fortunes 
of many ended before their lives, as the fortunes of others held out 
be}ond their lives. To reap, however, themselves, while alive, 
all jmssible benefit from what they might chance to leave others 
to enjoy after their death, they encouraged some of the meml)ers 
of a despicable class who seem to have constituted no inconsider- 
able part of Roman society. Parasites ready to minister to every 
pleasure, and to j)erform every possible service, waited on the man 
of wealth, in the hojw and expectation of enjoying a portion of it 
after his death. They were more desirai)le than children, both 
because they werf- able to give something more than mere un.sub- 
Btantial affection and esteem, and l>ecaii.se they were willing to 
give it. . . . It gave occasion to the law compelling parents 
to leave their children a certain part, a fourth, of their projxTty. 
Its prevalence may be judged of by the wording of the enactments 
increasinj; the <-hi!drcr!'« «haiT. . . . The gerier.=i! sf!fi:^hiif.-*.i of 
the principles guiding the conduct of individuals may be gathered 



il 



Sec. 6] INDUCTIVE VERIFICATION (ECONOMIC) 297 

from the prevailing proverb, " When I die let the world burn .' . . . 
Pasture took place of tillage ; corn was brought from the provinces ; 
and when the supply failed famine ensued. Even the construc- 
tion of ships for the transport of this, and other merchandise, would 
seem to have been an effort to which the accumulative principle 
was scarcely equal. It was found necessary to encourage it by 
rewarding those who prosecuted that branch of industry. Some- 
times land formerly cultivated was allowed to lie entirely waste, 
and passed altogether out of the class of instruments. The forest 
and wilderness gained on the Romans, as they would now, for 
similar reasons, on an Indian population, were some of these tribes 
put in possession of the domains, anciently the property of their 
race, at present yielding abundantly to the provident industry 
of the whites. Had there been no interruption of the barbarians, 
the Empire must have perished, more slowly perhaps, but as cer- 
tainly, from the operation alone of these internal causes of decay. 
They were occasioning a progressive diminution of the capacity 
which materials formerly possessed. Thus, it is to the Romans 
themselves as much as to the barbarians, that the destruction of 
the public edifices is to be ascribed. The stones were applied to 
private purposes." ' 

"Thus, among the Roman writers, the heir is always represented 
in an invidious light, and to save for him is represented as a folly. 
The WTitings of Horace, and the contemporary poets, throughout, 
exemplify the prevalence of this feeling." ' 

"In ancient Rome, interest was in reality exceedingly high, from/ 
12 to 50 i)er cent."' 

Tliest' rates doubtless refer to the degenerate days. 
Previously, at the time of the end of the republic, the rate 
was as low as 4 to 6 per cent.* 



-HA 



>r 



§ 5 

Tlie ehnraoteristics of foresight, self-control, and regard 
for po.«terity seem to be partly natural and partly accjuired 
within the lifetime of the individual. Among the cases 

' Loc. rit , pp, 95-99. • Lor. rit., p, 64. 

' Loc. rit, p. 129. liac's authority Ls Houchcr's Hutoirf dc L'U»ure, 
Paris, 1819. p. 25. 

' iSt ^-iiKiiiun'.t Principiei of Kcunomica, New York (Longmans), 
1905, p. 4U4. 



-I 



>H 



' t ■- 

: •■ -•;■ 

is. i 



ii. i: 



Ifl 



tt 



ISs 



L*t 



' = ii^ 



^ft 




UJ!1- 1 



298 



THE RATE OF INTEREST 



[Chap. XV 



which have been given ire conspicuous examples p'" both, 
although it is difficult here, as always, to disentangl the 
influence of nature from that of environment. We are 
accustomed, for instance, to ascribe to the Jews a natural 
racial tendency to accumulate, though this characteristic 
is certainly reenforced by, if not entirely due to, the ex- 
traordinary influence of Jewish tratlition. Of the Scotch, 
it would be ilitticult to say how much of their thrift is due 
to nature and how much to training handed down from 
father to son. Tlie American negro is regarded by nature 
as a happy-go-lucky creature ; but recent experience with 
industrial schools has demonstrated the fact that thea- 
characteristics can be largely reversed by training, if in 
fact they have not been entirely created by the lack of 
training untler conditions of slavery. There is now ac- 
cunmlating nmch testimony ' to show that there is more 
error than truth in the common opinion as to the relatively 
great importance of heredity as compared with environ- 
ment. 

WTien postal savings bar'-.s were first introduced in Eng- 
land, it was objected that the habits of the English T-uor, fur 
whom they were intended, were such that they would never 
make ust^ of them. But Gladstone insisted that habits 
were an arbitrary matter, and that the fashion of spending 
coukl l)e displaced by the fashion of saving as soon as the 
principle of imitation had had ♦ime to opt^rate. Tlie ex- 
jx?rience with English postal savings banks has justifitJ 
his prediction.' 

In lact, it would lie a serious mistake to assume that the 
characteristicsof man as to foresight, self-control, and regard 
for his own and his children's future are fixed racial or 
national (jualities. Tlie part which nature may play iu 

' For instance, the reports of the Children's Aid Society of \pw 
York; the child-saving work of Dr. and Mrs. J. H. KcllogR at Biittlo 
Cn«k; the evidence of the British Interdepartmental Committee 
on School Children, etc. 

' See The hfvelopnunt of Thrift, by Mary W. Brown, New York 
(Mucniillun), 1900. 



Sbc. 6] IWDUCTIVE VERIFICATION (ECONOMIC) 



299 



these inat*<»rs is as yc' lar from being understood; but 
however great that part may be, i*^ is certainly true that 
the influence of training is also great, and therein lies the 
possibility and hope of social reform in these matters. It 
should be one of the distinct aims of any intelligent modem 
education, whether in the home or the school, to inculcate 
foresight, self-control, anrl a tlue regard for the needs of 
future years and even of future generations. It goes with- 
out saying that individuals and nations with these char- 
acteristics have therein a more secure and permanent claim 
for success in all directions. 



§ 6 

but, as has been emphasized in previous chapters, t he rate 
of preference for present ove r future goods is not a^ (^s- 
tion of mere f3ersonal_characferistics, but jJ epends also upo n 
the character of one' s incom e:^trcam; namel y, on its size , 
shape , composition , and probability. In respect to size^ ou r 
the ory mainta ins that the larger thejnc ome, other things such 
as joredght and self-control being equal, the lowe r the rate o f 
preference fo r present oyer ruTuregoods. If this is true, we 
should expect to find poverty and riches associated re- 
spectively with a high and a low rate of interest, or with 
borrowing and lending, or with spending and saving, or 
with perishable and durable instruments. That this char- 
acterization is in general correct is not likely to Ix; denied. 
It is true of course that the amount loaned to the poor is 
small because each individual loan is nece.s-sarily small ; but 
the number of these loans is ver\' great . and the desire of the 
poor to borrow, when it exists, is verj- intense. Tlie nuny 
conspicuous exceptions to these rules are explainable on 
other grounds. It not infretiuently hajifjens that the poor, 
instead of Ijeing l)orrowers, are lenders; but in this ca.se 
either they have unusual foresight, self-control, regard for 
their children, and other qualities tending in the same direc- 
tion, or else their income-stream has such a time-shapo 






.» ,1 



300 



THE RATE OF INTEREST 



[Chap. XV 



M 




as to encourage lending rather than borrowing. Reverse 
conditions apply likewise to the case of many wealthy men, 
viz. those who are borrowers rather than lenders. Whether 
from wrong training or other causes, they lack foresight, self- 
control, regard for posterity, etc. But disregarding these 
factors and confining our view to the direct influence of the 
size of income, it is true, in a general way, that the po r 
I are more eager borr owers_than The rich, and w ill often pa t- 
' ronize pawn shops and plhi er agenctes jn "which the rate 

high; also that their dwellings 



nf inff>rpst jgiJuQtdm atel, 

or other structures are often of a very unsubstantial char- 
acter, such as would not "pay" except to those who put 
a very high estimate on present as compared with future 
goods. Tlie deeper the poverty, the higher the rates which 
the borrowers are compelled to accept. Even pawn- 
broking is not available for the extremely poor, but is 
patronized rather by the mmlerately poor. Those who are 
extremely poor cannot give the kind of security which the 
pawnbroker requires. On this account they become the 
victims of even higher rates of interest, pledging their 
stoves, tables, beds, and other household furniture for the 
loans they contract. Tliese loans are repaid in installments 
such that the rate of interest is seldom lower than 100 |x'r 
cent, per annum.' 

Turning from classes to countries, it is noteworthy that 
in the coui^tries in which there are large incpmes^e_findjo\v 
interest, a tendency to lend rather than borrow, accumulate 
rather than spend, and to form durable rather than perish- 
able instruments, whereas in countries where incomes arc 
low the opposite conditions prevail. Tlius, incomes are 
large and interest is low in Holland, Krance, and Englaml, 
whereas the reverse conditions hold in Ireland, Chuia, India, 
and the Philippines. In Ireland, for instance, esijecially 

' For details as to thirteen typical loanb of this chtiraclcr, «-e 
U. 8. Hurrnu of Labor Bulletin, Nn 64, May, t90«, pp fi?? fia?. 
Thus, "loan 1," 143 per cent., "loan 3," 224 per cent., "loan 7," 156 
per cen» 



m^ 



Sec. 7] INDUCTIVE VERIFICATION (ECONOMIC) 301 

in the early part of the nineteenth century, the rate of 
interest was high. The cottier was always in deljt, and his 
hut and other instruments were of the most unsubstantial 
variety.* Again in the Philippines the rates of interest 
on good security are often 2, 5, and even 10 pdr cent, a 
month. "The Chinese money lender frequently takes 
advantage of the Filipino's poverty.'" Many of these 
cases may be wholly or partly explained by otlier causes 
such as have been mentioned in the last section. The 
possibility of more than one explanation shows that in this 
field we can scarcely hope to arlduce any complete proof 
of an inductive nature. But since any of the possible 
explanations fit in with our theory, we are safe in saying 
that the facts do not at any rate contradict that theory. 



§ 7 



As to the influence of the compositir/n of income, it is 
even more difficult to obtain any statistical confirmation of 
value. In a previous chapter it wa.s shown that variations 
in the amount of that income which takes the form of food 
would have an effect on the rate of intere.st similar to the 
effect of variations in the total inconie itself. Scarcity 
of fo od should thpf pfore c ai'-^ Jii^5h_-ijatex*i*t,~aiuL_aiailj- 
uance of food, low interest. Certain presumptive evidence 
J?7ound in the observation of Jevons on the relation be- 
tween the price of wheat and the rate of d's.;ount.' Wheat 
being the most typical food in England, it may be a.ssumed 
with considerable probability that its price varies inversely 
with the amount of food consumed. J evons found th at ^ 

'See Longfield, "The Tenure of Land in Ireland," in Pr.loyn's 
Sy^Ums of Land C'Uture, Londun (Cassfll. Potter, and Oalpin), 1876, 
p 16 

' From a letter ti' the author from Pn)ff:sor E \V. Kfrninfrt-r ; see 
also his article in The Butineit Monthly, Pitt-burg, .\pril, 1WJ7, p 2. 

' 5tt- I tivtuiigaiion* in Currency and Finance, i^'>4, p xiv; also, 
Robert Goodbodjr, in Byron W. Holt's (iold Supply and PronvUy, 
p 166 



vi: 



i ■ 



• 'fj 




.-\ 






302 



THE RATE OF INTEREST 



[Chap. XV 



high price of wheat corresponded to hig h rates of intftrftst,, 
and vice versa . This would ahnost amount to saying that a 
relative scarcity of food was associated with high interest, 
and vice versa. During the siege of Paris the rate of inter- 
est was high, although other causes than the scarcity of 
bread were doubtless accountable for the fact. 



§8 

As to the influence of risk, we encounter similar diffi- 
culties. But evidence as to our main contention, namely, 
that m general riskjtends to raise the com mercial rate o f 
interest but to lower pure m teres t, is forthcoming" The 
first part of this proposition is a matter of so common ob- 
servation that no special collection of facts is necessary. 
Every lender or borrower knows that the rate of interest 
varies directly with risk. A bird in the hand is worth 
two in the bush. The principle applies not only to the 
explicit interest in loan contracts, but to the implicit 
interest which goes with the possession of all capital. 
WTiere there is uncertainty whether capital saved for the 
future will ever be of service, but there is certainty that 
it can be of service if used immediately, the possessor 
needs the possibility of a very high future return in order 
to induce him to save the capital for future use. I ' is note- 
worthy that in time of war there is a ruthless uestruction 
of crops and a tendency among the possessors of consumable 
wealth to enjoy it while they may. The same conditions 
are characteristic of communities which are in a perpetual 
state of uncertainty.' " The rate of interest is everywhere 
proportional to the safety of investment. For this reason 
we find in Korea that a loan ordinarily brings from 2 to 
5 per cent, per month. Good security is generally forth- 
coming, and one may well ask why it is so precarious to 

' On the uncertainties of Indian life, see The Sociological Theory 
ol Capital, pp. 69, 70. 



Sec. 8] INDUCTIVE VERIFICATION (ECONOMIC) 303 



■!rl 



lend. The answer is not creditable to Korean justice. 
... In a land where bribery is almost second nature, 
and private rights are of small account unless backed up 
by some sort of influence, the test apparent security 
may prove a broken reed when the creditor comes to lean 
upon it." ' 

There remains the second part of the proposition in re- 
gard to risk ; namely, that while risk tends to increase th e 
rate of interest on risky loans, it tends at the same time to 
decrease t h at on safe loans . This proposition is not familiar 
to most persons. It has usually caused surprise when, 
during a time of political stress and danger, the rates of 
interest on perfectly safe loans were found to be so small. 
Many such instances may be cited. At certain periods 
during the Civil War, when the greatest uncertainty 
prevailed, loans with good security were contracted at 
nominal rates, and bank deposits tended to accumulate 
for lack of sufficient outlet in secure investments. Times 
when public confidence is shaken are characterized not only 
by high rates on unsafe loans, but by efforts on the part 
of timid investors to find a safe place for their savings, even 
if they have to sacrifice some or all of the interest upon it. 
They will even hoard it in stockings and safe deposit vaults, 
or leave it idle on deposit in bank. "... In 19()3 . . . 
the public took alarm and began to hoard their capital 
in the form of banking credits, instead of bidding with it 
for securities. In the meantime, the scarcity of free capital 
in the market enabled the banks, which held the money 
of the public, to exact 5 and 6 per cent." * We may even 
o ccasion ally find cases in which the desire to obtain a safe 
mcthoa ot naing Pftpifftl ia ^n kectt afld SO diffi cult t o satisfy 
t hat the rate of interest is negative^ The investor is then 
in the position of tFe user of a safe deposit vault, thankful 
enough to receive the assurance that his capital, by being 

' H B Hisrihcrt, The Panning of Korea, New York. 1906, p 283. 
' Charles A. Conant, " How the Stock Market reflects Values," 
North American Review, March, 1905, pp. 346-359. 



^^f;:: 



304 



THE RATE OF INTEREST 



[Chap. XV 



intrusted to another, will not be diminished, to say noth- 
ing of being increased.' 



Its «i 



-I 




§ 9 

We still need to verify the most essential part of our 
theory ; namely, th a^the ratn nf interest depend s upon the 
time-shape of the income-stream . If the theory is correct, 
we should find, other things being equal, that when, in any 
commmiity, the income- str eams of its inhabitant s arc in - 
creasing, the rate of mterest will be hi^; t hat when tho} ' 
are de creasing^ the rate of interest-wULb c low ; and that 
when they alternate from one condition to the other, the 
rate of interest will also alternate according to the period of 
the loan. 

The most striking examples of increasing income-streams 
are found in new countries. It may be said that the United 
States has almost always belonged to this category. Were 
it possible to express by exact statistics or diagrams the 
size of American incomes, they would imdoubtedly show a 
steady increase since colonial days. Statistics almost equiv- 
alent to these desiderata are available (though not very accu- 
rate) in the form of the United States Census figures of 
"per capita wealth," as well as statistics of production and 
consumption of staple comnu lities and of exports and im- 
ports. These, combined with common obsei-vation and 
the statements of historians, lead to the conclusion that 
i^mpriciin incomes ha yp tv^p" "n thf iacrease for twojmn- 
(Jred years. It is also true that ^urmg thi■^ p fflpfl p f 
rising mconie s, the rate of interest has Wn hig h. Tlie 
simplest interpretation of these facts is that Americans, 
being constantly under the influence of great expectations, 
, have been alwaA 's tpa/^y *^" promise a rel atively large par t 
1 of their abundant future incmne for a rela tiyelyjmall_ad- 
- ditioajto^ their prejont, just as he who expects soon to 

' See Bagehot, Lombard Utreet, Chap. VI ; also, Macaulay, History of 
England, Chap. XIX. 



Sec. 9] INDUCTIVE VERIFICATION (ECONOMIC) 



305 



come into a fortune wishes to anticipate its realization by 
contracting a loan. 

Not only has the rate of interest been high in America 
as compared with other countries during this period of as- 
cending incomes, but some of the other conditions cciuiva- 
lent to a high rate of interest liave also been in evidence. 
Thus, the country- JiaiLJbeeiLJicm.'itjlcjiioii.sly^ a borrowing 
country, in debt to other countries. Tlie proceeds of 
such loans have shown themselves in increased imports 
and diminished exports, creating a so-called unfavorable 
balance of trade. These phenoini.'na have usu.'tlly been 
expressed as a "demand for capital'' ; but, while it is quite 
true that the exploitation of our natural resources required 
the construction of railways and other forms of capital, 
this fact is better and more fully ex{)rer;.-sed in terms of in- 
come. We wanted, not the railways and machinery- them- 
selves, but the future enjoyable products to which thi.-, 
apparatus led. The construction of these instruments 
necessarily diminished the immediate enjoyable income 
of the country- and added to that of the expected .uture. 
It was to even up this disparity of immediate and remote 
income that loans were contracted. It does not matter 
w hether the loans from the fo r eigner were received in ~ t he 
f orn^ of jnajchiner^and other instriimentjj^ production, or 
in the form of the comforts of life to su{jp()rt us while we 

In either case the 
;tream. 



ourselves constructed the instruments 

essential fact is the transformation of the inconi( 

and not the "need of capital." which is merely one of the 

means thereto. JLoiport jstaliitici .skavv that^ -as sl matisr 

of fact, we received gur loans from the foreigner jnjbgth 

forms. 

Not only have we witnessed the phenonx ^ of hijrh rates 
of interest and of borrowing during this period of .\inerican 
development, but it is also true that the character of the 
instruments created was for the most part of the unsub- 
stantial and "quickly returning" kinds. Our highways, 
as John Rae pointed out, were little more than the natural 



i-l 



306 



THE RATE OF INTEREST 



[Chap. XV 



surface of the earth after the removal of trees and rocks; 
our railways were lightly ballasted, often "narrow gauge," 
and crooked to avoid the necessity of excavations and tun- 
nels; our earliest buildings were rude and unsubstantial. 
Everything was done, not in a permanent manner with 
reference to the remote future, but in order to save a large 
first cost. 

During the last t wo decades these conditions have Ix'cn 
reversed. The rates of interest in America have fallen 
greatly, as the statistics in the Appendix will show.* We 
havc__ceased to he a borrowmg nation, and are buyin g 
back our securities from abroa d. Tliis repayment of debts 
is accomplished through the export of our now abuntlant 
products, and creates a so-calleil favorable balance of trade. 
Again, the character of the instruments which have been 
now for some time in process of construction is of thgjnost 
substantial kind. Steel rails have long since taken the place 
of iron rails, "broad gauge" of "narrow gauge"; railways 
have been straightened by expensive tunnels, by bridges, 
and by excavations ; * dwellings and other buildings have 
been made more substantial; macadamized roads arc 
gradually coming into vogue; and in every direction — 
industrial, agricultural, and domestic — there is an evident 
tendency to invest a large first cost in order to reduce future 
nmning expenses. 



10 





Thus i n America we see exemplified on a very large scale 
t he truth of th e theory that a rising income-stream raises 
and a falling m come-slream depresses tlie r 'afe"of interest . 
or that these conformations of the income-stream work out 
their effects in other equivalent forms. A similar causation 
may be seen in particular localities in the United States, es- 

' See Appendix to Chap. XIV, { 1. 

* It is estimated that Western railways in the United States have 
actually under way or in contemplation improvements amounting 
to $1,000,000,000. Wall Street Journal, December 19, 1905. 



i 



Sue. 10] INDUCTIVE VERIFICATION (ECONOMIC) 307 

p cially where changes have been rapid, as in mining com- 
munities. luXfllifomia, in the two decades between 1S.5() 
and 1870, following the discovery of gold, the income-stream 
of that state was increasing at a prwJigious rate, while the 
state was isolated from the world, railroafl connection with 
the East not being completed until J869, During this 
period of isolation and ascending income, "... oppor- 
timities for investment were innumerable. Hence the 
rates of interest were abnormally high. The current rates 
ilL thp 'early d ajra' w o r e quo te d f^ if^i pw ceuLamontb. 
. . . The thrifty Michael Reese is said to have half repented 
of a generous gift to the University of California, with the 
exclamation. 'Ah, but I lose the interest,' a very natural' 
regret when intere.st was 24 per cent, per annum." » After 
r ailway connectio n in 1869^ Eastern loans began to flow Id. 
The decade, 1870-1880. was one of tran.sition during which 
the phenomenon of high interest was gra^lually replaced 
by the phenomenon of borrowing from outside. The rate 
of interest con.sequentIy dropped from 11 per cent, to 3 
per cent. * "Since 18.80 the economic hi.stor\- of California, 
or at least of San Franci.sco and vicinity, ha^ not differed 
so very much from that of the rest of the country." * 
During recent years the rate on mortgages in San Franci.sco, 
up to the time of the earthquake and fire, ha.s been 4 to 4J 
percent, exclusive of the state tax. 

The same phenomena of enormous interest _rM£ii were 
also exemplified in Colorado and the Klondike. There 
were many instances in both the.«e place.s during the tran- 
sition period from poverty to affluence, when loans were 
contracted at over 50 per cent, per annum, an<l the bor- 
rowers regarded them.«elve.s a-s lucky to get rates so "low." 
It wa.s also conspicuou.sly true that the first buildings and 
apparatus constructed in these region.s wore verj- un.sub- 

' Carl C. Plehn. "N'otes concemine thf Rat*'.* of Interest in Cali- 
fornia," Quarterly PMieatumt of the Arrw.riean Stututical Attocia- 
tion, September, 1899, pp. 351-352. 

' Ibid., p. 353. 1 Ihid , p. 353. 



iA 




308 



THE RATE OF INTEREST 



[Chap. :." 




stantial. Rude board cabins were put up in a day. Thus, 
high interest, borrowing, and unsubstantial capital were the 
phenomena which attended these communities when under- 
going their rapid expansion. 

I gNey ad^Ju. ^hn .sf^vnn tina, when the mines were in- 
creasing their product and the income of its inhabitants was 
tending upwards, tligj-ate of interest was high and tti o 
people in debt. Tliebondetl state debt itself amounlfid-to 
$500,000 and drew 15 p er c(;nt. interest.' In the next dec- 
ade all these conditions were reversed. The mines were 
on the decline,' the rate of hitorest fell, and the state and 
territorial debts wore largely paid off.' The fall of the rate 
of interest in this case could not have been due to the in- 
troduction of loans from outside, except so far as old debts 
were refunded at lower rates; fresh loans were seldom 
made, as the state haii ceased to be a good place for new 
investments. In the last few years new Nevada mines 
in the gold-field region have been opened. Loans are again 
entering the state, and the same cycle of history as above 
described is aUjut to be repeatetl. 

^iUmbering^ communities often go through. -a^somcaiiat 
siniilar cycle. The virgin forests when first attacked tend 
to increase rapidly the income-streams of those who exploit 
them. Then coines a period of decrease. Thus in Michigan 
two or three Jecad'^s ago the lumber companies fountl a 
profitable invtsrment. and borrowed in order to exploit the 
Michigan fo-^'t^t^ .Aiter the exploitation was complete 
iind the fort^i- hmi In'en ;)ften unwisely) exhausted, those 
regions ceaseii : 'it a li-sirable place for investment, and 
their ownei^ -mF^- aii^^ he position, not of receiving, but 
of seekiniL ir5T't«iaESC& 

Airier rae Tarmk '^s»m railv^ay were completed, connect - 
ug tae "i^Ma^Hpis: '* j^- with the East, there arose a great 

msmi tm- loam- n exuioit the rich farming lands in that 



■^ Tue Uijvernor of the State of Nevada," 1S79. 
Jffti»e« sage Qtanten. 1982. Soecial Report U. S. Census, p. 255. 
aee- iiiiei ' M4~«afK~ of the Governor of the State of Nevada." 



iTlri> ♦vStSFT 



Sec. 11] INDUCTIVE VERIFICATION (ECONOMIC) 



309 



section of the countrj-. Tlie rate of intfn'st fn;f|uently was 
10 and 12 per cent., and f;vcn hif^her. During much of this 
time the Northwf;Htem Mutual Life In.surance Company, 
up to 188(), made an average rate on all it.s mortgage 
loans, $10.000.()(X) in amount, of nearly 10 per cent. 
Another striking proof of thf; rlernand for loans in the 
Middle West i.s .shown in the fxfjerif'ncf; of the New York 
and Connecticut life insurance companies. Xfjw Yorl:, 
up to 18^, ha^l a law prohibiting the life insurance com- 
panies in that .-tate from loaning on real estate outside of 
New Yr.rk. Connecticut ha^l no n'striction in this regard, 
and her companies loaned exten.sively in the \V(;st. Tlie 
result is seen in the rates of interest realized on mortgage 
loans of companies in the two states. Taking the fM.'rio<l 
1S6*0 to LW) as a whole, the Connecticut companies realized 
lj*j per cent, more than did the New York companies, 
^i nce 1880, the Middle West has developt^l rapidlyj^and 
loans on farming lands are now made at lo w ra tes. During 
the past two years, certain of the insurance companies have 
been making mortgage loans in Illinois at 4^ per cent.' 
A similar histor>- ha- recently bf;en enacting it.self in the 
northwest region of tne Unitn] States. During the period 
of^xj)loitation while the Great Xortht^rn and otheT railway s 
were deyeioping this territorv'j^ the phenomena o f hig h 
inter^L-aaiL borrowing, were almost uni v ersa. 1. But lat- 
terly, much to the .surprise of many Easterners, it has hften. 
found that the ratfs or interest in these states have b«,'en 
at times lower even than in m^jst American cities, and that 
the inhabitants have actually Yx^^n seeking to lend to the 
Ea:«t inst'^vi of to ^x)rrow from it. 



II 



Australia furnishes another example of a countr>- which, 
iiiiuugii iiiiprfjvcLiieQt in tne rrieaiis or traii.sp<ortation, 

' S*^ Zartman, Thf Inrf-'imfnti of Lift InJiurance ComptxnU* , 
New York (Holt;, 1906, pp. -Sd-Ql 



m 



310 



THE RATE OF INTEREST 



[Chap. XV 



mil 



created a great demand for loans. The rate during the 
fifties on safe securities was rather low. This rate increased 
until, during the seventies, 7, 8, and 9 per cent, were usual. 
Since 1880 the rates have declined.* 

England may perhaps be cited as exemplifying the same 
phenomena which we have seen in the case of Nevada, 
though in a less degree. Thus, as Nevada has exhausted 
its mines of precious metals, so England is on the road 
toward exhaustion of its coal and iron supplies. This fact 
has been noted with considerable alarm by many econo- 
mists, especially Jevons. It df^ ""^ n erpmarily mdic^^ e 
t hat the econom ic^owgr_Qf. FngiiHhmpn_yi",b? Cf-^tlx or 
e yen at all les s ened. _Jta-agBJficance shows i tself in t jjxe 
tendency of Eng la nd to become anjnyesting country;__It 
ia_the^art^of thiMC who have property in mines not to u se 
a ll of the prod uct as income, but to '•"Invpst in vrdvr ta 
maintain the capit al. This the Englishmen have done and 
are doing; and being imable to make satisfactory invest- 
ments at home, they have placed their loans all over the 
world. The income-stream produced for them by their 
native island is destined, perhaps, to decline, certainly 
not greatly to increase; but by saving from this declining 
income and investing in South America, Australia, South 
j Africa, and other regions where the natural resources are on 
the increase instead of on the wane, the Englishmen may 
still maintain their capital intact or even increase it. It 
is said, with how much accuracy I do not know, that 
Englishmen own an area in the United States as large as 
Ireland. The figures given by Giffen show that the na- 
tional income increased for several decades, but that the 
rate of increase slackened' for the decade 1875-1885 com- 
pared with 1865-1875; that whereas in the earlier decades 
there was a general increase in all directions, in the later 

■ Zartman, Tk» /ntmtmenfa of IaJ* Inauranee Companiu, p. 103. 

' Qiffen, Onwtk of Capital, London (Bell), 1880. See alao articles 
by Olffen in eontisuation of the same subject in Journal of Royal Sta- 
tiatieal Socuty. 



Sec. 121 INDUCTIVE VE&IFlCATICm (ECONOMIC) 311 



deode ttiere were many items of decrease,* the most nota- 
ble being of mines and ironworks ; * and finally, that among 
the greatest increases was that of foreign investments.* 

We thus see that the rate of preference for present over 
future goods, in its various manifestations — such as a high 
or low rate of interest, more or less lending and accumu- 
lation of capital, and the character of the instruments 
formed — depends upon the time-shapo of the income-stream 
of a community, as determined by its natural resources; 
that in virgin countries like the United States in the last 
two centuries, Australia and South Africa, rich in timber, 
untouched ore, and raw materials generally, the income- 
stream is of the ascending type and produces a high rate 
of preference, whereas in older countries like England and 
Holland, in which the natural resources have been fully 
developed, and are even declining, the rate of preference 
tends to be low ; such a country either uses up its income 
and thereby reduces its capital, or seeks economic salvation 
in foreign investment. 






51. 

n 



k 



5 12 

The time-shape of an inc ome-stream i s^howgyer, deter - 
mi ned in part by other causes t han natural resource s. 
Amon g thftafi ca uaft.q^ misfortune holds a hi gh p lace in 
causing temporary depressions in t he income-strea m, that 
is, giving to it a time-shape which is first descending and 
afterwards ascending. TTie effect of such temporary 
depression is to produce a high valuation of immediate 
income during the depression period as compared vith the 
valuation of the income expected after the depression is 
over. It is a matter of common observation in private life 
that loans often find their source in personal misfortune. 
The alK)ve-mentioned investigation of the conditions <rf 
borrowing among the poor* shows that the chief causes 



%'i 



' Ibid, p. 44. » Ibid, p. aa • Ibid, pp. 40-42. 

* U. S. Bureau of Labor Bulletin, No. 64, May, 1906, pp. 622 ff. 



312 



THE RATE OF INTEREST 



[Chap. XV 



■ 



for borrowing arc a tloath or birth In the family, or pro- 
tracted illness, the expense of which, even when amount- 
ing to only $10 or $20, would, without the loan, make 
serious inroads on the daily necessities. 

We may see the operation of the same principle on a 
larger scale in the case of the San Francisco earthquake, 
which, had it not been for the succor rendered by the whole 
count r}', would have cut down the income-stream of the 
city to the starvation point. In addition to the aid of many 
millions of dollars of gifts, there were needed also heavy 
loans. Wliether these loans were used to produce sus- 
tenance, which is direct income, or to offset the cost of 
rebuilding the city, which is outgo, the effect is the same, 
— -thoy were for the purpose of salving over a tenij)orar>- 
injury to the income-stream. The effect on the rate of 
interest was slight, because of the opportunity to borrc- 
heavily from outside. Had the city not had this opportu- 
nity, the depression in its income-stream could not have been 
mitigated, and the rate of interest would inevitably have 
risen to a level comparable with that which prevailed in the 
same region a half century ago during the gold fever. 

In much the same way is the income-stream of a nation 
affected by war. The effects in this case, however, are 
more complex, owing, first, to the element of uncertainty 
which the war introduces until peace is declared; and, 
secondly, to the fact that wars are apt to be more pro- 
tracted than most other misfortunes. The effect, accord- 
ing to previous explanations, should be that at the beginning 
of the war the rates of interest on risky loans would be high 
This would be especially true of the loans the periotls of 
which are short, or not long enough to outlast the war. On 
the other hand, the rate of interest on safe loans would be 
lowered for short-term loans, and raised for long-term loans. 
A short-terra loan relates to a descent in the income cur%e 
if repayable at a time when the income-stream is apt to be 
still further reduce<i T^js descent in the incn-nc-stresfn. 
together with the element of uncertainty, tends, as has been 



Sue. 12] INDUCTIVE VERIFICATION (ECONOMIC) 313 



seen, to lower the rate of interest on safe loans. On the 
other hand, for long-term loans intended to outlast the 
war, the rate of interest is apt to be hirrh, for the income- 
stream at the time of repayment may l)e expected to exceed 
the income-stream at the time of contract. 

At the close of the war, after peace is declared and the 
element of uncertainty introduced by it has disappeared, 
the rate of interest, even on .short-term loans, will b<! high ; 
for then the country is, as it were, beginning anew, and 
the same caases operate to make interest high as apply in 
the case of all new countries. The situation at this [M'rio<l 
is exemplified by the recent peace loan for Japan. 

When the effects of the war include the issue of depre- 
ciated paper money, the rate of interest is affected in a 
somewhat more complex manner, iKjing then .subject 
to the influence of depreciation, acconling to the princi- 
ples explainefJ in Chapter V, and statistically vcrifif-d in 
Chapter XIV. 

Among the most powerful rau.ses which affect the time- 
shape of income-streams has b<'en notcfl the effect of inven- 
tion. That the claims which have been made for the effect 
of invention are verified in fact can .'scarcr-ly he doubted 
when we consider the historj- of railway transjKjrtation. 
The ve-y fact that during the la.st half century the chief 
outlet for investors' savings has been in the creation of new 
railways, is sufficient testimony. ^Miat is tnie in the case 
of this single invention or group of invention? is more sig- 
nally true when a large number of inventions is \)i-\uir made. 
The effect of the activity of the inventive faculty- rmi.^t havCj 
Djaterially contributed to keep up the ratf of intrTesTln 
th e United S tates, and during the la.<f p-nfrMt i(jj] in Qcr« 
many. 

The striking way in which the ratf> of interf>f in Germany 
has been maintained during the past centun.- is -howti by the 
experience of the Gotha Mutual Life Insurance Company, 
t::e lar-jf-jt in Germany. From iS29 to In.S, thi.s rompany 
made an average rate of 3.9 per cent. During the years 






m^ 



I* 

1 1 



. ; 



r- 



314 



TOM RATE OF INTEREST 



[Chap. XV 



■i.j 



1850-1852, the rate realized was 3.9 per toA. In 1874, 

the rate had risen to 4.8, influenced partly by the 
same causes that had affected the interest rate all over 
the world, and partly by the great industrial progress 
which Germany was making. In 1885, the rate had fallen 
to 4.2 per cent., and in 1902 to 3.9 per cent., a rate the 
came as that which had been realized three quarters of a 
century before ! ' 

§ 13 
We have considered the effect on the rate of preference 
of those changes in the income-stream due to the growth 
or waning of natural resources and to the temporary in- 
fluence of misfortunes and inventions. There remain to 
be considert- '. those regular changes in th e income-strea m 
of a rhythmic or seaso nal charact er. Though most persons 
are not aware of the fact, it can scarcely be doubted that 
the annual succession uf seasons produces an annual cycle 
in the income-stream of the community. This is especially 
true of agriculture. Grains, fruits, vegetables, cotton, 
wool, and almost all the organic products flow from the 
earth at an uneven rate, and require for their production 
also an uneven expenditure of labor from man during dif- 
ferent seasons of the year. Statistics of consumption show 
that the income enjoyed conforms in general to a cycle. 
Food products are usually made available in the warm 
months when crops ripen ; logs are hauled out of the wood? 
in winter, floated to mills in spring, and made into lumber 
in summer. 

But the tendcnfx^^ cycle is modified by the exist encf 
of stocks of comnjiodities to" tide over the periods of s carcin- . 
The_ice of winter is stored for summer, and the fruitji o f 
summer are canned and preserved for winter, Only ?.i 
far as such storage and preservation are difficult and ox- 
pensive, or impair the quality of the goods thus held over. 
or, because of the perishable nature of the goods, are im- 

' See Zartrr.an, The lnt>t»tmtrU» of Lift Inaunnee Coml ut. 
pp. 105-106. 



S»c. 13] INDUCTIVE VERIFICATION (ECONOMIC) 315 

practicable, does there remain any cyclic change in enjoyed 
income. The cycle is different for different industries and 
for different classes of the population. The farmer is 
perhaps the most typical for the countrj' as a whole. For 
him the lowest ebb is in the fall, when gathering and market- 
ing his crops cause him a sudden expenditure of labor, or 
of money for the labor of others. To tide him ovor this 
period he may need to borrow. A whole group of other 
industries, particularly tho.se connectefl with transporta- 
tion, experience a sjTnpathetic fluctuation in the income- 
stream. In the parlance of Wall Street, ''money is needled 
to move the crops." The rate of interest tond.s upward, 
as the following table shows : ' — 

MONTHLY DISCOUNT R.\TES FOR PRIME T\VO-NA.ME 

60 TO 90 DAY'S' PAPER IN NEW YORK CITY 

(.\verage for 10 yeara, 1S96- 190.5) 

January 4..3 

February 4.1 

March 4.4 

April 4.4 

May 4.1 

June .3.') 

July 4.2 

August 4.7 

September .>.2 

©•'tober r,:> 

November 4.S 

December 4.^ 

In a community dominate*! by some other indu.strj' than 
farming the cycle would be 'lifForent. Even in the above 
table the rates are of course a composite in which thf cycles 
of the manufacturer and of other element.* are .-^upK rimpose^I 
upon the i\vcle of the farmer. The manufacturer's cycle 
b a little later than the fanner '.s and .shifts the high rate-s 
from fall towani winter. 

Accordingly in England, which is more dominate«l by the 
inar:ufac*urer. the cycle, though aimilar to that ju-t or>sfrrved 
'Compiled from dAily r&tea given in TKt Financial RevUw. 



hi 







316 THE RATE OF INTEREST [Chap. XV 

for the United States, is shiftea forward, as the following 
table shows : ' — 

MONTHLY AVERAGES OF MINIMUM RATE OF DISCOUNT 
OF BANK OF ENGLAND FOR YEARS 1845-1900 

January 49 

February 3,g 

March 35 

April 3.4 

May 3.6 

June 3,4 

July 3.3 

August 3.4 

September 3.4 

October 3,9 

November 4.2 

December 4.1 

§ 14 

The facts as presented in this chapter harmonize with 
the theor>' as presented in previous chapters. Acconi- 
ing to the theory, if there is a high degree of foresight. 
self-control, and regard for posterity, or if income-streams 
are large or plentiful in the food-element, or have a descend- 
ing time-shape, then, other things being equal, the rate of 
interest will be low, or capital will be accumulated, or the 
community will lend to other communities, or the instru- 
ments it creates will be durable. We find these results 
present in actual fact where the antecedent conditions 
enumerated are also present. Reversing the conditions. 
we find reversed results. Of course this inductive veri- 
fication is very rough, since we never can assert that 
"other things are equal," and thus isolate and measure 
any one particular factor, as in the more exact inductions 
of physical science. Yet the inductive study is wonh 
something, even if it be only in the fact that it does not 
contradict the theory ; for a false theory usually encounters 
facts with which it cannot be reconciled. 

• See Palgrave'a Bank Rate and the Money Market, New York Dul- 
ton), 1903, p. 97. 



CHAPTER XVI 



INDUCTIVE REFX'TATION OF 'MONEY THEOKV 



1 



§ I 

It would be impracticable, even if it wore worth while, 
to array before the tribunal of facts all the rival thf^ries 
of interest which have been presentf^l. We must rest our 
case largely on the statement of principles which has already 
been made. It was shown, for in.'-tance, that the common 
theorj', that interest varies inversf-ly with the quantity 
of money, was superficial, since money is merely a 
means for obtaining capital. It was also shown that the 
theories commonly given in economic tf-.\t-lx)oks. that the 
rate of interest depends on "(Quantity of f-apital," are only 
a little less superficial, sin^e ''apital its^^If i.s rnerfly a moans 
to income. We cannot reach the ultimate rosriilator of 
interest until w-e reach income ; arid it is only bofrms*'; of 
the lack of an adefjuate theor\' of income that oforiornists 
have been content with analyses so incomploto. 

It is often true that up to a certain p<jrit faot-- may lie 
adduceti even in support of a false r'. .n.-. It could doubt- 
less be shown, for instance, that inter^:::^t wa- often high 
when capital was scarce, and ^rice ':er-r. TTi''- rnioial tost, 
however, comes when an income-stream of an a.->cending 
t}-pe occurs wh^^re capital is plentiful, or of a d'-.-^conding 
type where capital is scarce. If incomes are ri.-inir, though 
capital be ; 'entiful. interest will be hizh. as in the L'nitfrfi 
States recently: and if incomes are falling, tho igh capital 
be scarce, interest will be low. A.s ««'xvn as oconornisrs think 
m terms of income, and giv^^ up thinking in f.frrris of f-apital, 
which is merely an expression for contemplat^-'i income, 
there can be no difficulty in reachins a f^orrect view of the 
problem, without the nect:sM!:y of coriiuting aii pre%'iou.H 
theories bv special facts. 

317 



- m 



r* 



i'L 



t 



318 



THE RATE OF INTEREST 



fCkAP.XVI 



s' 'i 



hi u 



[S : 



1 



The only theory for which its adherents will demand a 
test by facts is the theory, believed by many business men, 
I that the rate of interest varies inversely with the quantity 
of money. This theory, in spite of having been refuted 
by economists for over a hundred years, is still dominant 
among many if not most business men. The business m.an 
prides himself on reasoning by facts, and it is only by mis- 
reading facts, and not by any analysis of the problem, that 
he mclines to the money-theory of mterest. It follows 
that only by facts can he be convinced of his error. As 
Moody's Magazine well says : ' — 

"Slowly but surely the great financial, commercial, and busines<« 
imen of the world are reaching the conclusion . . . that an increased 
Jsupply of gold means higher, rather than lower, interest rates 

Most converts, however, are converts from the force of facts, rather 

than from reason and logic." 

§2 

So far as the matter of appreciation in its relation to in- 
terest goes, facts have already been adduced in sufficient 
numbers in Chapter XIV. At present we are to consider 
the theory that high rates of interest are associated with 
scarce money, and low rates with plentiful money. Since 
in general it is true that plentiful money means high prices, 
and scarce money low prices, if this theory were correct! 
we should expect to find that during those years when prices 
were high, rates of interest would be low, and vice versa. 

In the following table we see that there is no such inverse 
correlation between prices and interest as this theory calls 
for. The columns of the table relate respectively to dif- 
ferent decades. T\vo rates of mterest are given for each 
decade. The first, written opposite "high prices," is the 
average rate for those years of the decade whose price-levels, 
as shown by an index-number, were above the average price- 
level for the whole decade; the second is the average rate 
for the years whose prices were below the general average ;— 

' August, 1906. 



Sic. 2] REFUTATION OF "MONEY THEORY" 



319 



JIARKET RATES OF INTEREST IN RELATION TO HIGH 
AND LOW PRICES' 





1824 
to 

1831 
incl. 


1832 

to 
1841 
incl. 


1842 

to 

1851 

incl. 

3.6 
2.6 


1852; 1862 

to i to 
1861 1871 
incl. ; inrl. 

5.4 5.1 

3.0 2.6 

9.1 7.4 
9.1 6.7 


1872 

fo 
1881 
inrl. 

3.7 
2.5 


1882 

to 
1891 
incl. 


London, High prices . . 
London, Low prices . 


3.8 i 4.4 
3.2 3.2 


3.0 
2.5 


New York, High prices . 
New York, Low prices . 






7.0 
.5.1 


5.3 
5.1 


Berlin, High prices . 
Berlin, Low prices . 


. . 


. .!. . 4.6 

f ^3 4 


3.7 
3.2 


3.3 

2 7 










Paris, High prices . 
Paris, Low prices . 








4.1 
2.4 


2.6 
2.6 



' Calcutta, High prices . 



•I- 



6.2 



Calcutta, Low prices . . ' . .5.6 



'Tokyo, High prices . . '. .12.3 

Tokyo, Low prices . . ' . . ' . . | . . 12.0 

* Shanghai, High prices . . ! . . i . . | . . | . 

Shanghai, Low prices . . ' . . ! . . j . 



5.4 
6.2 

10.1 
10.1 



6.0 
5.7 



Of the 21 compari.sons contains! in this table, 
17 show higher rates for high-price years than for low-price 

' This table is constructed from th^ data ^ivf-n in the .\ppendix 
to Ch. XIV. For New York, the rates for the first docade are aver- 
aged from the column in the Appendix headfd "60 day.s," and are 
not to be compared with those for the remaining deradf.*, which are 
averaged from the column headed " Prime two-name 60 day.i." The 
index-numbers of prices which have been employed are those of 
Jevona (1824-1851), and Sauerbeck (18.52-1S9I; for PIngland, Soot- 
beer and Heinz for Germany, the Aldrich Senate report for the L'nited 
States and France, and the Japanese rcpcjrt for India, Japan, and 
China. (See Appendix to Ch. XIV, { .3.) 

' For Calcutta the rate for the bank of Bengal i.n employed, no 
"market" rate being available. The first column i.-i for IH7^1HHI 
instead of 1872-1881, for the reason that no index-number for 1872 
ia available. 

• For Tokyo the first column is for 187.3-1881 for the .-ame reason. 

* For Shanghai the p«riod w 1S.S.S-1S93 in.xtead of 18H2-1S91, 
for the reason that the available rates begin in lSS-5 and the index- 
numbers end in 1893. 



II-, 



■m 






320 



THE RATE OF INTEREST 



[Chap. XVI 



1 1 



k Ih 




Si'' 



years, one shows the opposite condition, and 3 show 
equal rates in the two cases. As the table covers 68 years 
for London, 40 for New York, 30 for Berlin, 20 for Paris, 
19 each for Calcutta and Tokyo, and 9 for Shanghai, or 
205 years in the aggregate, the result may be accepted with 
great confidence that high and low prices are usually as- 
sociated with high and low interest respectively. 

There are two probable reasons for this connection. One 
is that a high price-level is often due to a temporary scarc- 
ity of enjoyable commodities, as in a beleaguered city, in 
San Francisco after the earthquake and fire when bread was 
a dollar a loaf, or in the Klondike during the gold fever. 
In such cases the rate of mterest is high for economic, 
not monetary, reasons, —because, in fact, of the relative 
scarcity of present real income. 

The second reason is that the years of high prices are 
usually the culminations of periods of rising prices, during 
which the rate of interest has been rising through the de- 
preciation of money, in accordance with the principles ex- 
plained in Chapters V and XIV. If the tables given in the 
Appendix are examined, it will be found that prices usually 
rise to a point, and then often break suddenly after a crisis. 
The high-price years in this case evidently belong more often 
to the period of rising than to the period of falling prices. 

§3 

Whatever be the correct explanation, the facts give no 
countenance to the theory that the rate of interest depends 
upon the supply of money. 

It may be said that the preceding table is not conclusive, 
owing to the fact that the correlation it shows is one of 
prices and interest, and not directly of quantity of money 
and interest. But this objection can be readily met by 
constructing another table in which per capita circulation 
of money is stated in conjunction with the rates of 
interest : — 






Skj. 3] REFUTATION OF " MONEY THEORY " 321 

RATES O? INTEREST IN RELATION TO PER CAPITA 

CIRCULATION 





Per Capita Monet 


Intebbst Rate in N. Y. 




IN ClBCDLATIOM 


(Prime Two-Name 




IN U.S. JULT 1 


60D»y») 


1871 


18.10 


6.1 


1872 


18.19 


8.0 


1873 


18.04 


10.3 


1874 


18.13 


6.0 


1875 


17.16 


5.5 


1876 


16.12 


5.2 


1877 


IS 58 


5.2 


1878 


15.32 


4.8 


1879 


16.75 


5.0 


1880 


19.41 


5.2 


1881 


21.71 


5.2 


1882 


22.37 


5.7 


1883 


22.91 


5.5 


1884 


22.65 


5.2 


1885 


23.02 


4.1 


1886 


21.82 


4.7 


1887 


22.45 


5.7 


1.888 


22.88 


4.9 


1889 


22.52 


4.8 


1890 


22.82 


6.0 


1891 


23.42 


5.7 


1892 


24.56 


4.3 


1893 


24.03 


7.1 


1894 


24.52 


3.4 


1895 


23.20 


3.8 


1896 


21.41 


5.8 


1897 

1 


22.87 


3.4 


1898 


25.15 


3.8 


1899 


25.58 


4.2 


1900 


26.94 


4.4 


1901 


27.98 


4.4 


1902 


28.43 


4.9 


1903 


29.42 


5.5 


1904 


30.77 


4.2 


1905 


31.08 


4.3 



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322 



THE RATE OF INTEREST 



[Chap. XVI 




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An examination <irf this table will ahow that the per capita 
circulation goes up and down quite independently of the 
fluctuations of the rate of interest. If the money theory 
were true we should expect that when money shrank, in- 
terest would rise, and reversely. The two should vary in- 
versely. But as a matter of fact, out of the thirty-four 
pairs of consecutive years, we find that interest varied about 
as often directly as it did inversely with the per capita cir- 
culation. To be exact, it varied inversely in 15§ and 
directly in 18J cases.' Thus it happened to move a little 
oftener in the manner opposed to the money theory than 
in the manner favorable to that theory. 

A statistical study of the rates of interest and the pro- 
duction of the precious metals made by B. R. G. Levy leads 
to the same conclusion, that the rate of interest is not related 
to the quantity of money.* 

§ 4 

The preceding facts must convmce any one open to con- 
i viction that the rate of interest is not inversely correlated 
' 5 to the quantity of money. But business men familiar 
with banking will not be satisfied until some place is found 
in our theory of interest for the common observation that 
if money in general does not, certainly bank reserves do 
vary inversely with the rate of interest. That this ob- 
servation is correct is not questioned. It is the established 
policy of largo banks, like the Bank of England, to protect 
their reserve by raising the rate of interest. From these 
I facts the conclusion is drawn that the scarcity of bank 
I reserves produces a high rate of interest. But the facts 
fit in with the present theory of interest quite as well as 

• When the rate remained the same in two consecutive years, 
it was counted as one half a variation both ways. 

• " Du taux actuel de I'intdrftt et de ses rapports avec la production 
dc« m4taux pr^cieux et les autres ph&iomfenes eeonomique." B. R. 
Q. Levy, Journal de* Eeonomistet, March, 1899, p. 334; Apr .899, 
p. 28. 



m 



Sic. 4] REFUTATION OF "MONEY THEORY' 



323 



with the fallacious money theory of interest. A low bank 
reserve is merely a symptom of a general ebb tide in the 
income of the community. A bank of discount and deposit 
stands between those who have surplus income to deposit 
and those who wish to eke out a lean income by borrowing. 
Those persons whose mcome is larger than they need to-day 
are the ones who swell the deposits of a bank. When a 
fa-mer receives for his crops more money than he cares 
af once to turn into enjoyable income, he deposits some of 
it m a bank or trust company - >s ith interest if possible, 
without it if necessary. On the other hand, the same 
farmer, before his crop is sold, may wish to discount a note 
at the bank in order to pay off his help. Bank deposits 
grow, as compared with loans, when men's incomes are 
temporarily flush, that is, when their income-curves are 
de.-^cending; loans grow as compared with deposits when 
their mcomes are temporarily scant, that is, when their 
income-curves are ascending. The banker must keep in 
equilibrium between the two classes of customers, those 
who discount and those who deposit. If the loans increase 
too much, the banker's reserve will be endangered ; if he 
deposits accumulate, it will be idle. He regulates nis 
reserve by adjusting the rate of discount, raising it if his 
reserve is low, or lowering it if it is high. To him, his actior- 
appears in the light of protecting and utilizing his reserve 
but the banker is not the prime factor. Back of th^ 
reserve are the real causes, —the state of the incomes of 
his customers. If ascending incomes are preaominant, 
the reserve will need more "protection" than in the con- 
trary case. A rise of the discount rate is therefore due, 
in the last analysis, to the predominance of ascending « 
mcomes, and a fall, to the predominance of incomes of the? 
opposite type. The reserve is merely the football between 
the two sets of persons, those who deposit and those who 
loan- The basiness man regards the rate of interest too 
much from the banker's pomt of view. A banker or broker 
IS merely an intermediarj-. To regard him, or the gold that 



,j 



Mf^fi'iii^:. 



324 



THE RATE OF INTEREST 



[Chap. XVI 



U'- 




happens to be in his vaults, as primary influences on the 
rate of interest is as erroneous as to regard the operations 
of a grain broicer as primary influences upon the price of 
wheat, or those of a real estate agent as primary influences 
upon the price of land. The banker enables the lenders 
and borrowers to find each other ; they, and not he, in the 
end fix the rate of interest.' 

The theory of interest which does not look beyond the bank 
coffers is almost as crude as the theory which would ascribe 
the weather to the thermometer. In a Western town a 
servant was being instructed to prepare a bath at a partic- 
ular temperature, and was shown the point recorded by the 
thermometer when the bath was at the right temperature. 
To the constei nation of the housekeeper, when the servant 
had prepared the bath the next day its temperature was 
found to be far too co' The servant explained that she 
had used the "conjure ..tick," referring to the thermometer, 
but that it didn't seem to heat th^^ water at all! Many 
persons have a similar superstition that money is a soit of 
"conjure stick" potent to regulate the rate of interest, 
whereas in fact it is only a thermometer to faithfully record 
the variations of that rate. When there is " plenty of money 
in Wall Street," interest is low, and vice versa; but the causes 
which have influenced interest are the causes which have 
put the money on loan in Wall Street. 

M 

The money-theory comes nearest to scoring a point when 
applied to panics, for during a time of panic it is true that 
money loans are sought to be used as solvents of debtn. 
This fact has often puzzled economists who, while dis- 
believing the money-theory of interest in general, have 
felt that in this case at least it was true.* It is clear, how- 

' Cf. QeoiKe Clare, "A Monty Market Primer," London (EfRngham 
WilK>n), 1905, pp. 13*-135. 

' See Mill, PrineipUit of PolUieal Economy, Book 3, Chap. XXIII, 



"#I 



SW3. 6] REFUTATION OF "MONEY THEORY' 



325 



ever, that even a panic loan, from Peter to pay Paul, is a 
case of an effort to maintain the even flow of one's income- 
stream. The alternative, if one does not borrow, is to sell 
some of one's goods, necessitating the sacrifice of the income 
which they are designed to bring. The choice between the 
loan and the sale is between the necessity of repaying the 
loan when due, and the necessity of losing the income from 
the goods, — a choice between two bits of income different 
in amount, or kind, or distribution in time. The loan sub- 
stitutes one of these bits of income for the other, and is 
therefore in this respect exactly similar to any other loan. 
If one's solvency is in question, the same exchange occurs 
in a somewhat different form ; the loan is then undertaken 
in preference to the deformation of the income-stream 
which insolvency involves. 

It is true, however, that money, as money, is more 
vitally related to panic loans than to any other. In or- 
dinary loans, money enters merely as a convenient medium 
for securing something else — capital, and through that 
capital, income ; in a panic loan, however, the money enters 
as a necessary medium for the legal discharge of a debt. 
Again, in an ordinary loan, the borrower is free to adjust 
the amount borrowed according to the rate of interest; 
in a panic loan, on the other hand, there is no such elastic 
choice. The borrower must borrow that fixed amount 
necessary to discharge his debt, even if the rate of interest 
is exorbitant. If physical money is not sufficient to allow 
debtors to discharge their debts, the rate of interest will 
be high and there can be no escape from it as in ordinary 
times. In this case it may be truly said that scarcity of 
money has made interest high. Money of any kind brought 
into the market will relieve the stringency and lower the 
rate of interest. The United States has accomplished this 
by prepaying interest on bonds, and the clearing house has 
accomplished it by issuing clearing-house certificates. It 
is therofnrc important, in order not to have violent changes 
in the rate of interest, that the currency should be elastic. 



if 



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326 



THE RATE OF INTEREST 



IChap. XVI 



A panic is always the result of unforeseen conditions; and 
among those unforeseen conditions, and partly as a con- 
sequence of other unforeseen conditions, is scarcity of money 
on loan. Under ordinary and normal conditions, money on 
loan is so automatically adjusted as to make it a mere trans- 
mitter throu^ the medium of which borrowers and lenders 
act upon the rate of interest, just as a smooth-running gear 
transmits power from one wheel to another, without ex- 
erting any independent force itself. But when the gear gets 
out of order it may stick and oflFer a resistance of its own 
to the wheels with which it is in contact. 

It is therefore not asserted that money plays no rdle in 
determinmg the rate of interest. But its r61e is a minor 
one, and very diflferent from that often assigned to it. 
Its r61e normally is to efface itself and merely facilitate 
the frictionless workmg of economic machinery. Under 
the abnormal conditions of a panic, the dearth of it 
may create friction and enhance interest at that particular 
point. 

^ E i o a l ly, as we have seen in previous chapters, a change 
in the monetary standard will affect the number by which 
the rate of mterest is expressed, increasmg it if the monetary 
Btandard is depreciating, and decreasing it if the standard 
is appreciatmg. 

With these reservations, we may say that the rate of 
interest is not affected by the quantity of money. 



SUMMARY 



m 



% 



CHAPTER XVII 



5? 



§ 1 

We have seen that the rate of interest is subject to both 
a nominal and a real variation, the nominal variation being 
that connected with changes in the standard of value, and 
the real variation being that connected with the other and 
deeper economic causes. As to the nominal variation in 
the rate of interest, we found that, theoretically, an ap- 
preciation of 1 per cent, of the standard of value in which 
the rate of interest is expressed, compared with some other 
standard, will reduce the rate of interest in the former 
standard, compared with the latter, by about 1 per cent. ; 
and that, contrariwise, a depreciation of 1 per cent, will 
raise the rate by that amount. Such a change in the rate 
of interest, however, is merely a change in the number 
expressing it, and not in any sense a real change. Yet 
the appreciation or depreciation of the monetary standard 
does produce a r^ al effect on the rate of interest, and that 
a most vicious one. Hiis effect is due to the fact that the 
rate of interest does not change enough to fully compensate 
for the appreciation or depreciation. Thus, if the monetary 
standard is appreciating at the rate of 3 per cent, per annum 
and the rate of interest falls only 2 per cent., the deficieucy 
of 1 per cent, shows that the rate of interest has not really 
fallen, but risen. This rise of 1 per cent, is abnormal, 
being the result of an error in prediction. Had the debtor* 
and creditors concerned foreseen fvilly the change in the 
monetary standard, they would have forestalled it fully. 
'Hieir failure nn t-o do resulti in an un'.'xpectod loss to the 
debtor, and an unexpected gain to the creditor. What 

327 



'i;- 



i 



li ; 



328 THE RATE OF INTEREST [Chap. XVII 

iisually happens, therefore, as a consequence of an appre- 
ciation m the monetary standard, is that the rate of mterest 
nomiimUy falls, but reaUy rises, whsreas in the contrary 
case, if the monetary standard is depreciatmg, the rate 
of interest nominaUy rises, but reaUy faUs. It is conse- 
quently of the utmost importance, in interpreting the rate 
of interest statisticaUy, to ascertain in each case in which 
direction the monetary standard is moving, and to re- 
member that the direction in which the rate apparently 
moves is apt to be precisely the opposite of that in which 
it really moves. 



li' 



ii^ 



li* • 



If ^ 

u 

I 



§2 

Turning from the nominal to the real variation in the rate 
of interest, we see that the rate of mterest, considered in- 
dependently of fluctuations in the monetary standard, is 
determined by six causes, namely: (1) The extent of the 
effective range of choice of different incomes which are 
open to each individual; (2) the dependence of "time-pref- 
erence" upon prospective income — its size, shape, com- 
position, and probability; (3) the tendency of the rates 
of time-pref trence for different individuals to become equal 
to each other and to the rate of interest, through the loan 
market, or through buying and selling property; (4) the 
tendency of the various "rates of return on sacrifice "to be- 
come equal to each other and to the rate of interest, through 
the operation of free choice among available options ; (5) 
the fact that supply and demand are equal, that the 
modifications in the income-streams of individuals through 
buying and selUng or borrowing and lending mutually 
offset each other for each interval of time considered, — 
that what is lent must equal what is borrowed, and what 
IS gained by one in each year's income, by buying and scU- 
ing, la lost by some one else; (6) the fact that, for the 
same mdivido^^l, the estimated present values of the 
changes he elects to make in his prospective income-stream 



Sic. 3] 



SUMMARY 



329 



mutually offset each other; that is, the estimated present 
value of what he borrows is equal to the estimated present 
value of what he returns, or, more generally, the estimated 
present value of an addition to his immediate income is 
equal to the present value of the consequent reduction in 
his future income. 

Of these six conditions, many are so inflexible that they 
have Uttle influence on any variation in the rate of interest. 
The last four are of this relatively fixed type. We have 
remaining the first two as the only causes subject to im- 
portant variations. The fluctuations in these causes explain 
for the most part the changes in the rate of interest, as 
actually experienced. We shall now concentrate attention 
upon these two, — the range of known choice and the law 
of time-preference. 

§ 3 

As to the range of choice, each individual may, as assumed 
in our "first approximation," be possessed of one given in- 
come which is rigid (except as it may be altered by borrow- 
ing and lending) ; or, as assumed in the other approxima- 
tions and as found in actual fact, he may bo possessed of a 
given range of choice of many different income-streams. 
The range of choice actually open to any individual will 
depend principally upon the amount and character of the 
capital-property which he possesses. It follows that, 
for society as a whole, the range of choice of incomes will 
depend upon, first, the existing capital of the country ; that 
is, its "resources," or the amount and character of the 
different capital-instruments existing within it at the in- 
stant of time considered; and, secondly, the distribution 
of ownership of these capital-instruments throughout the 
community. In this tt'atement it is intended, of course, 
to include under capital-instruments the individuals them- 
selves who constitute the community, for they are the 
source, through their personal exertions, of much of the 



1 ' 



J. 



I; 



H I 

I s . 

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1 



I 

I. r 



1^' 



I. ' t 



N s 




330 



THE RATE OF INTEREST [Chap. XVII 



income which they enjoy. In short, then, the available 
range of choice will depend upon capital and its distribution. 
If the capital-mstruments of the community are of such 
a nature as to offer a toide range of choice, we have seen that 
the rate of interest will tend to be steady. If the range of 
choice is mrrow, the rate of interest will be comparatively 
variable. If the range of choice is relatively rich in the 
remotely future income as compared with the more immediate 
income, the rate of mterest will be high. If the range of 
choice tends to favor immediate income as compared with 
remote future income, the rate of mterest will be low. 
Thus, for the United States during the last century, its 
resources were of such a character as to favor a remote 
future income. This is true, for a time at least, in every 
undeveloped country, and, as we have seen, gives the chief 
explanation of the fact that the rate of interest in such 
localities is usually high. 

ITie range of choice in any community is subject tc many 
changes as time goes on, due chiefly to one of three causes. 
First, a progressive increase or decrease m resources; 
second, the discovery of new resources or means of develop- 
ing old ones; and thbd, change m political conditions. 
The impending exhaustion of the coal supply m England 
which has been noted by Jevons and other writers will tend 
to make the income-stream from that island decrease, at least 
in the remote future, and this in turn will tend to keep the 
rate of interest there low. The constant stream of new 
inventions, on the other hand, by makmg the available 
income-streams rich m the remote future, tends to make 
the rate of mterest high. This effect, however, is confined 
to the period of exploitation of the new mvention, and is suc- 
ceeded later by an opposite tendency. During the last half 
century the exploitation of Stephenson's invention of the 
locomotive, by presenting the possibility of a relatively large 
future income at the cost of comparatively little sacrifice 
in the present, has tended to keep the rate of mterest high. 
Aathe period of raiUx)ad building is drawing to a close, this 



Sec. 4] 



SUMMARY 



331 



effect is becoming exhausted, and the tendency of the rate 
of interest, so far as this influence is concerned, b to fall. 
As to the political conditions which affect the rate of interest, 
insecurity of property rights such as occurs during politi- 
cal upheaval tends to make the pure or "riskless" rate of 
interest low. At the same time it adds an element of risk 
to most loans, thereby diminishing the number of safe and 
increasing the number of unsafe loans. Hence the "com- 
mercial " rate of interest in ordinary loans during periods 
of lawlessness is apt to be high. Reversely, during times 
of peace and security, the " riskless " rate of interest is 
comparatively high while the " commercial " rate tends to 
be low. 

§ 4 

We turn now to the second factor determining interest ; 
namely, the dependence of time-preference of each in- 
dividual on his selected income-stream. We have seen 
that the rate of preference for immediate as compared with 
remote income will depend upon the character of the in- 
come-stream selected ; but the manner of this dependence 
is subject to great variation and change. The manner in 
which a spendthrift w U react to an income-stream is very 
different from the manner in which the shrewd accumulator 
of capital will react to the same income-stream. We have 
seen that the manner in which the time-preference of an 
individual depends upon his income will vary with five 
different factors: (1) His foresight and self-control; (2) 
his love of offspring or regard for posterity ; (3) the pro- 
spective length and certainty of his life ; (4) habit ; (5) 
fashion. It is evident that each of these circumstances 
may change. The causes most likely to effect such changes 
are, first, education and training in thrift, whether accom- 
plished through the home, the school, charitable organi- 
sations, or banks for small savings, building and loan as- 
sociations, and other similar institutions calculated to have 
an educational mfluence; second, the tendency toward or 



1^ ■ 
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332 



THE RATE OF INTEREST [Chap. XVII 



away from a epirit of extravagance and ostentation 
through social rivahy;» third, the changes in the c' ar- 
acter of the institutions of marriage and the family which, 
in one direction or the other, will profoundly affect the 
love of offsprmg and regard for the welfare of posterity; 
fourth, the development of the science of hygiene which may 
tend to make human life longer and more certain; fifth, 
the causes which tend to make the distribution of wealth 
either more concentrated or diffused, and also those which 
tend to make the existmg economic stratification of classes 
fixed and stereotyped or elastic and variable. These vari- 
ous factors will act and react upon each other, and will 
affect profoundly the rate of preference for present over 
future income, and thereby influence greatly the rate of 
interest. Where, as in Scotland, there are educational 
tendencies which instill the habit of thrift from childhood, 
the rate of interest tends to be low. Where, as in ancient 
Rome, there is a tendency toward reckless luxury and com- 
petition in ostentation, and a degeneration m the bonds of 
family life, there is a consequent absence of any desire to pro- 
long mcome beyond one's own term of life, and the rate of 
mterest tends to be high. Where, as in Russia, wealth tends 
to be concentrated and social stratification to be rigid, the 
great majority of the community on the one hand, through 
poverty and the recklessness which poverty begets, tends to 
have a high rate of preference for present over future income ; 
whereas, at the opposite end of the ladder, the inherited 
habit of luxurious living tends, though m a different way, 
in the same direction. In such a community the rate of 
mterest is apt to be imduly high. 

§ 5 
From the foregoing enumeration, it is clear that the rate 
of interest is dependent upon very unstable influences, 

' See Rat', The Sociological Theory of Capital, Cf . the writer's " Why 
has the Doctrine of Lajsez Faire been Abandoned? " Science, Jan 4, 



Sic. 5] 



SUMMARY 



333 



sp'-' 



many of which have their origin deep down in the social 
fabric and involve considerations not strictly economic. 
Any causes tending to affect intelligence, foresight, self- 
control, habits, the longevity of man, and family affection, 
will have their influence upon the rate of interest. The 
most fitful of the causes at work is probably fashion. This 
at the present time acts, on the one hand, to stimulate 
men to save and become millionaires, and, on the other 
hand, to stimulate millionaires to live in an ostentatious 
manner. Fashion is one of those potent yet illusory social 
forces which follow the laws of imitation so much empha- 
sized by Tarde,' Le Bon,' Baldwin,* and other writers. 
In whatever direction the leaders of fashion first chance to 
move, the crowd will follow in mafl pursuit until the whole 
social body will be moving in that direction. Sometimes 
the fashion becomes rigid, as in China, a fact emphasized 
by Bagehot ; * and sometimes the effect of a too universal 
following is to stimulate the leaders to throw off their pur- 
suers by taking some novel direction — which explains the 
constant vagaries of fashion in dress. Economic fashions 
may belong to either of these two groups, —the fixed or the 
erratic. Examples of both are given by John Rae.' It 
is of vast importance to a community, in its influence both 
on the rate of interest and on the distribution of wealth 
itself, what direction fashion happens to take. For in- 
stance, should it become an established cu.stom for million- 
aires to consider it "disgraceful to die rich," and believe 
it de riguer to give the bulk of their fortunes for endowing 
universities, libraries, or other public institutions, the effect 
would be, through diffusion of benefits, to lessen the dis- 

* Social Law*, by G. Tarde, Englwh translation, New York (Mao- 
millaa), 1S99. Also Le» LaU de I'lmitatwn. 

' The Psychology of SocialUm, English translation, London (T. 
Flaher Unwin), 1899. Alao The Crovd. 

' Social and Ethical Interpntation* in Mental Development, New 
Vork (Macmiilaa), 4ta ed., 1906. 

* Phyne$ and Politie$, Chap. III. 

* See The Sociolofieal Theory of Capital. 



M 



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334 THE RATE OP INTEREST [Chap. XVII 

parities in the distribution of wealth, and also to lower 
the rate of interest. 

§6 

From what has been said it is clear that m order to esti- 
mate the possible variation in the rate of interest, we may 
broadly speaking, take account of the following three groups 
of causes : (1) The thrift, foresight, self-control, and love of 
offspring which exist in a community; (2) the progress 
of mventions; (3) the changes in the purchasing power 
of money. The first cause tends to lower the rate of in- 
terest; the second, to raise it; and the third to affect only 
the nominal rate of interest, though practically it usually 
produces also a dislocation in the real rate of interest 

Were it possible to estimate the strength of the various 
forces thus summarized, we could base upon them a pre- 
diction as to the rate of interest in the future. Such a 
prediction, however, to be of much value, would require 
more painstaking attention than has ever been given to 
existing historical conditions. Without such a careful in- 
vestigation, any prediction is hazardous. We can say 
however, that the immediate prospects for a change in the 
monetaiy standard are toward its gradual depreciation; 
that a change m thrift, foresight, self-control, and benevo- 
lence, if It occurs, is for the most part likely to intensify 
these factors and thus to lower the rate of interest; and 
that the progress of discovery and invention seems apt 
to slacken m speed, both so far as industrial processes are 
concerned, and, what has hitherto been of more conse- 
quence, so far as the discovery of exploitable areas is con- 
cerned. It is true that the new chemical agriculture has 
the same effect as the discovery of new land. It is con- 
ceivable, perhaps, that the future development of these 
methods may be as potent as was the discovery and ex- 
ploitation of the American, Australian, and African conti- 
nents, which has tended to keep the rate of interest high. 



Sec. 6] 



SUMMARY 



335 



Yet this result can scarcely be regarded at present as prob- 
able. America and Australia have been already exploited 
to a large degree, and within another generation almost the 
same degree of exploitation is apt to occur in Africa. If 
we look forward, then, beyond the present lifetime, unless 
some invention or set of inventions comparable to those 
of steam and electricity are still in store for us, we see 
that the probable improvement *n thrift, foresight, self- 
control, family affection, etc., and '.he slackening in the 
activity or economic importance of inventive procevS.sos, are 
all in the direction of lowering the rate of interest. It 
may of course happen that counter currents will prove the 
stronger. There is certainly danger that the .spirit of ex- 
travagance and display, a spirit which we have seen leads 
to reckless loans and high interest, will become a national 
disease as it did during the decline of the Roman Em- 
pire. Only time can tell us whether or not we shall escape 
this danger. 

So far as the effect of the monetary standard on the rate 
of interest is concerned, the prospect of depreciation of 
gold tends, on the one hand, nominally to raise the rate of 
interest, but practically to make the rate of interest really 
not only low, but lower than it otherwise would be. With 
the influx of gold from Colorado, Alaska, California, 
Australia, and latterly Nevada, and with the resumption 
of mining in South Africa, there cannot be much question 
that gold will depreciate.' This result will tend to be 
h ^nsified by the fact that there are few if any large nations 
left which have not already adopted the gold standard or 
which are at all likely to do so, and thereby mitigate the fall 
of gold. The rate of interest is now, on ordinarily safe 
loans in civilized communities, in the neighborhood of 
4 per cent., expressed in money. We may surmise that 

' See "Sjrmposium," Moody' » Magazine, December, 190.5; Bjrron 
W. Holt, The Gold Supply and ProsperUy, N'. Y. (.Moody), 1907; 
also "The Depreciation of Gold," by Professor J. P. Norton, YaU 
Rmeic, November, 1906. 






fi 






336 



THE RATE OF INTEREST [Chap. XVII 



t ': 



i.» 



1^^ 



through much of the present century this rate will nomi- 
nally continue, but that the rate of mterest in terms of " com- 
modities" will be 1 or 2 points lower. The effect of these 
conditions on trade and on the relative fortunes of stock- 
holders and bondholders has been stated in Chapter XIV. 
The rate will not remain perfectly constant but will tend 
gradually to rise until the stringency thus produced cul- 
mmates in a commercial crisis. After such i. p-riod of 
liquidation, the same process of rising pri.^ v.it'.; hi,'?h 
nominal but low real interest will begin a -v. 

A discrepancy of 1 or 2 points betwer , n -ulo t.r ir 
terest as it is and as it should be I .;.»:!>• f ,0 
trifling importance. Its cumulati'.' . ...s, uC. iuh 
seldom realized, are serious. It is con •• ilv ~s. u » -i t* .- 
the rate of interest is a phenomenor. i ',< ir-l i . nio; cy 
markets and trade centers, and the pu lir ; r . > ,i ,r 
disapproval of the rate usually takes its ru( 'm-n r'.e 



If "money k 



he 



sentiments of the borrower, 
content 

The truth is that the rate of interest is not a narrow 
phenomenon applying only to a few business contracts, 
but permeates all economic relations. It is the link which 
binds man to the future and by which he makes all his 
far-reaching decisions. It enters into the price of securi- 
ties, land, and capital goods generally, as well as into rent, 
wages, and the value of all "interactions." It affects 
profoundly the distribution of wealth. In short, upon its 
accurate adjustment depend the equitable terms of all 
exchange and distribution. 



ill. /. 

r 






GLOSSARY 

[Consisting of definitions of technical terms used in this book. 
Meet of these definitions are more fully discusseil in The Nature of 
Capilal and Income, to which specific references are therefore 
made.] 

Basis. — The rate of interest yielded by a property when wjUI at 
a specified price. Capital and Iwome, Ch. XVI, $ !». 

commercial, of a security. — Thf; ba-sis correspondini^ to the com- 
mercial value of the security. Capital arul lic<om< , Ch. X\ I, 5 8. 

mathematical, of a security. — The ba.sis forrcsponding to the 
mathematical value of the security. Capilal and Income, Cli. 
XVI, § 8. 

rwfc/ess, of a security. — The basis corresponding to the riskless 
value of the security. Capital and rnrc.nc, Ch. XVI, ^H. 
Capital. — Abbreviation for Capilal yoodn, and Capital value 
Capital and Income, Ch. V, § I. 

instruments. — (See Capital Wealth.) 

property. — A stock (or fund) of property exwtinit at an instant 
of time. Capital and Income, Ch. V, § 1. 

wealth. — A stock (or fund) of wealth existing at an instant of 
time. (Syn. Capital instruments.) Capital and Income:, Ch. 

V, § 1. 

value. — The value of a stock of wealth or profx-rty at an in.stant 
Itisfmmd by discounting or "rapitftliziig"; the value of thf 
income expected from the wealth or propfrty. Capi' and 
Income, Ch. V, § 1. 

Capiulistic method. — .\ method of pro<luction requiring a tem- 
porary reduction in the income from speclncd capital. Ch. 
K, §8. 

CvcTiov, coefficient of. — The ratio of ronimerfial valuf to mathe- 
matical value. Capital and Inccne. Ch. XVI, J 6. 

Chance, of any event. — The ratio oi the ^.um^»-r of ca*j,s in which 
that event may occur to the total possible number of cases, 
when all the caaes are equally probable. .\ny two ra.sc.s arc 
equally probable (to any particular ^^rson at any parti^ula! 
time) if the person has no inclination to (xHr-v nn*> rathe 
than the other to be true. I'.Syn. Proh<ihiiU>i.) Capital ana 
Income, Ch. XVI, § 2. 
commercial tdue o,. — The value which the chance will .'\ctually 
z 3.37 



I? 'I 



:4i 



^^1 



338 



GLOSSARY 




M -i 



command in the market. It is equal to the mathematical 
value multiplied by the coefficient of caution. Capiial and 
Income, Ch. XVI, J 6- 
mathematical value of. — The product of the value of the price at 
stake multiplied by the chance of winning it. Capital and In- 
come, Ch. XVI, J 5. 
Coefficient, of caution. — The ratio of commercial value to mathe- 
matical value. Capital and Income, Ch. XVI, § 6. 
of probabUity. — The ratio of mathematical value to riskleas 

value. Capital and Income, Ch. XVI, { 6. 

of risk. — The ratio of commercial value to riskleas value ; henco 

the product of the coefficient of caution multiplied by the 

coefficient of probability. Capital and Income, Ch. XVI, § 6. 

CoifMERciAL value of a chance. — (See Chance.) 

Commodities. — Movable instruments not human beings. CapUal 

and Income, Ch. I, { 2. 
CoNSDMPTioN. — (See Services, enjoytMe objective.) 
Desirability, of goods (wealth, property, or services). — The in- 
tensity of desire, for those goods, of a particular individual 
at a particular time under particular circumstances. (Syn. 
VtMy.) Capital and Income, Ch. Ill, § 2. 
m^ginal, of a specified aggregate of goods. — Approximate 
definition : The desirability of one unit more or less of that 
aggregate, or the difference between the desirability of that 
aggregate and another aggregate one unit larger or smaller. 
Capital and Income, Ch. Ill, } 4. 

Exact definition : The limit of the ratio of the increment 
(or decrement) of desirability to the mcrement (or decrement) 
of the aggregate when the last-named increment (or decre- 
ment) approaches lero. (Syn. Marginal utUUy.) Capital 
and Income, Appendix to Ch. Ill, { 1. 
Discount curve. — A curve so constructed that, if one of its or- 
dinates represents any given sum, any later ordinate will 
represent the "amount" of that sum at a time later by an in- 
terval Pepr>sented by the horiiontal distance between the 
ordinates ; consequently a curve such that any earlier ordinate 
will represent the "present value" of that sum at a time 
earlier by an interval represented by the horizontal distance 
between the ordinates. Capital and Income, Ch. XIII, § 1. 
Discounted value. — (See Value, present.) 
Disservice. — A negative service. An instrument renders a 
disservice when, by its means, an undesirable event is pro- 
moU'd or a desirable event prevented. Capital and Incomr 
Ch. II, }2; VIII, SI. 



Iff 



B 



GLOSSARY 



339 



DBtmuTT. — Negative utility. (Syn. UndenrabilUy.) Capital 

and Income, Ch. Ill, S 2. 
Eabninos. — (See Income, earned.) 

Exchange. — The mutual and voluntary transfer of goods (wealth, 
property, or services) between two owners, each transfer being 
in consideration of the other. Capital and Income, Ch. I, { 4 ; 
II, 5 3. 
Flow. — The quantity of any specified thing undergoing any 
specified change during any specified period of time. Capital 
and Income, Ch. IV, S !• 
FcND. — A stock cf wealth or property or its value. Capital and 

Income, Ch. IV, 5 1. 
Goods. — A term to include wealth, property and services. Capi- 

tal and Income, Ch. Ill, § 1. 
Income. — Abbreviation for Income eervices and Income vo/ue. 
CapitiU and Income, Ch. VIII, } 1. 
account. — Statement of specified income and outgo, whether 
from capital or to a person. Capital and Income, Ch. VIII, 1 2. 
earned, by any capital. — Income realized plus appreciation of 
the capital (or minus its depreciation) ; i.e. that income 
which a given capital can yield tvithout alteration in its value. 
If interest be assumed invariable and all future income fore- 
known, this definition is equivalent to another; viz. the uni- 
form and perpetual income which a given capital might yield ; 
but the equivalpnce ceases if interest varies (see Capital and 
Income, Appendix to Ch. XIV, { 1) or if future income is un- 
known. (Syn. Earnings, Standard income.) Capital and 
Income, Ch. XIV, \ 4. 
enjoyable. — Income which consists of enjoyable services. Capi- 
tal and Income, Ch. VII, ( 6. 
gross. — Sum of all positive income elements. Capital and 

Income, Ch. VII, { 1. 
individual. — The income from the entire capital of an individual. 

Capital and Income, Ch. VII, § 7. 
money. — Income which consists of the receipt of money. Capi- 
tal and Income, Ch. VII, J 7 ; IX S 5. 
natur(U. — Income which consists of scrviLes not obtained by 

exchange. Capital and Income, Ch. VII, } 7; IX, { 5. 
net. — The difference between gross income and outgo. Capital 

and Income, Ch. VIII, i 1. 
psychic. — Agreeable conscious experiences. (Syn. Subjective 

income.) Capital and Income, Ch. X, J 3. 
realited, from any capital. — Its actual income, i.e. the vulue of 
its actual services. Capital and Income, Ch. XIV, j| 4. 



i I 

il 



I '* 



340 



GLOSSARY 



tervicet, of any capital. — The flow of services from that capital 

through a period of time. Capital and Income, Ch. VIII, § 1. 

tocial. — The income frr m the entire capital of society. Capital 

and Income, Ch. VII, § 7. 
standard. — (See Income, earned.) 
stream. — Synonym of Income. Employed to emphasize its 

duration in time. 
subjective. (See Income, psychic.) 

value, from any capital.— The value of its income-services. 
Capital and Income, Ch. VIII, § 1. 
Instrument. — An individual article of wealth. Capital and 

Income, Cli. I, § 1. 
Interaction. — An event whirh is a service of one capital and at 
the same time a disservice of another. (Syn. Interacting 
service, Intermediate service, Preparatory sendee. Coupled ser- 
vice.) Capital and Income, Ch. IX, § 2. 
Interacting services. — (See Interaction.) 
Intermediate services. — (See Interaction.) 

Interest. — The product of the rate of interest multiplied by the 
capital- value. Capi: I Income, Ch. XIV, § 4. 
explicit, rate of. — X .u\ of inten-st explicitly contracted for 

(in contradistinction to implicit interest). Ch. II, § 1. 
implicit, rate of. — The rate of interest realized on any invest- 
ment, the exact return of which is not explicitly contraitcd 
for, but is left to be determined by circumstances. Ch. II, 5 i . 
rate of. — Many meaniiiRs are give n lielow. The standard nuun- 
ing used in this book in that called "rate of interest in the 
premium sen-w reckoned annually." Capital and I now 
Ch. XII, 5 4. 
rate of. — In the price sense: The ratio between the annual rat.- 
of a perpetual annuity and the equivalent capital-value. Cnp- 
ital and Income, Ch. XII, § 2. 

The rate of inU^rest is said to Im> reckonc<l annually if the 
annuity is payable in annual installments; it is said to Ix' 
reckoned semiannually if the annuity is payable in semiaimujil 
installments; quarterly, if in quarterly installments; continu- 
ously, if payable continuously. 
rate of. — In the premium sense: The excess above unity of the 
rate of exchange between the values of future and prcw'iit 
giKxlH taken in relation to the time interval l)etweeii the two 
sets of go<Ml». (Hyii. riUe of interest m the agio sense.) Ca/Hliil 
and Income, Ch. XII, J 4. 

The rate of interest is said to l)e reckoned annuilbj if the 
two miU of goo<ls arc one year apart. This is the staiuiani 




- ' .■WTT'" 



GLOSSARY 



341 



meaning of the "rate of interest" as used in this book. It is 

said to be reckoned semiannually, if they are a half-year apart ; 

quarterly, if three months apart; continuously, if infinitesi- 

mally apart. 
rate of. — In agio sense: (See in premium sense.) 
rate of. — Reckoned annually, semiannually, quarterly, continu- 
ously: See under rate of interest in price senne and rate of 

interest in premium sense, 
total. — The difference between any sum and its "amount." 

Capital and Income, Appendix to Ch. XIII, § 7. 
Investinq. — Purchasing the right to remote income. Ch. VT . 

§4 
Labok. — Outgo in the form of human exertion. Capital and 

Income, Ch. X, § 6. 
La.nd. — Wealth which is part of the earth's surface. Capital 

and Income, Ch. I, § 2. 
Mathematical value of a chance. — (See Chance.) 
Optio.v. — Any one of a number of income-streams among which 

an individual may choose. Ch. IX, § 1. 
Outgo. — Negative income. Capital and Income, Ch. VIII, § 1. 
Preparatory services. — (See Interaction.) 
Price. — .\ ratio of exchange. Capital and Income, Ch. I, § 4. 
money. — The quotient ff>un(l by dividing the money ivchanged 

for goods by the quantity of the goods thcniscive.s. f'apital 

and Income, Ch. I, J 4. 
Principa!.. — The final payment on a bond or note, supposed to 

Ix- (but not always in fact) equal to (he original sum "lent. " 

Capital and Income, Ch. XIII, § 7. 
Probability. — (See Chance.) 
Production. — (See Transform/ ion.) 
Productive prock.ss. — (See Translormniion.) 
Productivity, phy.ncal. —The ratio of tlic quantity of services of 

lapifal [HT unit of time to the quantity nf the capital. Capital 

and Income, Ch. XI, J 2. 
Productivity, value. —The ratio of the v(due of services of capi- 
tal per unit of time to the quantitif of the capital. Capital 

and Income, Ch. XI, 5 2. 
Property (or pro{)erty rights). -- Hights to th<- chance of future 

service.i of wealth. Capital and Inromi, Ch. II, J 3. 
"•('jW, complete. — The exclusive riglit to all the services of an 

mstrument. Capital and Incom-. f'h. II, § 10. 
right, partial. -The right to part of the s«<rvi(ps of an instru- 
ment, other parts Ivlonging to otluT owners. ( apUal and 

In^wne. Ch II, } 10- 



342 



QLOSSARY 



I 
s 




RaruBN. — When uaed alone, "return " signifies the value of the 
advantage of one income-etream compared with another during 
any particular portion of its course. Ch. VIII, ) 8. 

RntTHN, phytieal. — The ratio of the quantity of services of capi- 
tal to the tuiue of the capital. Cajrital and Income, Ch. XI, i2. 
on tacrifiee, rate of.— That rate of interest, reckoning by which 
the discounted value of the " return " equals the discounted 
value of the " sacrifice." Ch. VIII, { 8. 
wUiu. — The ratio of the valiie of services of capital to the value 
of the capital. Capital and Income, Ch. XI, { 2. 

Rue, coefficient of. — The ratio of commercial value to risklcss 
value. It is equal to the product of the coefficient of prob- 
ability multiplied by the coefficient of caution. CapiUU and 
Income, Ch. XVI, i 6. 

RiSKuess, value. — The value which a thing would have if risk were 
eliminated. Capital and Income, Ch. XVI, \ 6. 

Sackificb. — The value of the disadvantage of one income-stream 
compared with another during any particular portion of its 
course. Ch. VIII, $ .S. 

Service. — An instnm:)ent renders a service when, by its means, 
a desirable event is promoted or an undesirable event pre- 
vented. (Syn. Uae.) Capital and Income, Ch. II, § 2. 

Services, coupled. — (See Interaction.) 
enjoyable objective. — Services received directly by human 
beings, and not (like interactions) merely received for human 
beings by other (objective) capital. (Syn. [not well chosen] 
Consumption.) Capital and Income, Ch. X, 5 1. 
intermediate. — (See Interaction.) 
preparatory. — (See Interaction.) 

Spending. — Purchasing the right to immediate enjoyable inponic 
Ch. VII, $ 4. 

Standard incoue. — (See Income, earrted.) 

Stock. — The quantity of any specified thing at any instant. 
(Syn. Fund.) Capital and Income, Ch. IV, J 1. 

TiMB-PRsrERBNCE, rate of. — The excess above unity of the ratio 
between the marginal utility (to a given person, under given 
conditions, at a given time) of (say) a dollar's worth of enjoyable 
income available at any time and a dollar's worth of enjoyable 
income available one year later. It follows that it is also the 
excess above unity of the ratio between the quantity of the 
later income and the quantity of the early income which will 
exchange for each other (both being expressed in the same 
standard, as dollars). Ch. VI, | 1. 
TiMi-SHAPi, of an income-stream. — The distribution in time uf a 




GLOSSARY 



343 



given income-stream as expressed by the relative amounts of 
the income accruing at specified periods. Ch. VI, { 6. 
Tbansformatign. — An interaction which is a change of form or 
condition of wealth. (S)m. Production, Productive process.) 
Capital and Income, Ch. IX, §} 2, 3. 
UNDSsnuBiuTT. — Negative desirability. {^yn.DisutUUy.) Capi- 
tal and Income, Ch. Ill, S 2. 
UnuTT or oooDS. — (See Desirability.) 

Valub. — The value of goods (wealth, property, or services) is 
the product of their quantity multiplied by their price. Cap- 
ital and Income, Ch. I, { 6. 

commercial, of a chance. — (See Chance.) 

discounted. — (See Value, present.) 

mathematical, of a chance. (See Chance.) 

money. — The quantity of goods multiplied by their money 
price. Capital and Income, Ch. I, § 6. 

present. — The present value of any given future goods is the 
quantity of present goods which will exchange for those future 
goods. (Syn. Present worth. Discounted value.) Capital arid 
Income, Ch. XIII, \ 1. 

riskless, of a chance. — (See Chance.) 
Wealth (in its broader sense). — Material objects owned by 
human beings. Capital and Income, Ch. I, § 1. 

(in its narrower sense). — Material objects owned by human 
beings and external to their owners. Capital and Income, 
Ch. I, i 2. 

article of.— A single object of wealth. (Syn. Item of Wealth, 
Instrument.) Capital and Income, Ch. I, J 1. 

item of. — (See Wealth, article of.) 
Worth, present. — (See Value, present.) 






*•! 



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APPENDICES 



AppKiroix 
Appendix 
Appendix 
Appendix 
Appendix 
Appendix 
Appendix 



TO Chapter II. 
TO Chapter IV. 
TO Chapter V. 
to Chapter VII. 
TO Chapter VIII. 
to Chapter XI. 
TO Chaiter XIV. 



Productivity Theories 
Bohm-Bawerk's Theory 
Appreciation and Interest 
First Approximation 
Second Approximation 
Third Approximation 
Statihtics 



''fi 



!t'l 



I: i 



It 













:,-1l 



APPENDIX TO CHAPTER II 

Pboductivitt Theories 

S 1 (to Ch. II, § 6) 

MAtbematical Proof that the Rate of Net Income from Reconstituted 
Capital ia equal io the Rate of Interest employed in valuing the Ele- 
ments of which that capital ia compoeed. 

That the ratio of the uet income from the machines to their 
capital-value is equal to the rate of interest used in calculate 
ing the value of each individual machine is a necessary truth 
and may be shown mathematically as follows : — 

For simplicity, let us assume that each machine yields its 
income in a single item at the end of each year. If a machine 
when new is to last m years and yields a certain annuity of a 
dollars each year, the value (i;,) of this machine is found by 
discounting the terminable annuity of a dollars for m years at 
a rate of interest i. This value will be 



1 + i (1 + 0' 



(i-i-o-'''"(i+«r 



(1) 



The gross annual income of a plant consisting of m machines 
will be nuL The net income of the plant, assuming that one 
machine wears out and is replaced annually, will be found by 
deducting from this gross income the cost, Vi, of a new machine. 
This annual net income ^ma — r,. 

The value of the plant of m machines can now be found 
by discounting the future income which the plant will yield. 
Let us assume that the plant is "kept up'' for n years, 
after which it is allowed to run down until exhausted. The 
period of running down will be m years, the life of the newest 
machine. We assume, of course, that whether kept up or run- 
ning down, the plant yields for each machine n dollars annu- 
ally. Under these conditions the value of the plant is the 
discounted value of two series of income : (I) n years of income 
of ma — V, per year, while the plant is kept up, and (2) m years 
of lucome which gradually shrinks from ma the first year 

347 



•. ir 



' , f 



13* 









«' 



it « 



348 



APPENDIX TO CHAPTER II 



when all the machines are in use, to (?n~l)a the second year, 
aft«r one machine has dropped out, (m — 2)a the third, etc., 
to a in the mth year, after which time the plant wi'l cease to 
exist We have, then, the present value of ma — Vi for each 
of n years, and the present value for m more years of ma, 
(to — l)a, (to — 2)a," ~" 
sive sums is evidently 



a. The present value of these succes- 



— Vl , TOO — i>, 



tma — V, 

t ma 
(1 + 0"*' ' (1 + 

which may also be written 
(ma-u,)| _-4 

va+'rJLiTt' 



TOO — 



(1 + 0* ^(1 

(TO-l)a 



+ 0"J 



(1 + 0" 



4 



(1+0* 

m — l 

■(1+0* 



(1 



+ 0"J 



+ 



'(1 + 0-J' 



(2) 



Of the two terms of which this expression consists, the first 
is the more important if the rate of interest, i, has a finit*- 
positive value, but the second is the more important if that 
rate is zero. In the former case, the longer the plant is kept 
up {i.e. the larger n is) the smaller will the second term be- 
come ; for the divisor of this second term, (1+0", will increase 
indefinitely and the other factors, a and the square bracket, 
remain constant. Hence, as n increases indefinitely, this second 
term becomes more and more negligible and approaches zero as 
a limit. That is, the value of a plant whose up-keep is indefi- 
nitely maintained is equal to the first of the two terms. This 
first term becomes, when n is indefinitely great,' 



(TOO-f,)±, 



(3) 

which expresses the value of the plant. In other words, the 
value of the plant is the capitolization of its annual net in- 
come, ma - r,. Or, again, the annual income mo - v, divided by 
the value of the plant {ma - v,) \ will equal the rate of interest i. 

nK* vM.''™"'' "* ^* ^''''"■* "•'' ^''^"''' ""'' Income, Appendix ic 




PRODUCTIVITY THEORIES 



349 



M 



The same result applies to a j.lant which contains more or 
less machines than m, since the size of the plant will affect both 
iocome and capital alike. 



.'Ml 

4 



§ 2 (to Cir. II, § 7) 

DiscuBsion of the Cane of Zero IntereHt aa Applied to the Valuation of 
Reconstituted Capital. 

The case of a zero rate of intf-n.-st offers a peculiarity not 
presented under ordinary circum.stancfs. In all other instances 
of per|)etual uj^keep, the net income capitalized gives the 
entire capital-value. Thi.s wa.s shown in § 1 of this Appendix. 
But in the ca.se of zero interest the piojosition is not true, as 
may best be shown by mathematics. I.i § 1 of this Appendix 
the expression for the value of a plant of m machines to be 
kept up for n years and then allowed to run down during m 
years was found to be 






ma — V, ma — )•, 



1 + «• (1+ «■/ 



+ 



mo — V, 



ma 



+ 



(m —l)a 



+ ■ 



In the previous section it was assumed that / w.is finite and 
positive, from which it followed tlint when n was indefinitely 
great the second sipiare bracket liecame nei^ligible. Hut under 
our present assumption that i is zero, the term i.s not negligible ; 
on the contrary, it is the first s<iuare bracket which now van- 
ishes. To show this we observe that formula (1) of § 1, 
giving the value of each machine, reduces, wh»-ii ( = 0, to 



i"i = 



rhence 



— ma, 



1" 



ma — I'l = 0. 

Hence the first term in equation (2>, being the prrjduct of 
ma — i\ (^zero) Ly a finite nunil)er, is zero. 
The second term of i'2) reduces, when i=0, to 



nfm m-l ^l f 

— I — i u. . . . J or a 



m( m -^ in 



J" 



'I- 



i: 



L 



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74 



350 



APPENDIX TO CHAPTER II 



which, since the first term is zero, represents the entire value 
of the m machines. The result is now independent of n. If 
m = 10, this expression becomes 55 a. The value of such a 
plant is then fifty-five times the annual yield of each machine. 
If this yield is $100, its value is $5500, which agrees with 
the calculation in the text. 








* .■* 



APPENDIX TO CHAPTER IV 
Bohm-Bawerk's Theobt 

§1(toCh. IV, §2) 
Nature of Various Meaiw— Arithmetical, Geometrical, Harmonical, etc. 

In general, a mean, a, of a number of magnitudes, a„ Oj, a» etc., 
is defined by an equation connecting these magnitudes and a 
in such a manner that if all of the magnitudes, a„ a^ a,, etc. 
are equal to each other, the value of o given by the equation 
will be equal to each of them. That this concept applies 
to the arithmetical, geometrical, and harmonical means is 
evident. These means may be defined by the following 
formulae, where, for convenience, the number of elements, 
a„ a» etc., averaged is restricted to three. This restriction, 
which may be very readily removed, is adopted solely for 
brevity. 

(1) Arithmetical, a + a + a = o, + a, + a3 or d = °'"^"*"^"* 

o 



(2) Geometrical, a d a = a, a, a. 



ord = </a,a,a. 



(3) Harmonical, J + ^+Ul + L + l ord = , ^ , 
a (/ a a, a, Oj ill 

a, a, a, 

The weighted arithmetical mean is given by the formula 
w,d + «;,d + tt'sd = ttfjo, + tt'^, + u-ja, or d = !^-±_1«^ + !^ 

where the " weights " are the coefficients w„ w» Wj. This is 
the mean employed by Btthm-Bawerk in the example given, 
the elementt averaged, a„ o» a» etc., being the different ages 
of the labor, 10 years, 9 years, 8 years, 7 years, etc., and the 
weights being the amount of labor, «20, $20, $5, $5, etc. 
The formula for both the geometrical and the harmonical 
averages may also be modiiiod by introducing " weights.*' 

351 



^.1 
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i 







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-' 


^k| 


k 


wii'. 


■1 


11 


tt|f' 



352 



APPENDIX TO CHAPTER IV 



III 

U ti 



I 'i 



By varying the formula we may evidently invent an 
infinite number of new kinds of means. Thus the formula 



defines a as a sort of mean, though a complicated (and 
unsymmetrical) one, of Oy Oj, Oj. 

§ 2 (to Ch. IV, § 2) 
Case Illustrating Futility of Measuring Average ftoduction Period. 

Bohm-Bawerk's chosen concept, which was doubtless adopted 
purely for convenience, that a given application of labor will 
yield its retuin in a single sum all at once, is far too simple 
to cover the facts as actually found. On the contrary, both 
the labor of forming instruments and their return are spread 
over a considerable period of time. This distribution in time 
may take any form, and some of its forms would render use- 
less the simple arrangement of Bohm-Bawerk of production 
periods into a series of varying duration. 

Suppose, to take an extreme case, that a particular applicar 
tion of labor issues in two items of income, namely : $5 ten years 
after date, and $100 one hundred years after date ; while another 
application of labor issues in only a single item worth .$15 
in twenty-five years. In this case it becomes impossible to call 
one of the production periods longer than the other ; for whereas 
the second is definitely 25 years long, the first may be 
measured as any period Ijetween 10 and 100 years, according 
to the method employed for averaging 10 and 100. Moreover, 
it is not true that one of the alternatives will be chosen if the 
rate of interest is high, and the other if the rate of interest 
is low, as would be the case if they were subject to Bolun- 
Bawerk's series. The apj)lication of labor which issued in 
the $5 and $100 would, oddly enough, be the most economical 
if the rate of interest were either very high or very low, 
whereas the other alternative uould be chosen in case the 
interest were at a more moderate rate. Thus, if the rate of 
interest were 5%, the present value of the $15 due in 25 
years would be .54.43, and that of the two items, $5 in 10 
years and $ 100 in 100 years, would be $3.83. On the other hand, 
if the rate of interest were I %, the value of the $5 and $100 
alternative wouul be $11.70 and of the $15 aiternativo $41.28. 



-if.l^ 



BOHM-BAWERK'S THEORY 



353 



AgMn, If tjerate c^mterest were 25 %, the value of the $5 and 
»100 would be $0.06 and of the $15 alternative, $0.54. Hence 
If tha r»te of interest is 6%, the $15 alternative will be prefer! 
able, whereas if the rate of interest is either 1 % or 25 % the 
other alternative will be chosen. ^ ' 

§ 3 (to Ch. IV, § 3) 

Showing how Periods of Production which are Relatively Long but 
Unproductive are Eliminated. 
That long processes (assuming their length to be measur- 
able) are more productive than short processes is, as Bohm- 
Bawerk says, a general fact, not a necessary truth. The reason 
les m selection It is not true that, of all r^ssmTZlZ 

ru7thmf''T''*" ^""^ "°^' P^^^-*-«' buwtl 
true that, of all productive processes actually employed the 

ongest are also the most productive. No one w 11 felt a 

ong way unless it is at the same time a better way. A 1 the 

long but unproductive processes are weeded out. Ihe follow! 

mg illustration will make the process clear • 

JoFr^Z *^** ^IT'^"' "^ ^^ ^*y«' ^*^^ '"^^sted to-day 
we can obtain a product of 100 units one year hence, or of 250 

hence, of 250 five years hence, of 320 six years hence, of 100 
seven years hence, of 300 eight years hence, etc-^ ser'es 

It oT k e'ininated those of 3. 5, 7, and 8 years, for 
each of these is outclassed by preceding choices. Thus, 
Ivl.?**'^"'^ /'''*^^°» ^'"^ ^'" ^ overshadowed by the 
mft^lT ^'^'^'"^ f^' ^'' '^'' prospective return, being 

J?S^^^*fu''"* T^'"""' '^^ ^^'^ * ^^^^'' present value 
Eliminating, then, these ineligible cases, we have left to 

^nrimT'?' '' '' '• ""'^ ' y«" P«"«d- Of these Ihi; 
r Jn ,i? ^ ^'^^ 1 ''^''^ *^" '^*"™ ^'" have the highest 

ves thrfoo 5 '°mT;' " "* ^^" '' ^"^ he profitable to in- 
vest the 100 days' labor so as to mature in four years. AB 

Ws curv *n» ^'"'^^r^^J" ^^ ^^"^" "^^ •'^ 9^^ f'^-" <^- Sine? 
ve ticLunrr °'' '^' *"P''' ^' ^"' ^"' °f *" the other 
IniT!Vx. ' '' P""*"t ^•''h.e (at 695,) of 300 in fn„r years 
Will b« the maximum of the present values of all the returns. 



V 




:| 




354 



APPENDIX TO CHAPTER IV 



100, 250, 50, etc. But if the rate of interest sinks to 2 %, as 
indicated by the discount-curve B'C, the point of maximum 
return is shifted forward to six years ; for the discount-curve 
B'C at 2 % drawn through C now passes above the tops (C, 
C, C", etc.) of all other lines, hence a six-year period will be 
chosen. If, on the other hand, the rate of interest were 10%, 
a similar construction would show that the two-year period 
would be selected, as the highest discount-curve would then 
pass through C". But in no case will the highest discount curve 
touch the top of one of the short lines, 100, 60, 260, 100. 




100 



250 



50 



300 



250 



320 



loo 



300 



3 



e 



ayears 



4 B 

Fio. 2S. 

§ 4 (to Ch. IV, § 4) 

Mathematical Refutation of Bohm-Bawerk'a Claim as to Ground of 
Preference for Present over Future Investment of Labor. 

Let the products obtainable by processes of 1, 2, 3, etc. 
years be pi, jh, Ps, etc., and the " marginal utilities reduced in 
perspective " beginning in 1888 be w„ Uf, u„ etc. Then, 
A MONTH'S LABOR AVAILABLE 



lit 18S8 TIKLDB 


IH 188t TIBLD8 


For the 

economic 

period 


Units of 
product 


Marfrind 

utUlty 

reduced 

In persp. 


Amount of 

value of 

entire 

product 


UntU 


Marft. 
utility 


Value 


1888 
1889 
1890 
1801 
etc. 


Pi «1 
Pa Vt 
Pi "a 

P« "4 

etc. j etc. 


Plttl 
PlUi 
P3«» 
PiUt 

itc. 


Pi 
Pi 

Ps 

etc. 


Ml 
tlj 
tl» 
t«4 

etc. 


PlMj 
P««S 
P3U4 

etc. 






BOHM-BAWERK'S THEORY 355 

We shall show that the labor available in 1888 is more valu- 

that is^that the maximum of the first series of pa's, relating 
to 1888 18 plater than the maximum of the second series, 
relating to 1889 (assuming of course that maxima exist). To 
prove this, select the maximum of the second series. Sup- 
pose It to be p,tt,. This is necessarily less than p,u, in the 
first series; for since u, < «, by hypothesis, it follows that 
PiVi<P3Ui. That IS, there necessarily exists in the first series 
a term greater than the greatest term in the second series 
A fortiori must the greatest term in the first series exceed the 
greatest 1° the second series. In other words, the value for 
1888 exceeds that for 1889, provided only the marginal utili- 
ties descend, whether or not the productivities ascend 



i 




4| 







*,« 



APPENDIX TO CHAPTER V 

Appreciation and Interest 

§ 1 (to Ch. V, § 2) 

History of Theory of Appreciation and Interest 

Investigation shows that the present writer was by no means 
the first to conceive the relation between appreciation and 
interest. Apparently the earliest was the anonymous author* 
of a remarkable pamphlet entitled: "A Discourse Concern- 
ing the Currencies of the British Plantations in America," 
Boston, 1740 (reprinted in the Economic Sttidiea of Amer- 
ican Economic Association, 1897). He writes : — 

'» The Arguments current amongst the Populace in favour of Paper 
Money, are, 

" I. In most of the Paper Money Colonies one of the principal Reasons 
alleged for their first Emissions ; was, to prevent Usurers imposing high 
Interest upon Borrowers, from the Scai city of Silver Money. It is true, 
that in all Countries the increased Quantity of Silver, falls the Interest or 
Use of Money ; but large Emissions of Paper Money does naturally rise 
the Interest to make good the pinking Principal : for Instance, in the 
Autumn, A. 1737, Silver was at 268. to 278. per Ounce, but by a large 
Rhode Island Emission, it became in Autumn 1739, 298. per Oz. this is 
7 per Cent. Loss of Principal, therefore the Lender, to save his Principal 
from sinking, requires 13 per Cent, natural Interest (our legal Interest 
being 6 per Cent.) for that Year. In Autumn A. 1733, Silver was 22s. 
per Oz. by large Emissions it became 27 s. in the Autumn, A. 1734; is 
22 per Cent, loss of Principal ; and the Lender to save his Principal ; 
requires 28 per Cent, natura; Interest for that Year. Thus Uie larger the 
Emissions, natural Interest becomes the higher ; therefore the Advocates 
for Paper Money (who are generally indigent Men, and Borrowers) ought 
not to complain, when they hire Money at a dear nominal Rate. 

"If Bills were to depreciate after a certain Rate, Justice might be done 
to both contracting Parties, by imposing the Loss which the Principal 
may sustain in any cerUin Space of ' .e (the Period of Payment), upon 
the Interest of a Bond or Price of Gooc3 : but as Depreciations are uncer- 
Uin, great Confusions in Dealings happen." 

• Now identified as the physician, William Douglass. 



1 . 



APPRECIATION AND INTEREST 



357 



TloW Sk i^iT^Pu'T ^ *^' '*"« ^•«^'' ^ ha^« also 

Eobert Goodbody,» Jacob de Haas,» and Professor John B 
Clark. A principle which apparently has been independently 
discovered by each of these economic students and quite pos- 
Bibly by others/ is likely to be of some importance 

The present writer published in 1896 a monograph* in which 
he worked out the relation between interest and appreciation 
in quantitetive form, its application to special cases, its statis- 
tical verification, as well as its significance in the theory of 
interest and in the practical problem of regulating the stand- 
ard of deferred payments. The major part of the material 
contained m this monograph is reproduced in Chapter V 
Chapter XIV, and this Appendix. ' 

That the appreciation or depreciation of money does actually 



' Priru^ples of Political Economy, Book 3, Ch. 23, § 4. [A single 

'Mr Robert Goodbody, Broker, New York, has for years in his 
trade-letters maintained the doctrine that the rate of interest 'is high when 
money « depreciating, and low when money i, appreciating. This he 
^scovei^d about 1876. when the decline in sifver w^attra^tSfg atSition 

f«r??!? ""f T"^""^ *° '''' "'^''^^ mathematics, and as he el 
pressed it. " accident or something caused me to differentiate the equation 

with respect to the variation of the standard of value. The result was 
that I found that the fraction formed by the ratio of call money as n" 

st!^^ *T "°"!^." '^^•"""•"atorwas smaller when the money 
sUndard was falling and larger when it was rising " 

^LtJ**'? ^^r^» *\"'* "*** °* l^^^restr Journal of the Royal 

s^tl^] "' '"''• ^^**- ^"^^ "^^"^^"^ Jiscussiou, w?th 

•"The Gold Standard in the Light of Recent Theory," Political 

twve™V] '* September, 1895. [Applied to the bimetallic con- 

twl^'' °^'^1 T- ""'* ^'''' ''^'^^ °'^" <="«« •« ^hich the relation be- 
eri!L*^?T f" T^ *"'*'"'" ''" ''«'° recognized. In his paper 
entit ed Interest and Appreciation " (Sound Currency, Vol. V, No. 22, 

of H.™ ^^'"il if.^"*'""" ■^""*' *" ^*^»^*' Professor T. N. Carver, now 

W.T'l'Tf "i I ®"''"*' "^ ^^"'"'^' '*"d Professor II. H. Powers, 
formerly of Leland Stanford. 

.nnJ!t^.f"*''''^i°? '^'^ Interest: a study of the influence of monetary 
tKtt n, ''''P"«='»»'°'» •"> the rate of interest, with applications to 
the bimeuilic controversy and the theory uf interest." Puhlicalion. of 
w« American Economic Atsociation. 1896, Vol. XI, No. 4, pp. 331- 



ii. 



m 



I 













i • 




358 



APPENDIX TO CHAPTER V 



influece the rate of interest is now well recognized by those 
who have given attention to the subject' 

§ 2 (TO Ch. V, § 3) 
FoHDula Connecting the Rates of Interest in two Diverging Standards. 

In order to state the general relation between the rates of 
interest and appreciation or depreciation, let wheat fall in gold 
price (or gold rise in wheat price) so that the quantity of gold 
which would buy one bushel of wheat at the beginning of the 
year will buy 1 + a bushels at the end, a being therefore the 
rate of appreciation of gold in terms of wheat. 

Let the rate of interest in gold be i, and in wheat be j, and 
let the principal of the loan be D dollars or its equivalent B 
bushels. 

Our alternative contracts are then : — 

For D dollars borrowed, D + Di or D(l + i) dollars are due 

in 1 yr. 
For B bushels borrowed, B + Bj or B(l +j) bushels are due 

in 1 yr. 

and our problem is to find the relation between t and j, which 
will make the D(l + 1) dollars =o= the J5(l +j) bushels.* 
At first, D dollars =o= B bu. 

At the end of the year, D dollars =o S (1 + a) bu. 

Hence at the end of the year D(l + i)dol\aTs ^B(l+a) (1 +t)bu. 
Since D(l + i) is the number of dollars necessary to liqui- 
date the debt, its equivalent B(l+a) (1 + 1) is the number of 
bushels necessary to liquidate it. But we have already desig- 
nated this number of bushels by B(l +j). 

1 See Professor Marshall's testimony, Indian Currency Report, 1800, 
Pt. II, p. 169; Graziani, Studi sulla teoria delV interresse, Turin, 1808, 
pp. 120-20; and Joseph F. Johnson, Money and Currency, Boston (Ginn), 
1905, p. 168. But the subject has as yet attracted little attention in 
the business journals. See The Bond Record, April, 1896 ; also the first 
number of Moody^a Magazine, 1005, in which the " Symposium " and 
editorial on the effects of increasing the supply of gold are partly de- 
voted to the relation between monetary depreciation and the rate of 
interest. The same material together with much else of importance is 
assembled in The Gold Supply and Prosperity, by Byron W. Holt, New 
York (Moody Publishing Co.), 190". See also J. P. Norton, "The Depre- 
ciation of Gold," Yale Review, ll«H)-7, pp. •M\i-30Q. 

* The symbol « signifies " equivalent to." 



APPRECIATION AND INTEREST 



359 



Our result, therefore, is : — 

Dollars 



Busb»Is 



Bushels 



at the end of one year D(l + i)^B(l+J) = B(l + a)(l + i),{l) 
which, after B is canceled, discloses the formula : — 

l+i=(l + a)(l+0, (2) 

O' j= i + a + ia. (3) 

or in words : The rate of interest in the relatively defn-eciating 
standard is equal to the sum of three terms, viz. the rate of inter- 
est in th> tppreciating standard, the rate of appreciation itself, 
and the product of these two elements. 

Thus, to offset the appreciation, the rate of interest must be 
lowered by slightly more than the rate of appreciation.' 

We may introduce depreciation in a similar manner. Instead 
of saying gold appreciates at the rate a, relatively to wheat, 
we may say, wheat depreciates at the rate d, relatively to gold.* 
This means that wheat has sunk in terms of gold in the ratio 
1 to 1 — d, and reasoning similar to the foregoing shows that 

l + t- = (l-d)(l+j-). (4) 

Equations (2) and (4) may be conveniently combined, thus : 
l+j_l-ha _ 1 



1 + t 



1-d 



(5) 



Since —~ is the ratio of the value of gold at the end of the 

year to its value at the beginning (all in terms of wh««at), that 
is, the ratio of divergence of the two standards fv ressed •> 

wheat, while— —is the same ratio of divergent e exps 1 

in gold, and since 1 + i is the "amount" of SI put at int. i, t 
for one year, while 1 +j is the " amount " of one bushil 
may state equation (5) as follows : — 

1 Professor Clark (Political Science Quarterly, September, 18W. 
plies that 1 '/„ appreciation is offset by less than 1 % reduction of int*-. 
But in making his calculation he has failed to "compound." The nuiiB^. 
cal illustrations of the eighteenth century pamphleteer (.oupra) are a». 
erroneous. E.g. Instead of 28 % the figure should be 2!t.32 %. Proff«* -r 
Marshall (Priticiples of Economics, Vol. I, M ed., p. (i74) gives a corr.'-. 
example, designed to show the losses from a flactuatinc currency. 

' The relation between d and a is (1 + a) (1 - d) = 1, which is e. 
dent from equation (6), or may be easily sliown independently. 






J 





ri,plil*'-r' 







360 



APPENDIX TO CHAPTER V 



The ratio of divergence between the standards equals the ratio 
between their "amounts." 

This is, perhaps, the simplest mode of conceiving the rela- 
tion, and stress is laid upon it, because it brings into promi- 
nence the " amount," or ratio of future payment to present 
loan, a magnitude which in most questions of interest plays a 
more important r51e than the rate of interest itself. 

Equation (5) gives the relation between i and > in terms of 
a or d. From it follows the value of j in terms either of i and 
a or or i and d, and also the value of t in terms either of i and a 
or of J and d, thus: — 



whence 



l+» 1 

J SB 1 4- a -f- ia 



or 



1-d' 
i + d 
l-d 

i=j-d-jd=J^i^. 
L + a 



(5) 
(6) 

(7) 

It follows that j exceeds i by more than the rate of appre- 
ciation, which in turn is more than the rate of depreciation 
(ic, i-i>a>d). 

§ 3 (to Ch. V, § 4) 

Formula, when Rates of Interest and of Appreciation are Reckoned 
oftener than Yearly. 

In case we take the half-year instead of the year as the inter- 
val for compounding the rates of interest and of appreciation. 
It may readily be shown that the formula 

1 +j = (l + i) (l+a) gives place to 

whence it also follows that instead otj^i + a + ia, we have 
the relation 

ia 

In case the interest and appreciation are compounded quar- 
terly, the formula becomes 



j=i+a+ 



ia 
4' 



APPRECUTION AND INTEREST 



361 



and so on. At the limit, when the rates of interest and appre- 
ciation are reckoned continuously, the last term vanishes and 
the formula becoines simply j = i + a. 

§ 4 (to Ch. V, S 5) 
Case of Partial Paymento. 

First, consider the case in which no interest is paid until the 
end of the term of years. Let us suppose, for instance, a 
savings bank which receives »100, gold standard, and repays 
the depositor in five years at 5% compound interest. Let 
there be an alternative standard, say wheat, worth, at the 
beginning of the loan, $1 per bushel; but suppose that, in 
terms of wheat, gold is known to appreciate constantly by 1 % 
per annum. What would be the rate of interest in terms of 
wheat? If the repayment were to be made in one year, the 
equivalent of the 5% would be a rate of interest in terms of 
wheat of 6^ %, since the "amount" of a dollar of gold put at 
interest one year would be «1.05, and this would be worth, in 
bushels c f wheat, 1.05 multiplied by 1.01, or 1.06^ bushels. 

This result, 6^ %, is as true for a series of years as for 
one year. This may be seen by separating the contract into 
se/eral contracts of one year each. If we imagine deposited 
to<iay :n separate savings banks $100 in gold, and its equiva- 
lent, 100 bushels of wheat, they will amount in one year 
respectively to $1.06 at 6%, and its equivalent, 106.05 bushels 
at 6^ %. We may now regard these equivalent amounts as 
withdrawn, but immediately redeposited for one year. Then, 
with the same rate of interest in gold and the same relative 
appreciation, we shall obtain the same rate of interest in wheat, 
so that $105 and its equivalent, 106.05 bushels, will amount in 
one year respectively to $110.25 at 6 %, and its equivalent, 
112.47 bushels at 6^%. In this way each successive pair of 
"amounts," including the last, will be equivalent. 

For simplicity we have considered only the case in which the 
debt is allowed to accumulate to the end. The most general 
case, however, is one in which the repayments are in install- 
ments. 

Suppose, as before, that the interest in gold is 5 % and that 
gold is known to appreciate 1% per annum relatively to wheat. 
A farmer mortgages his land for $1000, or its then equivalent, 



r 



1 
J 

1 



362 



APPENDIX TO CHAPTER V 










1000 bushels of wheat, and agrees to pay annually the interest 
and such parts of the principal as he can save, making the 
repayment complete in seven years. Our problem is to fim' 
that rate of interest in wheat which will make the contracts in 
gold and wheat equivalent in every respect. 

The solution is precisely the same as before, viz. 6^%. For, 
at the end of one year, the farmer's debt amounts to $1050 or 
its then equivalent 1060.50 bushels. Let us suppose that ho 
finds himself able to pay, not only the interest, $50, but also 
$50 of the "principal," that is, $100 all together. The equivar 
lent of this in wheat is 101 bushels. Hence he can either 
pay $100 on $1050.00 leaving $950.00 
or 101 bu. on 1060.50 bu. leaving 959.50 bu. 
and, since the "amounts" $1050 and 1060.50 bu. are equiva- 
lent and the deductions $100 and 101 bu. are equivalent, the 
remainders $950 and 959.50 bu. must also be equivalent; in 
fact, this may be seen directly, since, with gold appreciating 
1 %, $950, originally worth 950 bu., becomes worth 1 % more 
or 959.50 ha. 

Thus the faru, r's remaining debt at the end of the first year 
is the same whether measured in wheat or gold, and since the 
same reasoning applies to the second year, third year, etc., the 
equivalence remains to the end of the contract. 

It is worth noting here that the $100 payment in gold would 
be regarded as consisting of half "interest" and half "princi- 
pal," whereas the equivalent payment in wheat, 101 bu., will 
be regarded as 60.50 bu, " interest," and 40.50 bu. "principal." 

The liquidation of the contract during the seven years may 
thus be supposed to take place in either of the following equiva- 
lent ways : — 

GOLD STANDARD (dollars) 



At beginniiif; 
In 1 year 
In 2 years 
In .1 yean 
In 4 years 
In Ti years 
In (I years 
In 7 years 



iMIERmT 



50.00 
47.50 
45.00 
40.00 
34.60 
27.50 
15.00 



Amiii'NT 



1050.00 
mt7,50 
W.VOO 
840-00 
724.60 
677.60 
315.00 



I*»VIII1XT 



100.00 
07.50 
145.00 
150.00 
174.50 
277.60 
315.00 






I'HlNllr.H 
KEMAINIMi 



1000.00 

950.00 
»H).(M) 
800.00 
000.00 
650.00 
.300.00 
0.0(» 



APPRECIATION AND INTEREST 363 

WHEAT STANDARD (bushels) 



At beginning 
In 1 year 
In 2 years 
In 3 years 
In 4 years 
In 5 years 
Tb 6 years 
Ih 7 years 



INTIRE8T 



60.60 
68.05 
66.64 
49.87 
43.44 
34.97 
19.27 



Aaot'NT 



1060.60 
1017.55 
973.63 
874.11 
761.46 
613.03 
337.73 



Paymknt 



101.00 
99.46 
149.39 
166.09 
183.40 
294.67 
337.73 



Principal 
Kehainimo 



1000.00 
969.60 
918.09 
824.24 
718.02 
678.06 
318.46 
0.00 



In these two tables, every entry in one is equivalent to the 
corresponding entry in the other except those in the interest 
columns. 

We thus see that the farmer who contracts a mortgage in 
gold is, if the interest is properly adjuated, no worse and no better 
off than if his contract were made in a "wheat" standard. 

This principle, that debts in different standards are eqtiiva^ 
lent if the rates of interest in the two standards are properly 
adjusted, holds true, of course, no matter whether the "partial 
payments" are large, small, or none at all; no matter whether 
the interest payments are made in full, in part, or not at 
all. The principals in the two standards are not equivalent, 
except at the beginning, nor are the annual interest sums 
equivalent; but the excess of the burden of interest in one 
standard is accompanied by a deficiency in the burden of the 
principal, and vice versa. 

§ 5 (to Ch. V, § r>) 

Formulffi for Cases of Compound Intrrent and Partial Payments. 

The general case is precisely similar. If a debt in either of 
two alternative standards is to accumulate at compound interest, 
the rates of intere.st in the two standards must, in order that 
the contracts in each shall he equivalent, conform to the for- 
mula, l+j = (l-f-n) (l + f), which we found in the simpler 
ca.se of a one-year debt. 

To show this, resolve the oontract intd a series of one-year 
contracts. For the first year we have, by formula (1) of 5 2 
above. 




I ' I 

i 



\\% * 



364 



APPENDIX TO CHAPTER V 



Dolltn 
due 



Buiheb 
da* 



BnaheU 
du* 



In the second year the same formula applies exc^^pt that in 
place of Z>, the principal is now Z>(1 + i), and in place of 
B, B (1 +j) or B (1 + a) (1 + i). Making these substitutions 
in the formula, we obtain 

/) (1 + 1)» o JB (1 +J)» = J5 (1 + o)' (1 + »•)». 
And similarly the third year, 

Z>(H-t')'o-B(l+7)» = 5(H-a)»(l + t)», 

and so on. Each of the results evidently yields the formula 

l+J = (l + a)(l + t). 

If a debt in either of two alternative standards is to be 
liquidated in "partial payments," the rates of interest in the 
two standards must, in order that the contracts in each may be 
equivalent, conform to the same formula. 

The reason is simply that equivalent payments sub- 
tracted from equivalent "amounts" will leave equivalent 
remainders. The payment in any year forms the same frac- 
tional part of the " amount" in the two standards. We may 
designate this fraction at the end of the first year by /, the 
second year by/, etc., and we have the following results :— 
End of Fibit Year 



Dollars 
/i>(l-H)-o. 



HuihfU Buthela 

«(l+j)= B(l+a)(l + 
/B(l+j)= /£(l+o)(l + 



1^ 



Amount, 
Payment, 

Remainder, (1-/) D {l + i)<»{l-/) B (l+j)= (l-f) B {l + a) (l + i) 

In like manner the unpaia remainder at the end of the 
second year can be shown to be 

(1-/) (1-/) Z)(i-f .•)'=*(i-/') (i.-f)B(i+jy 

Iliithds 

-(l-/')(l-OJ3(l + a)«(l-f-0', 
and so on for any number of years. Each result again yields 
the formula (l+j)»(l+a) (l + i). Similar reasoning 
applied to each succeeding year yields the same formula. 

The case in which there are no partial payments is met bv 
putting/,/, equal to zero. 



APPRECIATION AND INTEREST 



365 



§ 6 (to Ch. V. § 6) 

Case of Separate Paymento of Intereat and Principal in one of the 
Two Standards and Equivalent Payments in the Other. 

Suppose alternative contracts in gold at 6 % and wheat at 
&5>f %, and suppose that the interest in the gold contract is 
annually paid and the principal redeemed in ten years. The 
following tables will show what are the equivalent operations 
in the wheat standard. 

LigniDATioH IK Gold Stakdabd, Cok§i8ti»o of Anucai, Intebest ($60) 

AKD Fl!»AL PbIWCIPXL ($1000). 



At beginning (Dollars) 

In 1 year 

In 2 years 

In 3 years 

In 4 years 

In 6 years 

In 6 years 

In 7 years 

In 8 years 

In years 

In 10 years 



I.VTIBIST 



60.00 

6000 
60.00 
60.00 
50.00 
60.00 
60.00 
60.00 
60.00 
60.00 



AMOI'HT 

Die 



Patmiht 



1050.00 

1050.00 
1050.00 
1060.00 
1060.00 
1060.00 
1050.00 
1050.00 
1060.00 
1050.00 



50.00 
60.00 
50.00 
60.00 
60.00 
60.00 
60.00 
60.00 
60.00 
1060.00 



P»I!«CIP4L 

Remiimino 



1000.00 
1000.00 

1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
0.00 



Eqditalewt LiQDiDATiojr iH Wheat Stakdaed ; AnwnAL Payments 
AEE Less thai* Ikterest (fl0.60Bu.) ahd Final Patmeict More 

THAW PBIHCIk-AL (1000 Bu.). 



At beginning (Bushels) 

In 1 year 

In 2 years 

In 3 years 

In 4 years 

In 6 years 

In 6 years 

In 7 years 

In 8 years 

In years 

In 10 Tears 



I.-ITIEKST 



ASKlIMT 



00.60 
61.10 
01.72 
62.32 
62.96 
63.60 
64.22 
64.86 
66.51 
fi«.17 



1060.60 
1071.10 
1081.82 
1002.63 
1103.56 
1114.59 
1125.73 
1136.MI 
1148.35 
U59M 



Pathint 



60.60 
Sl.OO 
61.62 
62.03 
62.55 
53.08 
53.61 
54.14 
64.68 
11.'iQ«4 



Pbikcipal 
Rbmaiiiiko 



1000.00 
1010.00 
1020.10 
1030.30 
1040.50 
1061.00 
1061.61 
1072.1S 
1082.84 
1003.67 
0.00 






366 



APPENDIX TO CHAPTER V 



11 



If we suppose, conversely, that interest in the wheat stand- 
ard is annually met and the principal redeemed in ten years, 
the equivalent operations in the gold standard will be as shown 
below. 

Liquidation in Wh«at Standard, Consisting of Annual Interest 
(60.50 Bu.) AND Final Principal (1000 Be). 



At beginning (Bushels) 

In 1 year 

In 2 years 

In 3 years 

In 4 years 

In 6 years 

In 6 years 

In 7 years 

In 8 years 

In years 

In 10 years 



Interbst 



60.60 
60.60 
60.60 
60.60 
60.50 
60.60 
60.60 
60.50 
60.60 
60.60 



AmoiTNT 
Die 



1060.60 
1060.50 
1060.60 
1060.60 
1060.60 
1060.60 
1060.50 
1060.50 
1060.50 
1060.50 



Payment 



Principal 
Remainino 



60.50 
60.60 
60.50 
60.60 
60.60 
60.50 
60.60 
60.60 
60.60 
1060.60 



1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
0.00 



Equivalent Liquidation in Gold Standard ; Annual Patmknts 
arb Orratbb than Intbrbst (fSO) and Final Payment Less 
THAN Principal (tlOOO). 



At beginning (Dollars) 

In 1 year 

In 2 years 

In 3 years 

In 4 yeats 

In 6 years 

In 6 years 

In 7 years 

In 8 years 

In years 

In 10 years 



Interest 



60.00 

49.60 
40.01 
48.63 
48.06 

47.67 
47.16 
46.63 
46.17 
45.71 



AMOt'NT 

Ultb 



1050.00 

1030.60 

1029.30 

1019.11 

1009.02 

909.03 

089.10 

979.30 

960.60 

960.08 



Pathent 



69.90 
60.31 
68.72 
68.14 
67.66 
66.00 
66.43 
66.87 
66.32 
960.08 



Principal 
Remaininu 



1000.00 
990.10 
080.29 
970.58 
060.97 
051.46 
042.04 
032.76 
823.62 
014.37 
0.00 



§ 7 (to Ch. V, § 5) 

Case of Separate Payments of Interest and Principal in both Standardi>. 

Let us next compare the liquidations in the two standards 
by Ihe simple annual payment of interest in each (t'.e. $50 in 



5: '3, 



APPRECIATION AND INTEREST 



367 



the gold standard and 60.50 bu. in the wheat standard, not 
inter-equivalent) and in ten years, final payment of principal 
($1000 and 1000 bu. not inter-equivalent). 

In this case the individual payments in the two cases do not 
correspond, but the present values of the debts, reckoned at any 
date whatever, are always identical. Thus, the present value, 
at the date of contract, of the interest and principal, separately 
computed, at 6 % and ft^^ % in the two standards respectively, 
will be:* — 



Present value of all interest payments. 
Present value of principal due in 10 years. 
Present value of total, 



DolUra Bushels 

386.09 < 444.24 

613.91 > 555.76 

1000.00 o 1000. TO 



If the present values were computed five years after the date 
of the contract, and the " amounts " of past interest were com- 
puted for the same point of time, the items would be : — 



Interest (present value and amounts), 
Principal (present value), 

Total, 



DolUra Bushels 

492.75 < 695.88 

783.53 > 745.50 

1276.28 <s 1341.38 



The two sums here, though not equal numbers, are equiva- 
lent magnitudes; for whereas at the outset $1 of gold and 
1 bushel of wheat were equivalent, now, after five years of an- 
nual appreciation of gold relatively to wheat at the rate of 1 %, 
we shall find $1 worth (1.01)* bushels, or 1.051 bu., whence 
$1276.28 will be worth 1341.38 bushels. 

We thus see that it would be just as much of a hardship to 
pay the higher interest in wheat during the whole period as to 
pay the more onerous principal in gold at last. 



§ 8 (to Ch. V, § 5) 

Case of Perpetual Annuity. 

The case of a perpetual annuity may be given special co-isid- 
eration. As is well known, the present value of a perpetual 
annuity is its " capitalized " value. Thus, if the rate of inter- 
est is taken at 5 %, the present value of a perpetual annuity of 
$60 per annum is $1000. Applying the same principle to the 

1 The xymbn! < i» here used for " is lesa than the equivalsn* of." and 
> for " is more than tiie equivalent of." 




m 



ii 





368 



APPENDIX TO CHAPTER V 



wheat annuity of 60.60 bushels and extending the previous 
reasoning, we find that the two annuities are equivalent. 

At first sight this seems impossible, since 6,^ % is a higher 
rate of interest than 5 %. This is true, numerically, and it is 
also true that the early payments of 60.60 bushels are actually 
more valuable than $60. But after a certain time (in this 
particular case 19 years) the reverse is true. The 19th pay- 
ment of $50 in gold is worth 60.40 bushels, while the 20th is 
wojth 61.01 bushels. That is, the recipient of the wheat an- 
nuity has at first a slight advantage over the recipient of the 
gold annuity, which ceases and becomes a slight disadvantage 
after 19 years. 

To derive the formula for the time at which the relative 
values of the two annuities become reversed, let the rate of 
interest in gold be i, in wheat J; let the two annuities be Di 
and Bj, their capitalized values being D and B, (D=o=Ba.t the 
beginning), and let x be the number of years in which Bj is as 
valuable as or more valuable than Di. Then 



At the end of x years. 



Baih«li DoUan 

Bj>Di 



At the end of « + 1 years, Bj < Di 

and since we know that in x years D^B(l + a); and hence 
Di => Bi(X + a)' ; and likewise in x + 1 years, Di =o Bi (1 + a)' +•, 
we see that the previous inequalities become : — 

Buahfis Bnabcla 

At the end of x years, Bj ^ Bi{\ + a)= 

At the end of x + 1 years, Bj < Bt(l + o) ' + * 

which may be combined in the formula : — 
i(l + a)'<;<.-(l + a)' + S 

or x<^°g->-H'<x + l 

=Iog(l-|-a) ^* + ^- 

That is, X is the integral part of the number 
logj-logt 
log(l + a) 
Thus, if I = .05, a = .01, and hence also J = .0605, then 
log J - log i _ 2.7818 - 2.6990 .0828 .q, 
log (1 + a) .0043 " .0043 * 

Hence x = 19. 



(8) 



APPRECIATION AND INTEREST 



369 



I I;'' 



§ 9 (to Ch. V, § 5) 
Cue in which the Rate of AppreciaUon changes each Tear. 

In this case the rate of interest in one or both of the two 
standards will change also. 

Beginning with a numerical illustration, let us suppose that 
a syndicate offers the United States government an alternative 
loan m gold or silver. Let it be known that 100 gold dollars 
will remain at par throughout the first year, but in two 
years will be worth 150 silver dollars, that is, gold will "appre- 
ciate, in the second year, 50% relatively to silver; also that 
m the third and fourth years it will appreciate 10 % and 5% 
respectively. We shall suppose that the rate of interest, if the 
contract be m gold, is 3 % for each year of the contract. 

Our problem is to discover what will be the rate of interest in 
silver It IS perhaps already evident that there will be a dif- 
ferent rate for each year. If the contract were made for one 
year only, the rate of interest in silver would also be 3 %, since 
silver remains this year at par with gold. If the contr^t (or 
aay unpaid part of it) were then renewed for a second year 
the rate of interest would be, by formula (3) : — 

j = i + a-i- ai 
= .03 + .50 + .015 
=s .545 

vi° "l'wu°?^; ^^ "^y ^'*^'''' *^^ ^**« °f '"terest in each 
year, with the following results : — 




belnhS* !?f "r''/'*" * «'"«'« "average" rate of interest 
standid " 'rregular series of rates in the silver 

h J^fK^T' *^^* T^ *" ''^"^^^ " °°<^ P«««ible if the debtor 
has the option cf arbitrary partial payments. If, for instance 
the average were 20%, and the government could pav off at any 



m 






fifflir 



370 



APPENDIX TO CHAPTER V 



time, it would evidently be tempted to refund the debt at the 
end of the second year, to which the lender would not agree. 
If, however, the conditions as to repayment are stipulated for 
in advance, an average can easily be computed on the prin- 
ciple of present values. 

Suppose the borrower agreed to extinguish the debt in four 
years by paying at the end of successive years 20, 40, 30, 
and 10 millions (these to include "interest"). The present 
value of these sums is 66.321 millions, which is therefore the 
amount of the loan received from the syndicate. This sum ia 
obtained by adding the present values of several payments. 
The present value of 20 millions, due one year hence, is 



20 
1.03' 



■■ 19.418 millions. 



and of 40 millions, due two years hence, is 

(1.03H1.5«) -'°'^°""°"' 

for evidently if this be put at interest for one year at 3 %, and 
for the next at 54^%, it will amount to 40 millions. Like- 
wise the third and fourth payments have present values of 

30 



(1.03) (1.545) (1.133) 
10 



(1.03) (1.545) (1.133) (1.0816) 



— = 16.639 millions; 

a 5.128 millions. 



The sura of these four present values is 66.321 millions. 
Now if we compute the present values of the four payments on 
the basis of a uniform " average " rate of 20.26 % interest, we 
obtain the same sum, thus: — 



20 



(1.2026) 

40 
(1.2026)' 

30 



= 16.631 millions 



(1.2026)3 
10 



= 27.659 millions 



= 17.250 millions 



= 4.781 millions 



(1.2026)* 
Total = 66.321 millions 



we 



APPRECIATION AND INTEREST 371 

The separate present values are here fictitious, that is, no one 
of them 18 the actual present selling price of the future payment 
to which It refers, but the deviations so offset each other that 
their sum la the actual present selling price of the whole set of 

fi!^»,^5T."lS-oo/' ^°"°"^' ^^""' P^^'^iples already stated 
hat the debt, 66.321 millions, can be liquidated by precisely 
the same payments (20, 40, 30, and 10 millions) whether the 
interest is reckoned separately at 3, 541. 13 A and 8Js </ «,. 
uniformly « 20.26 ». 'l„ , Jthe UisohTtltJ'^iZ 
in the two cases are : 



OsM 



In 1 year 
In 2 years 
In 3 years 
In 4 years 



^»8.»«i 13A. »^% 



(In Mllltoni) 



Interaat 



1.99 

26.33 

4.61 

.76 



Amount 



At 2n.2«% uniformly 



68,31 
74.64 
39.26 
10.00 



P»ym«nt Prlncl[.»ij|nt«re«t 

6fl..32 il IT" 

48.31 I 13.44 

34.64 12.11 

9.26 il 6.46 

0.00 il 1.68 



20.00 
40.00 
30.00 
10.00 



( In .MlMlonn ) 



Amount IPiyment 



79.76 
71.87 
38.32 
10.00 



20.00 
40.00 
30.00 
10.00 




We thus see that 20.26% is the "average" of 3 ^4i l^ 

and 8^ 9^,, in the sense that, reckoning invest by ihftitS: 
age, the same payments will cancel the same debt as if the 
^^parate rates were used. It is not identical with the ar th. 
metical average, which is 19.74%. 

To express the law of such an average symbolically, let 
us suppose that the rate of appreciation of one s Jdard 
m terms of the other is foreknown to be a, the first year 
a, the second year, a, the third year, and so on ; a so to K 
general as poss ble that the rates of interest in Sth stend- 

firstvr/".f ' ^!f^ '° '^' appreciating standard i, the 
first J ear. •» the second eU=. and in the depreciating standard, 
.;i^„ etc. Let the final settlement occur in n years. Then as 
above, we may regard the contract a^ equivalent to a series of 

thTont%% *"*" w'''''^^''^ '''''^"^ i'^ ^1»°1« or 'n part, 
the only difference being that the terms are all made in advance 
As equation (2) of $ 2 applies to each of these contracts, we have 

l-l-Ji = (l+rt,) (l + i\) 
l+y. = (l+a,)(l + /,) 



1+A = (1+0(1 + ..) 



(3) 







,f 




372 



APPENDIX TO CHAPTER V 



To obtain an expression for the average rate of interest in 
either standard, i.e., t,(or j,), we require a given series of pay- 
ments, Z>,, Dt, ... I\, in the one standard (or their equiva- 
lent Bx, Bt, ... B,, in the other standard). The aggregate 
present value of these payments, reckoned by the separate 
rates of interest, «,, »,, ... j, (or J,,^', ... j,) is 

A . D, , . A. 



l + 'i (H-.\)(l + /,) 



(l-l-«,)(H-t,)... (l + t,) 



(or the corresponding expression in terms of B'a and /s). 
Now the " average " rate »„ must be such that if applied to the 
same set of payments it will produce the same sum of present 
values; that is, t. is determined by 



A 



A 
A 



A 



A 



l + ,\'^(l + i,)(l + i,) 



a + iaY 
f ... 



(1 + U" 



(10) 



(H-.-,)(l + t-,)-(H-/.)' 



and ja is determined by the corresponding formula in B'a 
and fa. 

This equation has only one real and positive root or value 
of t^. It can readily be obtained by Horner's method.' We 
may call i^ and J„ the "present-worth-average" of t,, i,, ... /, 
and^",,^ ...j^ respectively.' 

We may define the average rate of appreciation of one of 
the two standards in terms of the other as that rate which 
would connect the two average interest rates if the latter were 
actual (instead of averages of actual) rates.^ That is, if the 

1 ..... .. ,- 1 1 



' For, by substituting for 



the single letter x, and for ■ 



1 -I- 1„ ■"•- "■••' "* "' " 1 -I- (1 • 1 -(- 1 . ' 

etc., the letters X\, x-2, etc., the equation becomes : 

Dix + DiX* + - + 2>„x» = DiXi + DiXiXt -f- ... +D^iXi - a:,. 
In the example given previously the equation becomes : — 
20x + 40a:« + 30 3c« + 10x«= 66.321, 
the required root of which is x = ,83166, 

which, applied to z = . , gives ja = .2026. 

* 1 + I'a becomes the "geometrical average" of 1 -|-ij, 1 + ^2, etc., when 
Di = Di= - =Z>,_, = 0. 

•It may be proved that tliis definition of Oa satisfies the general con- 
dition of an average, viz. that aa reduces to Oi, 02, etc., when the laictr 
an: all equal, whether i,, i.j, etc. (and ji, jj, etc.), be ail equal ornot. The 
proof is left to the reader. 



k.M 









APPRECIATION AND INTEREST 



373 



average rates of interest are i„ and^ the average appreciation. 
a„ IS given by the equation 

l+Ja = n + U)(l+a.); 

jn - »a 



or 



a„ = 



l + «. 



Thus, as in the example given abovf, suppose the averase 
silver interest is 20.26 % and gold interest 3 %, so that 

.202«_.o.'', 

or 16.76%. This average is not identical with the arithmetical 
average of 0, .%, 10, and 5%, which would be 1(;.25% nor is 
it identical with that rate 'vhioh, if uniform, would result in 
four years m the same divergence between silver and gold as 
was produced by the four successive rates 0, 50, 10, and S^^- 
this would be 14.70%. > > > '^/o, 



ii- 




'k 



,.9t i 



■\ 




APPENDIX TO CHAPTER VII 

First Apr <ioximation 
(This Appendix should be read as a whole after Chapter VII.) 

§1 

As the preliminary statement of the theory of interest 
enunciated in Chapter YII contains the kernel of our theory, 
it will be worth our while, before proceeding to introduce the 
various complications necessary to complete it, to give the 
first approximation a full mathematical expression. This 
mathematical statement will serve to make the preceding 
results clearer and more sharply defined. It will also ■:'> » 
to demonstrate the important fact that the number of det< 
mining conditions is exactly equal to the number of unknown 
quantities, and therefore is adequate for fully determining 
those unknown quantities. 

Inasmuch as the equations are necessarily numerous and 
complicated, it will aid the reaf'er in following them if we 
break the argument up into two steps, first considering an arti- 
ficially simple case where there are only two years of income 
to be considered, and then passing to the general case where 
there are any given number of years. 

Let us suppose, therefore, that the rate of preference for 
this year's income over next, in the case of each individual, 
can be expressed as dependent alone on the amount of this 
year's and next year's income, the incomes of all the future 
years being regarded, for the sake of argument, as fixed. Sup- 
pose also that the income of each year is concentrated at one 
point, say the middle of the year, making the two such points 
just a year apart, and that borrowing and lending are so re- 
stricted as to affect only this year's and next year's income. 

Let /i represent the rate of preference for this year's over 
next year's income, for individual No. 1, and let his original 
endowment of income for the two years be respectively 
Ci and t'l". This original income-stream, c,', c,", is modified 
by borrowing this year and repaying next year. The sum bor- 

374 



•i^ 



FIRST APPROXIMATION 



375 



r .wed thia year is x,', the value of which is yet to be deter- 
mined. This sum is therefore to be added to the present 
income c,'. Next year the debt is paid, and consequently the 
income c," for that year is reduced by the sum jiid. For the 
sake of uniformity, however, we shall regard both modificar 
tions algebraically as additions, the addition -'•' to tha first 
year's income being a positive quantity, and the addition, 
which we shall designate by ar,", to the second year's income 
being a negative quantity. Thus, if $100 is borrowed this year 
and $106 repaid next year, ar,' is f 100 and x," is — 105. Thus 
the first year's income is changed from c^' to c,' + x,' and the 
second year's from c," to c," + x,". liy this notation we avoid 
the necessity of employing minus signs. Then the first con- 
dition determining interest, namely, that the rate of preference 
for each individual depends upon his income-stream, is repre- 
sented by the following equation : — 

which expresses /, as a function of the income of the two 
years. la case the individual lends instead of borrows, the 
same equation may be taken to represent the resulting relation 
between his rate of preference and his income-stream as modi- 
fied by lending; the only difference is that in this case the 
particular value of x' is negative and of x", positive. 
In like manner, for individual No. 2 we have the equation 

f, = F,(c,'+x,>,c," + x,y 
For the third individual, 

f, = F,(c,' + x,',c," + x,''), 

and so on up to ihe last or nth individual, for whom the equa- 
tion will be 

These n equations therefore express the first of the four con- 
ditions mentioned at the close of Chapter VII. 

The second condition, that the n; rginal rates of preference 
of the n different individuals for resent over future income 
shall be equal to each other and equal also to the rate of inter- 
est, is expressed by the continuous equation : — 

/i =/a =/s ••• = — =/h = '• 



4 



ft i <, 



376 



APPENDIX TO CHAPTER VII 



These equations hold true, as we saw in Chapter VI, because 
if a particular /should be greater than its corresponding i, the 
individual would become a borrower, and if / should be less 
than i, he would become a lender. In the former case the effect 
of his borrowing would be to reduce his /until ii became equal 
to t. In the latter case the effect of his lending would be to 
increase his / until it became equal to i likewise. We have, 
then, as a result of borrowing or lending, the equation /= (, 
and as the same applies to every individual, all the /'s are equal 
to I and therefore to each other also. 

The third condition, namely, that the market must be cleared, 
or that the loans and borrowings must be equal, is expiessed 
by the following two equations : — 



X^" + X»" + -' + 



■ + xj =0, 



That is, the total of this year's borrowings is zero (lendings 
being regarded as negative borrowings), and the total of next 
year's returns is likewise zero (payments being regarded as 
negative returns). 

The fourth and last condition, that for each individual this 
year's loans and next year's returns discounted are equal, is 
fulfilled in the following equations, each corresponding to oue 
individual: — 








x,' + --.-0. 



S2 

We now proceed to compare the number of equations with 
the number of unknowns. There are eviddntly n equations in 



use 
the 

less 
feet 
ual 
to 
ive, 

= '■, 
ual 

ed, 

seil 



i 



ngs 

ext 

as 

his 

is 

)ue 



FIRST APPROXIMATION 



377 



the first set, n in the second, 2 in the third, and n in the fourth, 
making in all 3n + 2 equations. The unknown quantities are 



/l> ft) fil •'• > ••• > /■» 


or n unknowns. 


Xi', Xi',Xi', —, •-, a;,'. 


or n unknowns. 


<,^"X3", ..., ..., X,", 


or n unknowns, 


and finally, i. 


1 unknown, 


making in all 3n + 1 unknowns. 





We have, then, one more equation than necessary. But ex- 
amination of the equations will show that they are not all 
'■'.dependent, since any one equation in the third and fourth 
sets may be determined from the others of those sets. Thus, 
to determine the first equation of the third set, add together 
all the equations of the fourth set. The addition gives 

(x/+x,'+x,'+ ... + ... +x:)+ '''"+"''"+^'''+- + -- :±g="^o. 

1 + t 

In this equation W9 may substitute zero for the numerator 
of the fraction, as is evident by consulting the second equation 
of the third set. Making this substitution, the above equation 
becomes 

Xi + X,' s- X,' + ... + ... -f- X.' = 0, 

which is identical with the first equation of the third .set. 
Since we have here derived the first equation of the tliird set 
from all the other equations of the third and fourth sets, the 
e<iuation8 are not all independent. It follows, therefore, that 
of the 3 n 4- 2 equations, one may be dispensed with (namely, any 
one of the equations of the third or fourth sets), so that there 
are left only Sn-f-l independent equations, which are there- 
fore exactly equal in number to the unknown quantities to be 
determined. There are, therefore, just sufficient equations to 
determine those unknown quantities, namely, the/'s, or rates of 
preference for different individuals, the x''h and x"'s, or the 
loans and their repayments, and finally, /, the rate of interest. 



ith 
in 



§3 

In order to obtain an explicit exDression for !\ wemav "solve 
with respect to » " all of the preceding equations that can be 



4 



■mi 



■■ f ' 



ii-1 




II' 



378 



APPENDIX TO CHAPTER VII 



so treated. Thus, to take one of the equations from the third 
set, namely, x,' + :p—, = 0, it is evident that, solving for j, this 
equation may be written 



-X," 



To interpret this, we recall that Xj' is a sum borrowed this year 
(say $100) and thus added to this year's income, and Xi", being 
the sum "added" next year, and hence a negative quantity 
(say — 106), it follows that — x," is the positive quantity (as 105) 



returned. Hence 



is the rati^/ 



eig)»' 



the sum re- 



turned to the sum borrowed, or the ratio of exchange 

— x" 
between this year's and next year's goods, and i 1 

[ as — - —1, or 6 % J is the premium above par of the rate of 

exchange. Since this premium is the definition of the rate 

-x,'- 



of interest, the equation i = — ^ — 1 is merely an equation 

of definition. 

The results of the proposed transformations may be summa- 
rized as follows : — 

«•=/. =/, 

= F.(c,' +x,',c,"+x,")=F,(c'-|-x,',c,"-|-x,")= 

— r" —r" 



'F,(etc.) 

ir 



— X. 



-1. 



These three equations give the value of t, subject to the addi- 
tional condition : — 

x,' + x.'+ - + - +«,' = 0, 

the other equation of the same type as the Last l)eing omitted 
as the one superfluous equation. The equation above written 
could be itself dispensed with by sulwtituting in the previous 
equations the value of x,' derived from it, namely, 

— t'—...—t' 

— X| — ••• — X, . 

These equations state that the rate of interest, under the 
conditions of the problem, will be «»qual to the rates of tinie- 
prefereuc* for all the individuals, as well as equal also to a 






FIRST APPROXIMATION 



379 



certain definite function of the income-streams as finally de- 
termined by the loans and to the premium of exchange of this 
year's income in terms of next year's income. These con- 
ditions, taken together with the condition that the sums lent 
mudt be equal to the suras borrowed — that is, that the rate of 
interest must be such as just to clear the market — will yield a 
complete determination of the rate of interest, which is the 
object of our search. 

It may be remarked in passing that the first of the three 
continuous equations given above is closely analogous to the 
third ; in fact, the first may be called the subjective proto- 
type of the third, which may, in like manner, be called the 
objective expression of the first. The third equation states 
the definition of the rate of interest as the premium in the 
ratio of exchange between this year's and next year's income, 
and the first states that the rate of interest is equal to the 
premium in the relative desirability of the two. It is not diffi- 
cult to express the analogy algebraically by putting the /'s 
equal 'o the excess above unity of the ratio between the mar- 
ginal a 'ability of this year's income and the marginal desir- 
ability Oi .ext year's income. 

If we desire only to obtain the simplest expression for deter- 
mining i, the above equations may be condensed still further. 
The first continuous equation may be omitted altogether. 
For, to omit it will evidently rid us of as many unknown 
quantities as equations, namely, n. Again, since the third 
continuous equation is evidently nothing more than a defini- 
tion of the rate of interest, we may, if we choose, omit the 

X. " 

letter i and employ the expression i 1 in its place. We 

X,' 

shall then have, instead of the three continuous equations 
above expressed, simply the following continuous equation : — 



-%-! = - 



= -F,(r.' + ar.',c."+x,"). 

This equation, together with the equation for clearing the 
market, ati'-t-at^'H — -f-x,' — 0, will fully determine the rate 



X," 


-1 = . 


r " 


r* 




= F,(c,'-hx,',tV'+x,") 



t 



4. 




ti > V 



K 




380 APPENDIX TO CHAPTER Vll 

of interest. But, as was shown, the equation for clearing the 
market may be omitted, if we first obtain from it the value 
of one of the unknowns it contains, say, a;,', and substitute this 
value in the previous continuous equation. The continuous 
equation, so amended, will then of itself yield a complete solu- 
tion of our problem. 

§4 

In the preceding solution, the loan transactions were sup- 
posed to extend over two years only. This restriction was 
made in order that the mathematics might be as simple as 
possible in our first formulation. We shall now remove this 
restriction and proceed to the case in which more than two 
years (let us say m years) are involved. We shall assume, as 
before, that the a's, representing loans or borrowings, are to 
be considered of r -^tive value when they represent additions 
to income, and of negative value when they represent deduc- 
tions. The equatiius in the first set will now be in several 
groups, of which the first is : 

/i' = -F,.(c,'-|-x,', c,"+x,", c,"' + x/", ...c,<'"'-f x,"->), 
/;= Fr (c,' + X,', c,"+ X,", c,'" + X,'", ... c<""+ x,<»>), 

/.' = K (cj + x;, c," + X.", c,'" + x,"', . . . c.<-) + x,'">). 
These equations express the rates of preference of different 
individuals (/,' of individual No. 1,/,' of individual No. 2, etc.) 
for the jirat year's income compared with the next. To ex- 
press their preference for the second year's income coni])areil 
with the next there will be another group of equations, namely : 
/," = F,. (c," -f X,", c.'" + x/", ... c,<"> -f x,<->), 
A" = F, (c,"+ X,", c/"" + ^,'"0. 

/«" = F^. (c," + X.", c„<"" -I- xj"'). 

For the third year there will he still another group, formed 
by inserting "'"" in place of «"", and so on to the «i-lst 
year j for the m — 1st year is the last one which has any ex 
change relatir, js with the next, since the next is the mth or last 
year. There will therefore be »i — 1 groups of equations, ami 
since each of these (w — 1) groups contains n separate equa- 
tions, there are all together rt(m-l) equations in the entiro 
set 



^"f'l 



FIRST APPROXIMATION 



381 



Turning to the second set, we first observe that we are now 
compelled to assume a separate rate of interest for each year. 
The rate of interest connecting the first year with the next 
will be called i\ that connecting the second year with the next, 
t", and so on up to i'"~". 

Under these conditions we shall find, as before, that the 
rates of time-preference for each year will be reduced to a 
uniform level for all the different individuals in the com- 
munity, — a level equal to the rate of interest. Algebraically 
expressed, this condition is contained in several continuous 
equations, of which the first is 

This expresses the fact that the rate of time-preference of the 
first year's income compared with next is the same for all 
the individuals, and is equal to the rate of interest between 
the first year and the next. A similar continuous equation 
may be written with reference to the time-preferences and 
interest as between the second year's income and the next, 
namely : — 

Since the element of risk is supposed to be absent, it does not 
matter whether we consider these second-year ratios as the 
ones which obtain in the minds of the community to-day, 
a year in advance, or those which will obtain next year ; under 
our assumed conditions of no risk, these are necessarily 
identical. 

A similar set of continuous equations applies to time-ex- 
change between each succeeding year and the next, up to that 
connecting the m — 1st and the inth year. There will therefore 
be m — 1 continuous equations. Since each continuous equa- 
tion is evidently made up of n constituent equations, there 
are in all n(m. — 1) equations in the second set of equations. 

The third set of equations, which expresses the "clearing 
of the market," will be as follows : — 

*i' + a;,' ->r- + x^ =0, 
aT,"-far," + ...4.a-„" =0, 



, (m) 



-t-aV"'-f ...-f X. 



:0. 



There are hore m equations. 



l:^ 



382 



APPENDIX TO CHAPTER VII 



The fourth set of equation 3, expressing the equivalence of 
loans and repayments, or more generally, the fact that for each 
individual the total 'additions" to his income-stream, alge- 
braically consider-jd, will have a present value equal to zero, 
as expressed in the following equation : — 

X," X.'" fl-*") 

' ^l+i" (:+i')(l+,")^ (H-t')(l+t")...(l+i<— ") 

=0. 
Similar equations will hold for each of the n individuals : — 



«i' + 



1 + i' 



= 0, 



^'+i^ + - = o. 



X. 



+ ... = 0, 






" 'H-t' 
making in all n equations. 

We therefore have as the total number of equations the 
following : — 

n(m — 1) equations of the first sot 
n(m — 1) equations of the second set 
m equations of the third set 

n equations of the fourth set 

2 mn + n — n equations in all. 
We next proceed to count the unknown quantities. First 
as tofs: for individual No. 1 these will be /i',/,", •••,/!'""'' the 
number of which is m — 1, and as there are an equal number 
for each of the n individuals there will be in all n(m, —1) un- 
known /'s. 

As to x's, there will be one for each of the m years for each 
of the n individuals, or mn. As to I's, there will be one for 
each year up to the next to the last, or m — 1. In short there 
will be 

n(m — 1) tinknown f^a, 
mn unknown x's, 
m — 1 unknown i's, 

or 2mn + m — n — 1 unknown quantities in all. Comparing 
this with the number of equations, we see that there is one 
more equation than the number of unknown quantities. This 
is due to the fact that not all the equations are independent. 



! 51 



FIRST APPROXIMATION 



383 



This may be shown if we add together all the equations of the 
fourth set, and substitute in the numerators of the fractions 
thus obtained their value as obtained from the third set, 
namely, zero. We shall then evidently obtain the first equa- 
tion of the third set. Consequently we may omit any one of 
the equations of the third and fourth sets. There will then 
remain just as many equations as unknown quantities, and 
our problem is exactly determined. 

In the preceding analysis, we have throughout assumed a 
rate of interest between two points of time a year apart. A more 
minute analysis would involve a greater subdivision of the 
income-stream, and the employment of a rate of interest be- 
tween every two successive elements. This will evidently 
occasion no difficulty except to increase the number of equa- 
tions and unknowns. 

§ 5 

The elaborate system of equations which is involved when m 
years instead of two years are considered introduces very few 
features of the problem not already contained in the simpler 
set of equations first given. The new feature of chief impor- 
tance is that, instead of only one rate of interest to be deter- 
mined, there are now a large number of rates. It is too often 
assumed, in theories of interest, that the problem is to deter- 
mine " the " rate of interest, as though one rate would hold true 
for all time. But in the preceding equations we have m — 1 sepa- 
rate magnitudes, t', i", i'", ... t'" ". Is there any tendency at 
work to make these rates of interest equal ? Is the rate of in- 
terest which expresses the ratio of exchange between this year's 
and next year's income normally equal to, or nearly equal to, the 
rate of interest which expresses the ratio of exchange between 
next year's income and the year after? Bohm-Bawerk' put 
this question, and answered it affirmatively, stating that a 
species of arbitrage transactions tended to prod ice this result. 
If, however, we examine his reasoning closely, we shall see that 
the only proposition he has proved is that, if the rate of inter- 
est expressing the premium on the goods of 1888 as compared 
with 1889 is equ"' to the premium of 1889 over 1890, then a 
contract for the exchange of the goods of 1888 for those of 1890 
will take place at this same rate. But what is really needed 

' Pntttivf. Theory of Capital, p. 280. 







384 



APPENDIX TO CHAPTER VII 



■M 't: - -r 


f-^r-r 




a. wj 


^^■T^Tsraf 


m 



is to know whether (as B6hm-Bawerk assumes) the rate of 
interest connecting the years 1888 and 1889 is the same as 
the rate of interest connecting the years 1889 and 1890, and 
if so, why? 

Under the hypothesis of a rigid allotment of future income 
among different time intervals, there is nothing to prevent great 
differences in the rate of interest from year to year, even when 
all factors in the case are foreknown. This is clear from the 
fact that, by a suitable distribution of the values of c„ Cj, etc., 
there may be produced any differences in the values of i', i", i'", 
etc. If the total enjoyable income of society should be fore- 
known to be, in the ensuing year, 10 billion dollars, in the fol- 
lowing year one billion, and in the third year 20 billion, and 
there were no way of avoiding these enormous disparities, it 
is very evident that the income of the middle year would have 
a very high valuation compared with either of its neighbors, 
and therefore that the rate of interest connecting that middle 
year with the first year would be very low, whereas that con- 
necting it with the third year would be very high. It mi,qht 
be that the members of such a community would be willing to 
exchange $100 of their plentiful 10 billions for the first year, 
for only $101 out of their scarce one billion of next year, but 
would be glad to give, out of the third year's still more plenti- 
ful 20 billions, $150 for the sake of $100 in the middle and 
lean year. The reason that, in actual fact, such abrupt and 
large variations in the rate of interest as from 1% to 50% are 
not more frequently encountered is that the supposed sudden 
and abrupt changes in the income-stream seldom occur. The 
causes which prevent their occurrence are : — 

(1) The fact that history is constantly repeating itself. 
For instance, there is regularity in the population, so that at 
any point of time the outlook toward the next year is very 
similar to what it was at any other point of time. The indi- 
vidual may grow old, but the population does not. As indi- 
viduals are hurried across the stage of life, their places are 
constantly taken by others, so that, whatever the tendency in 
the individual lifp to make the rates of preference go up or 
down, it will not le cumulative in society. Relatively speak- 
ing, society stands still. 

Again, the processes of nature recur in almost ceaseless 
regularity. Crops ft- peal themselves in a yearly cycle. Even 



FIRST APPROXIMATION 



385 



when there are large fluctuations in crops, they are seldom 
world-wide, and a shortage in the Mississippi valley may be 
compensated for by an unusually abundant crop in Russia or 
Asia. The resultant regularity of events is thus sufficient 
to maintain a fair uniformity in the income-stream for society 
as a whole. 

(2) The fact that the income-stream is not fixed, but may 
be modified in other ways than by borrowing and lending. 
The nature of these modifications are considered in Chanter 
VIII. ^ 

§6 

Let us now return, for fuller discussion, to the second con- 
dition, that the rates of preference of the different individuals 
are erual to each other and to the rate of interest. 

It was shown in Chapter VII that when the individual de- 
termined his income stream so that his marginal rate of pref- 
erence for present over future income was equal to the rate of 
interebt, he thereby maximized his present " total desirability." 
The two statements, that his preference rate is equal to the 
interest rate, and that his " total desirability " is a maximum, 
are thus interequivalent, and either may be deduced from the 
other. Mathematically this may be shown either by geometry 
or by algebra. We shall begin with the algebraic method. 

Assume at first that only two years are considered. The 
fact that total desirability depends on the amount of income 
this year and next year may be represented by the equation 

U=F(c' -{-x\c" + x"), 

where U represents total desirability or i-tility of an individ- 
ual, and the equation represents this U as a "function" of 
his income-stream consisting of c' -f- x' this year and c" -f- x" 
next year. As we shall here consider only one individual, we 
omit the subscript numbers, 1, 2, etc., previously used to dis- 
iguish different individuals. The individual will attempt to 
adjust x' and x" so as to maximize U. By the theory of dif- 
ferential equations, the condition that V shall be a maximum, 
is that the « total differential " of U or of its equal P{c' + x', 
c" + x") shall be zero, thus 



'^t'\ 



2c 



.t;=?^^.+?^)....=o. 



'.i. 



4.1 




m 



386 



APPENDIX TO CHAPTER VII 



•where the S's represent the " partial differentials " with respect 
to x' and x", and the blank parentheses stand for 



(c' + x",c" + x"). 
From this equation it follows that 

dx''^ SFi ) / SF( I 
dx' 



7' 

S** / Sx" 



The Ze^-hand member is 1 + i, as may be seen by differen- 
tiating the equation of the loan as originally stated, viz. : 



rfa;" 



x'4- -- — = 0. This differentiation yields — -— = 1 + i. 

-* 1 -" -I'll*' 



1 + t 



tc' 



The rj'^Af-hand member, being the ratio of this year's marginal 
desirability to next year's marginal desirability, is by defini- 
tion equal to 1 +f. Substituting the new value for the right 
and left members, we have 

1-1-1 = 1 -f/, 

whence it follows that t =/. 

The same reasoning, applied to three or more years, may 
now be expressed. The total desirability for any individual 
is a function of the total future income-stream. In other 
words, 

U=F(c' + x', H-x", c"'-f-x"', etc.). 

The individual tries to make this magnitude a maximum. In 
terms of the calculus, this is equivalent to making the first 
total differential equal to zero, namely. 

This total differential equation is equivalent to a number of 
subsidiary equations obtained by making particular suppositions 
as to the different variations. Let us, for instance, suppose 
that only x' and x" vary in relation to each other and that x'", 
x"", etc., do not vary. Then in the above equation all terms 
after the second disappear and the equation reduces to 

_(lx" SF( ) / 8F( ) 
dx' ~ 8x' / Sx" 

In other words, 1 -f- »' = 1 +f, and therefore i' =/'. 



%'Hi: 



FIRST APPROXIMATION 357 

This expresses the relation between the first and second 
years. If we wish in like manner to express the corresponding 
connection between the second and third years, let us assumf 
that a:* IS constant and x", etc., constant. Then the first term 
of the equation disappears and all after the third term, and 
the equation reduces to 

dx" ~ Sx" / ~h^- 
In other words, 1 + 1" = 1 +/', or i" =/" ; and so on for each 
succeeding year. We therefore see in mathematical language 
that the point of maximum desirability is also the point at 
which the marginal rate of preference for each year's income 
over the next year's -nme is equal to the rate of interest 
connecting these two yt. -s. 

§ 7 

We turn now to the geometrical interpretation In Fijmre 
26, let the point P be found such that its coordinates are c/ 



^" 102030405060 70^ 




and c,", the values of this year's income and next year's in- 
come respectively, c,' being laid off along the horizontal axis 



4ii 

' \ Uiii 




(> 



7V 





388 



APPENDIX TO CHAPTER VII 



0X\ and c/' being laid ofE vertically. In the same way any 
other income-stream may be represented by another point, the 
coordinates of which represent the values of this year's and 
next year's income respectively. By borrowing or lending, 
the income-stream P is changed to another point Q to be 
determined. We shall assume, as before, that the modifica- 
tion of this income-stream, c/, c,", through borrowing and 
lending or buying and selling applies only to the first and 
second y'^js; all subsequent years are therefore omitted 
from c calculations. The income-stream that is the com- 
bination of the two magnitudes Ci', Cj", — the fixed income 
with which the individual is supposed to be endowed, — is 
represented by the point P. But this income-stream, c,', c,", he 
modifies by adding algebraically a;,', through borrowing (or lend- 
ing, if Xi' has a ..egative value) this year, and adding next year, 
when the loan is paid, the sum x,", which is equal to x,' put at 
interest, but of opposite sign ; in ot herwords, x," = — x'(l + i) 

X " 
or Xj' -f T—!— . = 0. It is first proposed to determine x/ and Xj", 
1 -|- 1 

assuming that the rate of interest is a fixed and given magni- 
tude. The new income-stream, c' + x', c" + x", will be repre- 
sented by a new point, Q, different from P. 

To find this point, Q, draw the line AB through the;* point P 
a<- r. s^ i T detcririned by the given rate of interest, namely, so 

that 77": = 1 -{- 1. Then the new point will lie somewhere upon 
OA 

this straight line. For (1) the present v?lue of the modified 

income-stream (h' + Xy", c^'-f Xj" is the same as that of the 

original income-stream c/, c," ; and (2) the straight line AB is 

the " locus " or assemblage of all points the present values of 

the income-streams represented by which are the same as the 

present value of the income-stream represented by the point P 

through which AB is drawn. 

That (1) the present values of the original and the modified 

income-streams are the same is due to the fact that the loan 

Xi and its repayment x\" are equivalent in present value. This 

may be seen by transforming the formula for the present 

value of the modified income-stream, as follows : — 



'V+-V + 



c," + j-v 



l + i 



= c.' + 



l + i 



,• + 



(^V + 1^)-' 






FIRST APPROXIMATION 



389 



since the magnitude in parenthesis is zero by the original 
hypothesis as to x,' and x,". 
That (2) the lire Ali locates all points of present value 

*^' + fIJIi ^8 evident from analytical geometry, and may be 

shown, among other ways, as follows: 

The present value of the original income-stream c,', c," is 
equal to the length OA. For 

OA=OC+CA 



= c,' 



1+i' 



for OC=Ci' by construction and CA- 



1+i 



by the similar tri- 



angles ^CPand AOB, whose proportional sides "ive -'^'- = ^ 

" CA OA 



= 1 + 1, or CA = 



1 + i 



Similar reasoning applied to any other point on the line 
AB will show, in like manner, that the present value of the 
income representee by that point is also OA. Hence ever,, 
point on the straight line AB represents an income-combination 
or income-stream having the same present value, OA, as that 
of the income-stream c', c" represented by P. Similar reason- 
ing shows that no print out of AB represents an income-stream 
of this present value. Therefore the individual who is pos- 
sessed of the income-stream represented by P, and who 
modifies this income-stream by borrowing and lending, merely 
shifts the point representing his income-stream aloyig the line 
AB, as from P to Q. Which of all the points on tliis line 
open to his choice will he select ? Evidently he will select 
that one which will give, for him, the maximum present de- 
sirability. In order to determine this point, let us suppose 
that the desirability corresponding to every point upon the 
plane is indicated by a number attached, and that through 
the points which have equal desirability, lines of equal de- 
sirability, like isothermal lines on a weather map, are drawn.' 
These may be called iso-desirability lines. If any two points 

> Ci. the writ4>r's " --'"lematica! Iiivt-sligalion.s in the Theory of Value 
and Prices," Part II, ^' .isactions of Conn. Academy, New Haven, :'K)2. 
p. 68. 



, I 



^*i 




m 



390 



APPENDIX TO CHAPTER VII 



on one and the same iso-desirability curve be compared, it will 
be seen that one of them represents an income richer this year 
and poorer next year than the income represented by the 
other; the superiority of the former income over the latter 
this year exactly compensates for its inferiority next yn.-. .0 
that, all considered, the two incomes are equally d* oivable. 
It is clear that these iso-desirability lines will con.'.-tr ea 
"family " of curves, each approaching the axes OX' an 1 OA' ' 
and that the numbers attached increase in magnitude as il;*^ 
curves recede from the origin 0. The curve drawn nearest 
the axes is labeled " 10 " at each end, to signify that all 
points upon that curve have a desirability to the individual 
represented by 10. The point P evidently has a desirability 
between 10 and 20. As we proceed from P toward B along 
the line AB, it is evident that the desirability first increases 
and then decreases, reaching the maximum at Q, where the line 
AB is tangent to one of the fam'Iy of curves. This point Q is 
therefore the point sought, and represents the income-combina- 
tion which has the maximum present desirability. Thus, for 
the individual, the solution of the problem of how much to 
borrow or lend is determined geometrically by drawing through 
tlie point /*, representing his fixed original incouie-endowment, 

a straight line at the slope — - = 1 -f «', and finding the poitit 

Q upon this line at which it is tangent to some one of the num- 
berless curves of ecjual desirability. Q differs from P in 
having one of its coordinates larger (by x,") and the other 
smaller (by —x^). 

The fiict that the iso-<lesirability curves at the right s1(>|h! 
less tlian 45° interprets the fact, which should not be lost sight 
of, that if this year's income is sufficiently abundant or next 
year's income sufficiently soarce, or both, tliat this year's 
goods may exchange for next year's on less thau even terms ; 
that is, that the rate of time-preference may be negative. 



§ 8 
Not only is it true that Q represents the point of nmximuin 
desirability, but also that at the point Q the rate of prefereneo 
/, is "onal to the rate of interest. First we observe that the 
rat ' prelVri'iiee for present over future income at any point 
dej ats upon the slope of the iso-dcsirability curve whuit 



t-.ae=iv. 



FIRST APPROXIMATION 



391 



passes through that point. To make this clear, let us consider, 
on any of the iso-desirability curves, such as 70-70, the point 
M and an adjacent point N. The substitution of the income- 
combination represented by JV for that represented by M in- 
volves the sacrifice of an amount of this year's income repre- 
sented by MS, which may be called - Ax', for the sake of an 
addition to next year's income represented by NS, or Ax". 
If the points M and N are iiulefiiutely near together, we 
may represent MS by - dx', and XS by dx". The loss in 
desirability by surrendering MS is represented by the 
difference in number between the iso-desirability curves 
through M and S, namely, 70 - CO, or 10. Likewise, the gain 
in desirability by the addition of .S\V to next year's in- 
come is represented by the difference between the numbers 
corresponding to iso-desirability curves through S and .V, 
also 70-60, or 10. In other words, the loss in desirability 
through the surrender of MS is equal to the gain in desira- 
bility through the addition of SN, or, the desirability of the 
loss of MS of this year's income equals the desirability of the 
gain of NS of next year's income. Since, therefore, SM and 
SN, or — Ax' and Ax", are the amounts of income for the two 
respective years which possess equal desirability, it is evident 
that the degree of desirability per unit of income for this year 
and next year will be in the inverse proportion. Thus, if SM 
is two hundred and -S^Vis three hundred dollars' worth of in- 
come, this means that, for the particular individual for whom 
the figure is drawn, having an income-stream represented by 
the point M, $200 taken from this year's income would be 
exactly compensated for in present estimation by the addition 
of $300 to next year's income. Hence the desirability per 
dollar of the present income is 1^ times the desirability per 
dollar of next year's income. 
Symbolically these relations are: — 



Desirability of A x' -|- desirability of A x" =0. 

.0, 

0, 



„ desir.Ax'^ ,,desir. Ax'' ,, 
Or-^-^_ Ax'+— ^-^„-- Ax" »0, 



or 



Am., a (/ 

— -, Ax' -I- —--7, Ax" 
Ax' A x" 



or 



A u _Au 

A ''" ' x'Ax 



Ax" : -Ax' =NS:MS 



ifij 



li 



!H 



i 'if 



u * 



t%„ 







1 1.' 



•i 






rliJTty^EM 



392 



APPENDIX TO CHAPTER VII 



That is, the desirability of an additional present dollar is 
to that of an additional dollar next year, as ^'S to MS, or the 
slope of the line joining M and jV". If the points M and ^are 
indefinitely near together, the slope will be the slope of the 
iso-desirability cu»'ve through M. Thus the slope of any of 
the curves in the uiagram at any point is the geometrical rej)- 
resentation of the relative valuation of present and future 
income which the individual feels when in possession of the 
income-stream represented by that point. We have already 
specified that the slope of the straight line ^iB represents the 
ratio of exchange of this and next year's income. Thus the 
slope of the curves represents the subjective, and the slope of 
the line the objective, ratio of equivalence for the two years. 
The former slope, the ratio of the marginal desirability of this 
year's income to the marginal desirability of next year's income, 
is, by our previous definition, 1 +/„ just as the latter slope is 
1 + i. 

Applying these ideas to the particular point Q, it is clear that 
the slope of the iso-desirability curve through Q is equal to the 
slope of the straight line BA. But the slope of the desirability 
curve is 1 -f /„ and the slope of the straight line AB is 1 -|- /, 
therefore, for any individual. 



or 



A = '. 



Hence the individual who modifies his income from P by ;i 
loan at the rate j will shift it to a point Q, such that his sul>- 
jective rate of preference/, which corresponds to that point will 
be equal to the objective rate of interest », — or, speaking gtiv 
metrically, so that the "slope" of his curves will oe maiie 
equal to the "slope" of the market. 

We have ])resented the 'geometrical method in considerable 
detail, in the belief that it is well worth mastering. It will 
be found especially helpful when extended so as to apply to 
the more complicated problem discussed in the Appendix to 
Chapter VIII. 

§9 

If we proceed from the consideration of two years to that of 
three, we may still represent our problem geometrically In- 
using three dimensions. I^et us consider three mutually per- 
pendicular axes OX', OX", (fX"', and represent the income- 



•■Jik' 



URST APPROXIMATION 



393 



combination or income-stream for the particular individual by 
the point P, whose coordina'-»s c', c", and " are the three 
years' income-installments with which the individual is initially 
endowed. Then through the j>oint P draw, instead of the 
straight line in the previous representation, a plane ABC cut- 
ting the three axes in A,B, and C. This plane has a slope 

with reference to the two axes OX' and OX" of ^^ eaual to 

OA ^ 
l-J-i', and has a slope with reference to the axes OX" and 

The letters t' and 



OC 

OX '" represented by --'"^ equal to l-|-t". 
OB 



i" here represent, as before, the rate of interest in the ex- 
ihancre of this and next year's goods, and of next year's and 
the year after. Now suppose the space between the axes to 
be filled with iso-<lesirability curved surfaces like the coats of 
an onion, such that for all points on the same surface the total 
desirability of the income-stream represented by those points 
will be the same. These surfaces will Ije such as to approach 
the three axes and the planes between them, and also such that 
the attached numbers representing their respective total desira- 
bilities shall increase as they recede from the origin O. The 
plane .1J5C' drawn through Pat the slope fixed by the rates of 
iuterest, as ji: ^ ' dieated, will now be tangent to some one of 
the iso-desirabii..y surfaces at a point Q, which is the point at 
which the individual will fix his income. For every point on 
the plane ABCvfiW have the same present value, and every point 
on this plan" .s available to him by borrowing and lending (or 
buying and selling) at the rates i' and i", but not all of them 
will have the same desirability. He will select that one which 
has the maximum desirability, and this will eviilently be the 
point Q, at which the plane is tangent to one of the family of 
iso-desirability surfaces. Reasoning similar to that given for 
two dimensions will show that this point will be such that 
/,' = i' and /," = »". 

To procetu beyond three years would take us beyond the 
limitations of space; for we should then neet' in our represen- 
tation more than three dimensions. Such a representation is 
of little meaning except to mathematicians, since it cannot be 
fully visualized. For the practical purpose of visualization, 
the simple geometrical representation in two dimensions, 
t .ough limited to two years, is the most helpful. 







■^JTV] 




394 



APPENDIX TO 'CHAPTER VII 



10 



Having shown the geometrical representation as applied to a 
particular individual, we now proceed to show how the rate of 
preference is determined for a series of individuals. To recur 
to the geometrical representation in Fig, 26, where only two 
variables are considered, the problem is as follows : — 

Given a number of different individuals, each with his own 
separate point P and his own separate set of iso-desirability 
curves, we are required to draw through these points straight 
lines parallel to each other at such a slope as to "clear the 
market," in other words, such that the sum of the x"s for the 
different individuals shall be zero, and, as implied thereby, 
that the sum of the x"'8 shall also be zero. 

It is evident that, according as the slope of the lines AB 
changes, the points of tangency, the Q's, for the different indi- 
viduals will vary, which means that the amount borrowed or 
lent, namely, x' and x", will change. We have then a swarm ur 
group of fixed ^wints, the P's, and another swarm of variable 
points Q's. By rotating the lines each about its pivot P, and 
bo that all remain parallel to each other, we can evidently shift 
the position of the second swarm of points, the Q's. The solu- 
tion is found by fixing upon such a slope of the lines that tlie 
center of gravity of the Q swarm is brought into coincideiue 
with the fixed center of gravity of the P swarm. The slope of 
the lines vlB which will accomplish this result is the rate of 
interest which will just clear the market ; for the horizontal 
deviations, x,', x,', etc., between the P and Q for each different 
individual will then be self-canceling, their algebraic sum being 
zero, and the same is true for the vertical deviations x,", Xj", tie. 

For three dimensions, we have precisely similar determina- 
tions. The problem of the rate of interest is here solved by 
finding such an orientation for the various planen througli the 
points called P's as will bring the center of gravity of the 
tangential points, the Q's, into coincidence with the fixed center 
of gravity of the P's. 



APPENDIX TO CHAPTER VIII 
Second Approximation 

(Thia Appendix should be read as a whole after Chapter VIII.) 

§1 

In the Appendix to Chapter VII we found that the number 
of equations available for determining the rate of interest was 
equal to the number of unknown quantities, and therefore that 
the rate of interest and the other associated variables were 
determinate under the assumption there made. This assump- 
tion was that all income-streams were unalterable, except as 
they could be modified by borrowing and lending, or buying 
and selling. We now introduce, in place of such a fixed income- 
stream, the hypothesis of a range of choice between different 
income-streams. This, however, does not destroy the detur- 
iiiinateness of the interest problem ; for along with the new 
variables introduced, we find an equal number of new equations. 

Let us, then, state and count the equations which, uuder our 
se :eral hypotheses, determine the rate of interest. The in- 
ccme-stream, we must remember, no longer consists of known 
and fixed elements, .-,', c,", t-,'", etc., as assumed in Chapter VII, 
elements which can Ikj modified only by exchange, it now con- 
sists of unknown and variable elements which we shall designate 
kv .Vi) ,Vi"» .Vi"'» etc. This elastic income-streaiu may be nu' 1- 
itied in two ways : by the variations in these //'s, as well as by 
tile method which we found aiiplicuhle for rigid income- 
streams, namely, the method of exchange — borrowing and 
lending or buying and selling. The alterations effected by the 
latter means we shall designate as before by j-,', r,", j,'", etc., 
for successive years. These are to be algebraically added to 
the original income-items (the y's), deductions being includ-d 
m this addition by assigning negative values. The income- 
Ktrenui as finally deteiMiiiied i,s therefore exi.res.sed by ihw 
installments, y,' -f- j-,', y," + j.,", »/,'" -|- j-,'", etc. 

395 



'.r 




Life 
'•Hi 




396 APPENDIX TO CHAPTER VIII 

One of the determining conditions stated in Chapter VII i 
that the individual rates of preference are functions of the in 
come-streams. Algebraically stated, this condition gives th 
equations : — 

A = Fy (y,' + a;,', y," + x,", ... y, <-' + a^'-)), 

/.• = F,. (yj + xj, yj' + X.", ... y,'-' + x,<«'> 

These equations express the individual rates of pref 3renci 
for the ^rsf year's income compared with the next To expres 
the preference for the second year's income compared with th( 
next, there will be another set of equations, namely : — 

/,• = ^, CV." + X,", y,'" + X,'", ... y,<-) + x,<-'), 
A.. = F^(y," + x,", y,<-> + a^<"'), 

fn- = F,..(yJ' + x:', y;-) + x,'->). 

For the third year, as compared with its successor, then 
would be another similar set, with " '" " in place of " " ", anc 
so on to the next to the last or (m — 1) year as compared witl 
the last. Since each of these m — 1 groups of equations con 
tains n separate equations, there are all together n (m — 1) equa 
tions in the entire set. 

The next condition, that the rates of preference and of inter 
est will be equal, is the same as in the first approximatiou,' 
and is represented by the same n(m— 1) equations, namely : — 

• =/i =ft = —fnf 

* — /l —J3 — —Jn ) 

l("»-i)_ /•(«»-i) ... _y(«-i) _ =/■<""". 

The two sets of equations which express the " clearing of the 
market" and equivalence of loans and repayments will also 
be the same as before, and represented by the same m equa- 
tions : — 

X,' -fx,' + ••' +xj =0, 
x," + x,"+... +a;." = 0, 

x,<-' + x,(-' 4- . . . + x.<"' = ; 
» See Appendix to Ch. VII, § 4. 



BECOND APPROXIMATION 

and the same n equations : 

X,'" 



397 



x,' + 



X," 



1^.+-+ 



(m) 



1+i' (i+i')(i+i")^ ^ (i+,-)(i+,")..(i:mS)=''. 



■=.■ + 1^,+ - 



Juo 



(m) 



(l + i')(l + i")..(l + i-) = 0, 



' + 



§2 



= 0. 



These four sets of equations are the same in number as 
the corresponding sets given in the Appendix to Chapter 
VII, namely, 2mn + m — n, or, for reasons there given, only 
2mn + m — n — 1 independent equations. These equations dif- 
fer from the equations of the preceding Appendix only in the 
first set, which contain y's in place of c's. The c's were con- 
stants, but the y's are unknown quantities. Consequently, 
the number of unknowns is greater than the number in the 
first approximation, whereas the number of equations thus far 
expressed is the same. We therefore need to seek for new 
equations to supply the deficiency. These additional equa- 
tions are found from the condition that the choice among the 
optional income-streams will fall upon that one which possesses 
the maximum present value. 

The range of choice, i.e. the complete list of optional income- 
streams, will include many which are ineligible. By an ineli- 
gible income-stream is meant one whijh would not be selected 
whatever might be the rate of interesv,— whether zero or one 
million per cent., — being smaller for every year than some 
other stream on the list. Excluding these ineligibles, the 
remaining options constitute the effective range of choice. This 
effective range of choice is subject to the "technical" limita- 
tions ot productive conditions, and constitutes the technical 
conditions which influence the rate of interest. If this list of 
options be assumed, for convenience of analysis, to consist of 
an infinite number of options varying from one to another, not 
by sudden jumps, but continuously, the complete list can be 
expressed by those possible values of y,', y^", ... y/-) which 
will satisfy an empirical equation 

01 (yi, yi" ... yr') = o, 

thfi form of which depends on the particular technical condi- 
tions to which the capital of individual No. 1 is subjected, 



\^1 






398 



APPENDIX TO CHAPTER VIII 



whether dependent on his personal characteristics or on the 
physical and technical conditions of his business. Thus the 
form of the function ^ will be one thing if the capital of 
the individual, which vields the y's, consists largely of mines 
which are failing, an . quito another if it consists of forests 
recently planted. In the former case, the equation will be 
satisfied only by values of the y's such that the earlier y's (as 
y'l or y,") are comparatively large and the latter y's (as y/" -'' or 
y<"')are comparatively small ; whereas in the latter case the series 
of y's must conform to the opposite condition. The equation, 
therefore, while it admits of an infinite number of arrays of 
y's, does not admit of their variation ad libitum. It represents 
the limitations to which the variation of the income-stream 
must conform. Each set of values of y,', yj", ... y,<»> which 
will satisfy this equation represents an optional income-stream. 
Out of this infinite number of options, that particular one will 
be selected of which the present value is a maximum. 

Now the present value V^ of any income-stream y/, y^", ... 
y/'"^, of individual No. 1, is evidently 



Fi = y/-f- 



Vi 



yi" 



l-ht'^(l + t')(l + i") 



-fete. 



The condition that this expression shall be a maximum is that 
the first differential quotient shall be zero. That is 

dyr 



dV,=.dy{. 



dyi" 



H-t'^(H-t')(l + f") 



-f- etc. r= 0. 



This last equation expresses the relations which i^nst exist 
between dyi', rfy,", dyi'", etc., in order that the income-stream 
Vif y", yi"> etc., may have the maximum present value. This 
condition contains within itself a number of subsidiary con- 
ditions. To derive these, let us consider a slight variation in 
the income-stream, affecting only the income-installments of 
the first two years, y,' and y," (the remaining installments, 
yi'", etc., being regarded as invariable), and let us denote the 
values of dyt', dy,", under this assumption of restricted varia- 
tion, by iyi', 8y,". Then, remembering that, under the sup- 
posed condition, dy,'", dy,'% etc., will be zero, the above 
equation becomes 



8E00ND APPROXIMATION 



399 



from which it is evident that 

But the hft-hand member of this equation is evidently the 
marginal rate of return on sacrifice as between next year's 
income and this year's income, or the ratio of the increase 
which may be effected in next year's income by a given sacri- 
fice in this year's income. If we call the premium in this 

S'/i" ^ 

7 as 1 -f- r/, and write 



ratio of return r/, we may express 
the above equation thus : — 



% 



or thus : — 



l + r/ = l + i', 



In other words, the condition that the marginal rate of return 
on sacrifice is equal to the rate of interest follows as a consequence 
of the general condition that the present value of the income- 
stream must be a maximum. This proposition and its proof 
correspond to those in regard to desirability, which have 
already been discussed in Appendix to Chapter VII, § 6, that 
the condition of maximum desirability is equivalent to the 
condition that the marginal rate of preference is equal to the 
rate of interest. 

The same reasoning may be applied to successive years. 
Thus, if we assume variations in y" and y'", without any vari- 
ations in the other elements of the income-stream, y', y", etc., 
the original differential equation becomes 

M" , 8y.'" ^ 

l-l-t'"^ (l + i')(l + i")~ ' 



or 

or 
or 






Corresponding analysis applied to each successive year will 
show that the annual successive marginal rates of return on 
sacrifice are equal to the annual successive rates of interest. 

All this reasoning implies that there is a possibility of con- 
tinuous variation, and that at the margin it is possible to make 
slight variations in any two successive years' incomes without 



■% 





r, '-n 






400 



APPENDIX TO CHAPTER VIII 



disturbing the incomes of other years. The values of 1 + r/, 

e„ (I jy in 
l4-r,",etc.,or— 7=^, — f~ (therate at whichthe second year's 

income may be increased by decreasing the first year's income, 
and the rate at which the third year's income may be increased 
by decreasing the second year's income, etc.), may be found in 
terms of y^, y/' ••• y/"' by differentiating the equation for the 
effective range cf choice, <l>i(yi, y", ••• Vi*"'*) = 0. This diifer- 
entiation gives 

-^' =^i--(yi',.V.",etc.), 

-^="/'rO/i',yi",etc.), 

etc. 

Writing together the equations of partial differentiation, we 
have, as our new set of equations : — 

1 + t'= 1 + n' = 1^,, (yA 2/,", etc.) 
= 1 + ri"=: i/fj.. (yj', y,', etc.) 

= l + r,' = iA«. (y,',y»", etc.). 

These equations, 2 n in number, relate to the rates of interest 
and return-on-sacrifice only as between the first and second 
years. The following dimilar 2 n equations relate to the rates 
between the second and third years : — 

1-f i"= 1 + r,"= ^,.. «, yr, etc.) 
= l + r,"=^^.(y,",y,"',etc.), 
etc. 

Exactly similar equations apply to each year as related to its 
successor, until we reach the final set, which connects the next 
to the last year with the last, viz.: — 

1 + 1<"-» = 1 + ri<"'-'> = ^,(—1) (yi", y,'", etc.). 

As there are here (m— 1) sets of equations and 2 n in each set, 
the total number of equations in these sets is 2 n (m — 1). These 
equations, together with the n equations of effective range of 
choice for the different individuals, viz.: — 

<^i (yi, y", etc.) = 0, 
<^» iVi, y^", etc.) = 0, 

<f>.{yn',yJ',etc.) = o, 



.1- 



SECOND APPROXIMATION 



^1 



give therefore 2n (m-1) +n or 2mn-n, the total number of new 
equations in addition to those repeated or adapted from Appen- 
dix to Chapter VII. The number of independent eqjfons 
tiius repeated or adapted from the previous Appendiic was 
Jmn 4- TO — n — 1. Hence we have: 



number of old equations, 2mn + m _n 
+ number of new equations, 2 mn 



■1, 



— n. 



= number of total equations, 4mn + m-2n-l. 
Examination will show that the number of unknowns will 
alsobe4mn + m-2n-l. For all of the 2 mn + m- n-1 
unknowns previously used (in Appendix to Chapter VII) are 
here repeated, and in addition, the new unknowns, the y'a and 
the r's, are introduced. There is one y for each individual for 
each year, the total array being 



Vi, Vt", ' 






y-'»y.",...y.""\ 



The number of these ^s is evidently mn. 

There is one r for each individual for each pair of succes- 
sive years, i.e. first and second, second and third, etc and 
next to last and last, the total array being ' 



n', r,",...r.'"-'), 

'2 



r,', r/'j-.-rJ"-') 



»•«'.'•-",• ••r,"»-'>. 
The number of these r's is evidently T)(m — 1). 

In all, then, the number of new unknowns, additional to 
those of the previous Appendix, is mn + n (m - 1) or 2 mn -n 
Hence we have : 

number of old unknowns, 2 tnn -\-m — n — 1 
number of new unknowns, 2mn —n 

total number of unknowns, imn + m — 2n—l, 
which total is the same as the number of independent equa- 
tions. Therefore the problem of the rate of interest and 
related magnitudes is determinate under the conditions ore- 
scribed. ^ 

The complication mentioned in Chapter VIII, § 14, that the 

S D 



i: 




.iiii 



m 



402 



APPENDIX TO CHAPTER VIII 



o 



income-stre im itself depends upon the rate of interest, does 
not affect the determinateness of the problem. It leave* the 
number of equations and unknowns unchanged, but merely 
introduces the rate of interest into the set of equations express- 
ing the influence of the technique of production. These now 
become 

«^i(3/i', Vi", etc., i', t", etc.) = 0, 

etc., and their derivatives, the \fi functions, are likewise altered. 

§3 

The intricate system of equations just stated may be better 
understood by means of a geometrical representation. 

First we shall represent the range of choice. Let us suppose, 
for simplicity, that only two years need to be considered, so 




if 





that the only uiikmiw- j/V or -nccnm^mssii Tf«it3 are »/' and y", 
all the t/'s for succewiinp jetcr^ tTi<»inir Terarffini as tixed. In 
other words, let us suiTposH- tne laaw id a. lamaer wao is consid- 
ering the choice between aifieprair iEBPi3<iUj5 sa cultivating his 
farm for this and nee: ymx. bur iocs not va&e into considera- 



SECOND APPROXIMATION 



403 

tion any possible variations in the income from his farm for 

frilf '"^JfwC "' ^^ '^' °P"°"^ °f ^"«^''°S his land to 
he fallow both the years; or to lie fallow the first year and 
yield an income the second year ; or to yield an income the first 
year and he fallow the second ; or to cost him a net loss t h s 
year in order to add to the income next year ; or to yield him 

:Zth"o' ht ^^^"' - f-- -*hing up'to the mlxirum p ^ 
sible though the maximum for one year would be incompaUble 
with the maximum for the other. The farmer has here a 
choice among an indefinite number of income-streams 

Let us in Fig. 27 measure ,/' along the axis Or, and v" 
:!7d V' Z is^^f- I'V"-' !'-*/> has for its coordinates 
V-v'' This n ,in Th '"'''' ''' = ''' ^'^^ ^«' ^'^ ^^'ii^ate. 

streams. In hke manner we may represent all other options 

Out ofThf "I P"'"''' "' ^^^"" ^^ '''' 'i^ts in the diagram 

Out of this swarm of points, each representing a particular option 
only one will of course be chosen. The point to be selected w^n 

en^l V'f^'-^^^'^ corresponds to the n.aximum pre^ 
ent value To find it we do not need to consider all the pSt 
n the entire swarm, for some of them are evidently out of 
the question. Thus, if through the point ;, we drawVe line 
Op and prolong ,t to ;,', it is evident that the combina ton 
or op, on represented by the point;,' will have a higher 
present value than that represented by;,, no matter what the 
rate of interest may be; for p' evidently has both of it cc! 
ordinates ,' and y" larger than the coordinates of ;, In 
other words y represents an income-stream which is larger 
than ^ both this year and next year, and must eonsequ Sy 

Ifo or 100%. Consequently, of all the points along the line 

Opwe may disregard all except the one poiit (p') remotest f 1 

he ongm O, or on the honndary of the entire mass of pointT 

ha .h ""'"r^' ^^ ^'■""•"^ °^'" ^•"«« f-"^ we miy see 
ndl l' °^ ^ ^T ^^''^ ""''^ *" b« considered are the 

po nts "^TH '" '*' '""*"'^ ''''' «f ''^« ^°*i- -^-^^ of 
Amon. th.™ '?/'■'' so to speak, the only eligible points. 
Among them, the one which represents the final choice will 
d ffe according to the rate of interest, but whatever the rate 
of interest, the choice will always fall on a pomt in the dest 

darv of"thr • ''f "^'"^ *'^ P^"'"^*^^ ^'^' -^■' 'h« ^^^ 
dary of the swarm, alone represents the effective range of choice. 



«t! 



404 



APPENDIX TO CHAPTER VIII 



" J. 
i III 







The efEectire range of choice includes only the convex por- 
tions of the boundary, the portions which would be points of 
tangency t of a straight line such as ab, touching and not cut- 
ting the boundary, and revolving about the boundary as an 
" envelope." We may still further restrict the portions of the 
boundary to be included by limiting the position of the revolv- 
ing line ab to the vertical position at the right and to the 46' 
position at the left Any further rotation to the left would 
imply a negative rate of interest, which need not be considered. 

The configuration of this boundary line is the geometrical 
representation of those technical conditions which limit the 
income-stream available from capital. This boundary line 
representing the effective range of choice will be quite different 
for different times and places. It will be different according 
to whether the capital of the individual considered consists 
largely of land, of machinery, or of other forms of wealth. 
It is at this point, then, that the technical conditions of in- 
dustry enter into our problem, and show their influence upon 
the rate of interest. 

In order to find what point on the boundary will be selected 

as the final choice, let us draw the line AB such that all points 

upon it will represent options possessing a fixed present value 

OA. AB will then be a straight line of which the slope ial+i ', 

depending on the rate of interest' We know that the present 

value of the income-stream represented by the point p is given 

by the formula 

v" 
Fai y' + 1" :; + constant terms, 

in which equation, as in those which follow, the subscripts "i", 
etc., are omitted for convenience, as it will readily be remem- 
bered that the equations and diagrams always refer to a particu- 
lar individual. The constant terms represent the discounted 
income of the years beyond the second year, the income-install- 
ments of which are by hypothesis fixed. If now we give to V 
a fixed value, and transpose to the left-hand member the 

1 It may be worth observing that, of iU interoepU OA and OB, OA ia 
equal to the value of the Income -atream yi', t/i", aa reckoued by diacount 
in advance, and OB ia equal to that value multiplied by the factor l+<'. 
Hence OB ia the value of the aame income-stream reckoned by accumula- 
tion next year. 8m The yature of Capital and Ihcovm, Appendix to 
Ch. XIII, i IS. 






SECOND APPROXIMATION 



405 



"constant terns," the left-hand member may be represented 
by a constant K, and the equation becomes 



K=y> + 






This is evidently the equation of the straight line AB drawn 
so that OA is equal to iTand OJB is equal to K (1 + C) > 

We see, therefore, that all points on the line AB drawn in 
the manner described represent optional income-streams of equal 
present values. The line A'B', parallel to AB, drawn somewhat 
more remote from the origin O, will in like manner represent 
the assemblage (or " locus ") of all points which have a present 
value equal to OA' larger than OA} 

§4 

We see at once that to select the point, among the entire 
swarm of pomts, which has the maximum present value we 
need simply find that point which will be on a line parallel to 
AB and removed as far as possible from the origin 0. Evi- 
dently such a line is ab, tangent at t to the boundary line p'tR 
It 18 evident, therefore, that t is the point which possesses the 
maximum present value out of the entire mass. If the rate of 
interest rises, the slope of the line ab will be steeper and the 
point of tangency t will shift toward the right. In other 
words, the option now chosen will be one which has a larger 
y but a smaller y"; that is, a larger income for the present 
year and a smaller one for next year. On the other hand if 
the rate of interest falls, the slope of the line ab will be more 
nearly horizontal and the point of tangency will rise, making 
y" larger and y' smaller. 

Not only is it true that t is the point at which the present 
value of the income is a maximum, but it is also true that at 
this point the "marginal rate of return on sacrifice" will be 
equal to the rate of interest. We have seen that the slope of 

' See preceding footnote. 

•That^'i?' will be parallel to AB la evident from the rule for oon- 
structlon. for OA' muat equal a consUnt A"", and Oli* murt equal 
Uon lot V' ^'**"'"" " *" *^'^*"' **'**• co"'l'«riDg the aimiUr construc- 

ConsequenUy A'B' is parallel to AB. 






Iff! 



;% 






' T t 






406 



APPENDIX TO CHAPTER VIII 



the line aJb represents the ratio of exchange between next 
year's and this year's income, namely 1 + »'. In like manner 
the slope, at any point, of the boundary line p'tR represents 
the ratio of the return on sacrifice, or 1 + r'. This may be 
seen clearly from Fig. 28, where a slight variation from t" to t' 
produces in y' a small increase A:^', but in y" a small decrease 
ki". kt' may be designated by iy', and kt" by — Sy", and we 




Fio. 28. 



may state that iy' represents a slight increase in this year's 
income, and — iy" the consequent slight decrease in next year'.s 

income. The ratio of these two, namely . ', , is what was 

called the marginal ratio of return to sacrifice, or 1 + r* ; that i.s, 



-8y" 



.l + r*. 



Returning to Fig. 27, it is evident that at the point of 
tangency t the slope of the straight line ab will be identical 
with that of the curve p'tH. In other words, 

H-»' = l + »". 

Whence it follows that »' = r'. 
We see, then, from the diagram: (1) that the point ( for a 



SECOND APPROXIBIATION 



407 



particular individual, with a particular rate of interest, is de- 
terminate, and (2) that the point t is the one which corresponds 
with the choice of maximum present value, where r' = i'. 



§5 

We shall now proceed to the consideration of the case of 
three years instead of two. A geometrical representation may 
still be used, by employing three dimensions and three mu- 
tually perpendicular axes, OT, OT', OY"'. Any point P 
will indicate a possible income-stream for the three years ; for 
its coiirdinates y', y", y'" may be taken to indicate the income- 
installments for the first, second, and third years respectively. 
Representing the various options by various points, we have a 
mass of points occupying three dimensions, like a swarm of 
bees, and we wish to select from this series of points that one 
which has the maximum present value. It is evident that we 
need not consider as eligible every point in the swarm, but 
nt.d only consider its boundary, or outside surface. For, if 
any point P be joined to the origin and prolonged beyond P 
to the remotest point P in the mass, it is evident that P, hav- 
ing all of its three coordinates larger than the coordinates of P, 
will have necessarily a larger present value. Therefore, the only 
point on the line OP which needs to be considered is P farthest 
from the origin 0, or on the surface bounding the swarm. 
Having restricted ourselves, therefore, to the bounding surface 
as including the effective range of choice, we next ask, what 
point on this surface has the maximum present value. To 
answer this question we observe that the assemblage or locus 
of all points or options which have a given present value V is 
found by drawing a plane cutting the three axes OT, OT', 
and 1'"'. The expression for the present value of the income- 
stream is evidently 



V«y'+-y + 



+ constant terms. 



l-l-i ■ (I4.,')(l + ,-"') 

If we transpose " constant terms '' to the left, and remember 
that V is for the moment rf garded as itself constant, we may 
call the entire left-hand member a constant K, and have the 
equation 



A'=y + 



.V 



1 -I- ." a + 0(1 + «■") 



408 



APPENDIX TO CHAPTER VIII 






This is, in analytical geometry, the equation of a plane 
which cuts the T' axis at a distance K from the origin, and 
cuts the T" axis at a distance ^(1 4- »') from the origin, and 
the Y"' axis at a distance K{1 + i') (1 + 1") from the origin. 

Similar considerations will show, just as in the case of the 
previous representation in two dimensions, that the farther 
the plane is from the origin 0, the larger the present value of 
the choices represented by points in this plane. Our problem, 
therefore, consists merely in finding that point on the bound- 
ing surface which is also on the plane farthest from O among 
the parallel planes just drawn. This is evidently the point of 
tangency, and may be called t as before. It is also clear that a 
change in the rates of interest »' or »" will change the slope of 
the tangent plane, and therefore the point of tangency t. 

The algebraic interpretation of this case will be similar to 
the algebraic expression already given i'r two variables. 

When we proceed to consider four or more years instead of 
simply two or three years, the geometrical representation fails 
us, since the mind has difficulty in picturing spcjes of 4, 5, 
... and m dimensions. 



§6 

In order to show how the new equations which have just 
been expressed enter into the determination of the problem of 
interest, we construct Fig. 29, applying to the case only two 
unknown quantities y' and y". The incomes for the third and 
succeeding years are regarded for the moment as fixed. The 
diagram refers to a particular individual, and shows (1) the 
curve WPZ, giving the effective range of choice among different 
options open to him, and (2) a series of curves for total util- 
ity or desirability, as explained in the Appendix to the pre- 
ceding chapter. The line AB is drawn at a slope equal to 
1 + i and tangent to the curve WZ at the point P. This 
line will be tangent to one of the family of desirability curves 
at some point Q. P represents, out of all the options, the par- 
ticular income-stream chosen by the individual. This income- 
stream P is, of course, as yet unmodified by borrowing and 
lending or buying and selling. The point Q represents the 
income-stream as finally thus modified. The coordinates of 
P are y' and y", and the coordinates of Q are y' -f- «', y" -f x", 
where x' and x" are tht; (algebraic) additions to the income y'. 



SECOND APPROXIMATION 



409 



y" by borrowing and lending or buying and selling. P and Q 
thus represent graphically the double choice explained in Chap- 
ter VIII. We saw there that the individual first chooses, among 
the various eligible income-streams of different present values, 
that which is of maximum present value. WZ now represents 
the series of eligible income-streams, and P the income-stream 
of maximum present value. Also, we saw that after the indi- 
vidual had chosen this income-stream he modified it by select- 
ing another income-stream of the same present value but of 
maximum desirability. Q now represents this final choice. 

It is worth our while in passing to emphasize that the indi- 
vidual would not follow out this program unless the final step 



10 203040 5060 '^O 




of modifying his income-stream by exchange were open to him. 
For, if he were shut off from exchange {i.e. compelled to accept 
P, unmodified to Q), the income-stream of maximum present 
value (P) would not necessarily be that of maximum desira- 
t y. In this case the maximum desirability would evidently 
be iound at S, the point of tangency between WZ and a curve 




410 



APPENDIX TO CHAPTER VIII 




' ;'! 



(not drawn) of desirability, and 5 would be chosen instead o^P. 
The choice of P is made only if there is freedom to replace it 
immediately by Q of higher desirability although of the same 
present value. 

The only difference between this determination of the point 
Q and that shown in the Appendix to Chapter VII, where we 
assumed a fixed or rigid income-stream, is that there the point 
P was assumed as a Jixed point, whereas here it is considered 
as a point of tangency to a Jixed curve WZ. In the previous 
chapter, if the rate of interest changed, the line AB revolved 
about the point P. Under our new and more general hypoth- 
esis, if the rate of interest changes, the line AB rolls upon the 
curve WZ. If the range of choice is reduced and the curve 
WZ is thereby restricted to smaller dimensions, the difference 
between the two cases is diminished, until, as a limiting case, 
we may suppose the curve WZ to shrink into a point, when 
the range of choice disappears entirely and the present diagram 
reverts to the one used in the previous Appendix. 

If now we consider the case of three unknown quantities 
y'j y"> y"'> it is only necessary to introduce three dimensions, 
replace the curve WZ by a surface, the line AB by a plane, 
and the curves of desirability by successive surfaces in concen- 
tric layers, as shown in the Appendix to Chapter VII. The 
plane is now drawn tangent to the surface representing the 
effective range of choice, and the point of tangency P repre- 
sents the income-stream chosen among all those eligible, while 
the point upon this plane Q, at which the plane is tangent to 
one of the desirability surfaces, represents the income-stream 
as finally modified by exchange. 

The previous discussion applies to one individual only. 
When we pass from the individual to society, we can no longer 
consider the plane (or in two dimensions, the line) as fixed in 
inclination. The problem of determining its inclination is 
the problem of determining the rate of interest. This is equiva- 
lent to determining the inclination at which a series of parallel 
planes (or lines), for different individuals, must be passed, each 
tangent to its own surface (or curve) WZ, and such that the 
center of gravity of all the Q's coincides with that of all the i*s. 
This condition will evidently make the algebraic sum of all 
the ar''s zero, and likewise of the a;"'8, etc. In other wordc, 
it will niukc the sums lent equal to those borrowed. 



SECOND APPROXIMATION 



411 



This determination may be mentally represented by consid- 
ering the set of parallel planes (or lines) to be first placed in 
any arbitrary inclination, corresponding to an arbitrarily 
assumed rate of interest for each year. Each of these planes 
(or lines) will have a P and a Q; but unless the centers of 
gravity of the P's and of the Q's happen to coincide, the 
algebraic sum of the x"a, x"'s, etc., will not be zero, that is, 
the assumed rates of interest will not clear the market. We 
therefore now conceive the set of planes (or lines) to roll on 
their respective boundary surfaces (or curves) WZ, and to roll 
in unison, that is, so that they may be always mutually 
parallel. When such a position is found that the center of 
gravity of the /*'s coincides with that of the Q's, the market 
is cleared and the inclination of the planes (or lines) then 
found will represent the rate of interest. The rolling process 
here conceived simply visualizes the process given in Chapter 
VII, § 7, of finding tentatively the rate of interest which will 
clear the market. 

We see, then, from our diagrams, how the different influences 
cooperate to determine the rate of interest, as rep-esented by 
the common slope of the parallel planes (or lines). These 
planes (or lines) have the same slope as the two curved sur- 
faces (or lines) to which each is tangent. There is truth, 
therefore, both in the subjective and objective theory of 
interest. That the rate of interest is equal to the subjective 
rates of preference is indicated by the tangency of the plane 
(or line) to the desirability surfaces (or curves); that it is eq-.a! 
to the rate of return on sacrifice is indicated by its tangtncy 
to the surface (or curve) of effective range of choice. These 
two equalities are not incompatible, as has too often been 
assumed. Interest is determined partly by objective or tech- 
nical factors which supply the range of opportunity (the 
boundary surfaces or curves) ; partly by subjective factors 
which determine individually t'ne choice (the desirability 
curves). 



We have now seen how, on the sinijjle hypothesis that the 
income-stream, or the group of optional income-streams, are 
foreknown, the problem of the rate of interest may be repre- 
sentpd and solved, both algebraically and gconietricaily. We 
found that two of the interest-determining conditions were based 



1 



•! 



:i 



ft '• • »< 
11 -ffct 



' 11 




412 



APPENDIX TO CHAPTER VIII 



on the principle of finding a maximum. One of these two con- 
ditions was that the income-stream selected should have the max- 
imum present value; the other was that this choice should be 
modified by exchange so as to secure the maximum desirability. 
We shall now proceed to show that these two conditions may be 
united into one, namely, that both of these choices tend simply 
to secure the one end of maximum present desirability. It is 
true that maximum present value and maximum present de- 
sirability are not interchangeable concepts, and we have seen 
that if an individual is, for any reason, not free to borrow or 
lend, his choice of income-streams will be determined in a dif- 
ferent manner; the point of maximum desirability under these 
circumstances will have nothing to do with the straight line 
PQ, but will be at the point at which the curve WPZ of effec- 
tive choice is tangent to a utility curve. But, given the freedom 
to interchange parts of the income-stream at the market rate 
of interest, the individual will, under these circumstances, gain 
the maximum desirability by first seeking that use of his capital 
which has the maximum present value, and then modifying the 
income thus obtained by the loan or sale market. This sub- 
serviency of the principle of maximum present value to the 
principle of maximum desirability was made evident in Chapter 
VIII. It becomes very clear geometrically. 

In Fig. 29 the individual is free to select any point on the 
line PQ, and to place this line at any distance from the origin, 
provided it passes through one of the swarm of points repre- 
senting his total range of choice, and provided also that its 
slope always accords with the market rate of interest. It has 
already been made clear that, wherever he places the line, the 
point upon it of maximum desirability is Q, where it touches 
a desirability curve. It only remains to show that if the line 
were drawn, not through P, but through a different point in 
the swarm, while keeping the same slope, Q would be a point 
of lower desirability. This is evident, for if PQ is not drawn 
through P, its only other possible position must be parallel to 
that position, out not so far from the origin O. But in that 
case, Q would evidently be on a curve of lower desirability, 
since the family of such curves ascends as we recede from 0. 

S8 

We may now summarize both the geometrical and algebraic 
determinations of the rate of interest : — 



SECOND APPROXIMATION 



413 



1. We have the condition that, for each individual, the 
effective range of choice among income-streams is limited to 
a specific set of options, owing to the technical limitations of 
bis capital, etc. 

Geometrically, this condition is represented by the surface 
(or curve) WZ. 

Algebraically, this condition is represented by n equations 
of the type ^ 

*(y',y",etc.) = o, 

each relating to an individual. 

2 We have the condition that the rate of preference for 
each individual for each year, as estimated in the present, 
depends upon the future income-stream as indicated bv iU 
annual installments. 

Geometrically, this condition is represented by the familv 
of desirability surfaces (or curves). The slopes at each point 
correspond to the rates of preference, and the cotirdinates of 
the point correspond to the installments of the income-stream 
The fact that the slopes depend upon the position of that point 
represents the fact that the rate of preference depends on the 
income-stream. 

Algebraically, this condition is represented by nim-Vi 
equations of the type ' 

each relating to a single individual and a pair of consecutive 
years. 

3. We have the condition that the market rate of prefer- 
ence of each individual is equal to the rate of interest and 
to each other; or, equivalently, that his total desirability is a 
maximum. 

Geometrically, this condition is represented by the fact that 
at Q the inclination of the plane (or line) is the same as that 
of the desirability surface (or curve) at that point, -in short, 
that they are there tangent and further that the directions of 
the desirability curves at all the Q's are parallel, -in short, 
that the planes (or lines) drawn tangent to them are parallel 
to each other. 

Algebraically, these conditions are represented by m-1 
contmuous equations of the type 

f\ —ft = • • • =/, = i. 



jl 



j 

i " 



i 



l! 'If- 



■| 



414 



APPENDIX TO CHAPTER VIII 



each relating to two successive years, making n(m — 1) equa- 
tions in all. 

4. We have the condition that out of the effective range 
of choice, that particular one of the income-streams is selected 
which possesses the maximum present value, or, equivalently, 
that one is selected such that, when it is compared with its 
nearest neighbor, the marginal rate of return on sacrifice is 
equal to the rate of interest. 

Geometrically, this condition is represented by the fact that 
the plane (or straight line) AB is tangent to WZ for each 
individual. 

Algebraically, this condition is represented by 2»t(m — 1) 
eqi?ations, consisting of n(m — 1) pairs, of which the following 
is the type 

l + t = l + r = V (y', y", etc.), 
there being one such double equation for each individual for 
each pair of successive years. 

6. We have the condition that the sum added (by borrowing 
and lending, or buying and selling) in any year to the income 
of one individual is equal to that taken from others, or, equiv- 
alently, that the algebraic sum of such modifications is zero. 

Geometrically, this condition is represented by the fact that, 
for each individual, the center of gravity of the 0*8 coincides 
with that of the P's. 

Algebraically, this condition is represented by m equations 
of the type 

Xi + Xt + X3-\ +X^ = 0, 

one for each year. 

6. We have the condition that for each individual the posi- 
tive and negative modifications of his income-stream in dif- 
ferent years mutually offset each other in present value, or, 
in more common language, what is borrowed is repayable with 
interest. 

Geometrically, this condition is represented by the fact that 
for each individual, P and Q lie in the same plane (or straight 
line)^B. 

Algebraically, this condition is represented by n equations of 
the type 

+ etc. = 0, 



x" . x'" 



*"''l + i''^(l-f-f')(l+r") 



one for each individual. 



N" 



SECOND APPROXIMATION 415 

Counting up the total number of equations thus indicated, 
we find : — ' 

For the 1st condition, n equations, 

2d condition, n{m - 1) equations, 
3d condition, n(m — 1) equations, 
4th condition, 2 n(m - 1) equations, 
6th condition, m equations, 
6th condition, n equations, 

making a total of 4mn + m - 2 n equations, 
of which, for reasons given in the Appendix to Chapter VII 
only 4ma + m - 2 n - 1 are independent equations. ' 

The niunber of unknowns is as follows : 

number of y's is mn, 
number of as'a is mn, 
number of r's is n(m — l), 
number of /'s is n{m— 1), 
number of t's is m — 1, 

the total of which is also 4mn + m-2n - 1. Hence the prob- 
lem of interest is determinate. 

So much space has been devoted to stating these six condi- 
tions in mathematical form, because, to those conversant with 
the mathematical tongue, the algebraic statement will show 
more definitely and clearly than is otherwise possible the 
determinateness of the problem, owing to the equality between 
the number of equations and the number of unknowns: while 
the geometrical method enables them to form a mental picture, 
clearer than would otherwise be possible, of the various factors 
at work, and especially of the manner in which the objective 
or "technical" conditions, as represented by WZ, cooperate 
with the subjective conditions which influence the rate of 
interest. It was, in fact, only through the geometrical repre- 
sentation that the writer was first enabled to grasp the signifi- 
cance of the "effective range of choice" in its general bearings. 
If the r51e of the curve WZ is grasped, the most difficult part 
of the theory of interest is mastered. 



if 

i 



APPENDIX TO CHAPTER XI 



c> 



ft. 



p II 

h 

u 



I V 




Third Api boximation 
§ 1 (TO Ch. 11, § 8) 

To attempt to formulate in mathematical language, in any 
useful manner, the complete laws determining the rate of in- 
terest under the sway of chance, would be like attempting to 
express the complete laws which determine the path of a pro- 
jectile when affected by random gusts of wind. Such formulae 
would need to be either too general or too empirical to be of 
much value. In science, the most useful formulae are those 
which apply to the simplest cases. For instance, in the study of 
projectiles, the formula of most importance is that which ap- 
plies to the path of a projectile in ideal vacuum. Next come the 
formulae which apply to a projectile in still air. It is seldom 
that the mathematician attempts to go beyond this, and take 
into account the effect of wind currents ; and if he does so, he 
still falls short of actual conditions, by assuming the wind to 
be constant in direction and velocity. The truth is that 
science always stops short of the final approximation necessary 
to reach reality. This is due to the nature of science itself, 
which is a study of what tootUd happen under assumed condi- 
tions, and only an approximate application of what does hap- 
pen under actual conditions.* The consequence is that, in 
order to reach the final goal of real conditions, we usually cut 
the Gordian knots which remain; and for such summary solu- 
tion, especially when the solution is general instead of numer- 
ical, ordinary language is usually better than mathematical 
formulae. Accordingly, in treatises on projectiles we do not 
find any attempt to state their trajectories in general formulae 
which include the effects of gusts of wind. Still less is there 
any attempt to construct a formula for the path of a boomer- 
ang or of a feather thrown out of a window. 

To apply the analogy to the problem in hand, we have 
already stated the laws determining interest under the simpler 

1 See the writer's " Economics as a Science," in Science, Aug. 31, 1900. 

416 



lil 



THIRD APPROXIMATION 417 

conditions, -first, when it was assumed that the income- 
streams of individuals were both certain and fixed, and 
secondly when it was assumed that the income-streams were 
certain, but flexible. When we introduce the element of un- 
certainty, our formula cease to have the characteristics of 
simple clarifying shorthand which justify their use, and take 
on the characteristics of what Marshall calls the "lengthy 
translations of political economy into mathematics." WhUe 
therefore, it is not difficult to make these translations, they 
add htt e or nothing to our understanding of the problem 
Inasmuch as it is our aim to employ mathematics only when 
they add something which cannot be conveyed without thtir 
use, we refrain from wearying the reader with cumbersome 
equations. 



2k 



'Mi 




n 

53 



m 






Ai PENDIX TO CHAPTER XIV 
Statistical Data 

U 

The writer has found so much difficulty in securing a long 
series of yearly averages for rates of interest that the results 
are here presented in the hope that they may be of use to 
others. 

YEARLY AVERAGE RATES OF INTEREST' 





London 


Hkri.in 


Paris 


Nkw Yobk 


CALrrTTA 


Tokyo 


Shanuhai 




1 




■tf 
5? 


M 

1 




1 


I 


m 

s 


a>9>5S 


M 

a 


4' 

7. 


S 




J* 

I 


1824 
1825 
1826 
1827 
1828 
1820 
1830 
1831 
1832 
1833 
1834 
183« 
1836 
1837 
1838 
1839 
1840 
1841 
1842 
1843 


.6 
.9 
.5 
.3 
3.0 
3.4 
2.8 
3.7 
3.1 
2.7 
3.4 
3.7 
4.2 
4.A 
3.0 
5.1 
5.0 
4.9 
3.3 
22 


4.0 
40 
5.0 
4.5 
4.0 
4.0 
4.0 
4.0 
4.0 
4.0 
4.0 
4.0 
4.4 
5 
4.1 
5.1 
5 1 
5.0 
43 
40 














. . . 


\ \ 




,'. " 


* 



'The Ix)ndon, Berlin and Paris market rates are on flrrt claw 
merchants' bill». The figures for 1824-68 are from the evidence of 1). B 
Chapman before the Committee on the Bank Act, 1857, 8ess. 2. X. pt. I, 
p. 483 (also reprinted in llunVt Mfrehant*' Magazine, Vol. 41 (186»). 
p. t»6). The remaining figures are compile*! from the Eronomitt. For 
thoae for 1884-94, the writer is indebted to I'rofessor F. M. Taylor of 
Michigan University, who hail collected tliem from the EmnnmiH for a 
different purpose. The Bank of England rates for 1824-4:1 are reduced 
from " Burden's Official Intelligencer" (IHJM), p 1771. Tlie remainini; 
ones for England. Germany, and France are reduced from those given in 
the Report of the Koyal Commission on Dcpresaiim of Trade, 1886, p. .573, 
and the SronnmUt. They represent the bank " minimum." The rates 
189t-19ai are from A. Sauerbeck's Ubles, Jonrnal Roynl Statittiral 
Socirty, V,."i. LXVII, I'an I, p. BH. The New York rates are Uken, llw 

418 



fif 



* 



STATISTICAL DATA 419 

YEARLY AVERAGE RATES OF INTEREST- Con^„««, 




flm two columns, from a table bv F n wii!-,.. r , 
actuary) in the (New YortrnaL,;'. u (afterward government 

given « ..60 da 8 "apwrentwSL.f ''''':"'' ''^'*- '^^'^ q»«tationa 
column to 1890 i. comS from id t™ '';f f T'" '^^'- '^''^ """» 
rate, prepared at YaZSe^ by M T P^RnJl ' Tl'"^*" """^"'y 
and haa been completed tlTn LFfnan/inTl "V"* "**" "' '«»*' 
highcHt and lowest weekly X« It hLh^.„/^'''r' ^^ """^'"S '»»« 
the New York table ^k "yond 84^ tZ f ""^"'''' ^ *'««'«* 
cally reported The cScuSl «/. ' , ^* ""*' ""^ ""* systemati- 

Gougb. brokers, of Calcutta."^ reSefm^oT ToWo '*'°'^ "^ 

cTnU:u\l''*o^theTbre'ar',H';;-''r'; '' '-"^'"•^ T^uboya.'^T^ 
one of my studentlnd tlXLlTlX ZSST^.nZ t'X 

1>epare;.' ofXrult;;;Xd" ctlrcri^ ^^.r^ ^ " 
are n Japanese onlv ^ Th» ..ku , il I ''"^*'' sources 

through ,fe kL:i'if pro\T^'Vmi:r'i\r ;•""" "^-^""i 

Oriental lllstorv ..f v.i- r- n ■" **""""* °' l^e dtpartment of 

mis rate Is only from 8«pi«tnb«" wh^n -ho -ir-«.> * v « 



I i 



420 THE RATE OF INTEREST 

YEARLY AVERAGE RATES OF INTEREST— Conrfuaed 




ml 





LoiiDoa 


Beklim 


Pa«i« 


New Toiik 


Ualcutta 


TulLTO 


5UAMUIIAI 




31 


1 


1 


i 

4.1 


a 


1 

4.5 


6.6 


S 




1 


1 


M 
i 


s 


M 


1855 


4.7 


2.0 




9.3 




9.7 


.. 


^ , 




• . 


1856 


5.0 


6.1 


. 


4.0 




5.5 


73 


9.9 




6.5 




■ • 




• . 


1857 


7.1 


6.7 


. . 


5.8 




6.1 


6.9 


10.4 




7.0 


. , 


. . 




• • 


1858 


3.1 


3.2 


. 


4.5 




3.7 


3.8 


6.7 




6.1 




• . 




• • 


1859 


2.5 


3.7 


. . 


4.2 




3.5 


5.0 


7.2 




4.9 


"^ 


• • 




. . 


1860 


4.1 


4.2 




4.0 




3.6 


6.1 


8.4 


i.i 


4.2 


kI 


• • 




. ■ 


1861 


6.5 


5.3 


3.6 


4.0 




5.5 


5.4 


9.0 


6.6 


4.2 


tet 


. . 




. . 


1862 


2.4 


2.5 


3.0 


4.0 




3.8 


5.6 


6.8 


6.4 


6.1 


?- 


. . 




. . 


1863 


4.3 


4.4 


3.5 


4.1 




4.6 


5.0 


6.7 


6.8 


6.5 




. . 




. . 


1864 


7.4 


7.4 


5.1 


5.3 




6.5 


7.2 


9.3 


8.0 


8.7 


• • 




• • 


1865 


4.0 


4.8 


4.6 


5.0 




3.7 


6.1 


10.2 


8.2 


6.9 




. . 




. . 


1866 


6.7 


6.0 


6.2 


6.2 




3.7 


6.9 


7.8 


6.3 


0.1 


. . 




13. 


1867 


2.." 


2.6 


2.0 


4.0 




2.7 


5.9 


8.7 


7.2 


5.1 


. . 




11. 


1868 


1.8 


2.1 


2.5 


4.0 




2.5 


5.8 


8.8 


7.3 


6.8 


16. 


18. 




12. 


1868 


3.0 


3.2 


3.2 


4.1 




2.5 


6.0 


10.8 


0.1 


6.0 


18. 


18. 




12. 


1870 


3.1 


3.1 


4.5 


4.8 




4.0 


5.1 


8.1 


7.2 


6.7 


18. 


18. 




11. 


1871 


2.7 


2.0 


3.8 


4.2 




5.7 


4.5 


6.0 


6.1 


4.7 


14. 


18. 




12. 


1872 


3.8 


4.1 


4.0 


4.3 


4.2 


5.1 


5.6 


9.0 


8.0 


6.0 


14. 


18. 




10. 


1873 


4.5 


4.8 


4.5 


5.0 5.0 


5.2 


6.3 


9.8 


10.3 


3.0 


14. 


14. 




10. 


1874 


3.5 


3.7 


3.3 


4.4 4.0 


4.3 


3.0 


6.4 


6.0 


6.2 


12. 


14. 




10. 


1875 


3.0 


3.2 


3.7 


4.7 3.2 


4.0 






6.6 


6.7 


12. 


14. 




9. 


1876 


2.2 


2.6 


3.1 


4.1 23 


3.4 






6.2 


6.8 


12. 


16. 




9.5 


1877 


2.3 


2.0 


3.3 


4.4 1.8 


2.3 






5.2 


8.4 


10. 


13. 




9.5 


1878 


3.5 


3.8 


3.4 


4.3 2.0 


2.2 






4.8 


5.3 


11. 


15. 




9. 


1879 


1.8 


2.5 


2.7 


3.7 2.2 


2.6 






6.0 


6.3 


11. 


16. 




9. 


1880 


2.2 


2.8 


3.1 


4.2 


2.6 


2.8 






6.2 


4.6 


13. 


17. 




8.6 


1881 


2.0 


3.5 


3.4 


4.4 


3.7 


3.9 






^.2 


5.3 


14. 


17. 




8. 


1882 


3.4 


4.1 


3.0 


4.5 


3.4 


3.8 






5.7 


6.6 


10. 


17. 




8. 


1883 


3.0 


3.6 


3.1 


4.1 


2.6 


3.1 






6.6 


6.8 


7.9 


11. 




8. 


1884 


2.6 


3.0 


2.0 


4.0 


2.4 


3.0 






6.2 


6.4 


12. 


16. 




8. 


1885 


2.0 


2.0 


2.9 


4.1 


2.5 


3.0 






4.1 


6.4 


13. 


11. 


4.6 


7.6 


1886 


2.1 


3.0 


2.1 


3.3 


2.2 


3.0 






4.7 


6.0 


8.8 


0.2 


6.1 


7. 


1887 


2.4 


3.3 


2.3 


3.4 


2.4 


3.0 






6.7 


6.6 


9.0 


8.8 


6.5 


7. 


1888 


2.4 


3.3 


2.1 


3.3 


2.8 


3.3 






4.9 


6.5 


10. 


9.7 


6.0 


7. 


1880 


2.7 


3.6 


2.7 


3.7 


2.6 


3.1 






4.8 


7.0 


10. 


10. 


6.2 


7. 


1800 


3.7 


4.5 


3,7 


4.5 


2.6 


3.0 






6.0 


5.8 


11. 


11. 


7.2 


7. 


1891 


2.5 


3.3 


3.0 


30 


2.6 


3.0 






6.7 


3.1 


9.4 


0.4 


3.6 


7. 


1892 


1.5 


2.5 


1.8 


3.2 


1.8 


2.7 






4.3 


3.5 


8.3 


8.4 


6.0 


7. 


1893 


2.1 


3.1 


3.2 


4.1 


2.2 


2.6 






7.1 


4.9 


7.8 


7.8 


6.9 


7. 


1804 


1.0 


2.1 


1.7 


3.1 


1.8 


2.5 






3.4 


5.4 


9.3 


0.4 


3.8 


^. 


1805 


.8 


2.0 , 2.0 


3.1 


il.6 


2.1 






3.8 


4.3 


9.6 


9.6 


2.8 


fi.r) 


1S«>6: 1.4 


2.5 3.0 


3.7 


18 


2.0 






6.8 


* t 


11.0 


0.3 




. . 


1807 1.8 


2.6 3.1 


3.8 


1.8 


2.0 






3.4 


• * • 


U.4 


9.9 




. . 


18081 2.6 


3.3 3.6 


4.3 


2.1 


22 






3.8 


. . • 


12.3 


11.4 




. . 


18001 3.3 


3.8 


4.5 


5.0 3.0 


3.1 


. . 




4.2 


• . < 


10.4 


8.8 






190013.7 


4.0 


4.4 


5.3|3 2 


3.3 ! . . 




4.4 


. 


12.1 


10.8 




. . 


inoi 3.2 


3.8 


3.1 


4.112.5 


3.0 1 . . 




4.4 


. . > 


13.1 


U.O 




. . 


1002 30 


3.3 


2.2 


3 3 2.4 


3.0 






4.9 


. * 


12.1 


10.4 




. . 


]003)3 2 


3.8 


3.0 


3.8 2 8 


3.0 






6.5 


. . . 


10.7 


. . 




. . 


1904 i 2.7 


3.3 3.1 


4.2 2 2 


3.1) 






42 


. . . 


10.8 


. . 






lOM 2.6 


3.0 2.0 


3 8 2.1 


3.0 






4.3 


. 


. . 


. . 






10061 4.0 


4.3 4.0 


6.1 2.7 


3.0 






5.7 


. . . 


• ■ 









Il*^' 



1^ 



STATISTICAL DATA 



421 



AH the rates in the foregoing table are entered as rates of 
" interest," though the rates for the Banks of England, Ger- 
many, and France are rates of discount. Although the two 
are not quite equivalent, for the purposes of the foregoing 
work the distinction between them is unnecessary, because, 
in a continuous series, the error, if auy, affects all items 
nearly alike and thus cancels itself out in the comparisons. 

Had it been necessary, some of the tables could have been 
extended backward. Thus the Bank of England rate could 
be given as far back as 1696, but it was too inflexible to be 
of use. The Berlin and I'aris bank notes could also be ex- 
tended and the Paris market rate could be given back to 1861 
(except for 1870 and 1871) from data in the Economist. 

Many of the sources from which the table has been drawn 
also contain other information such as the rates for other 
money centers than those named, the weekly or monthly 
rates, the variation with the seasons, etc. 

§2 

Of sources not mentioned in the above note, the chief which 
the writer has encountered are : — 

Eleventh Census of the United Sutes, Bulletin 71 (on real estate mort- 
gages, 1880-89). 

This it probably the most elaborate series o( interest averages ever con- 
strncted. 

Twelfth Census of the United States, Special Reports, wealth, debt, and 
taxation, pp. 143, 147, 804. Rates of interest on public debts. 

"Commercial Valuation of Railwa.^ Operatirg l^rojierty in the United 
States, 1904," United States Census Bulletin 21 (1906). 
Gives rates of return on railway securities to investor for 1904. 

Reporto of the Secretary of the Treasury. 

Reports of the Comptroller of Currency. 

The last two references contain statistics of rates of Interest realized on 
some United 8tat«k Oovemment bonds. 

R. A. Bay ley, "National Loans of the United States" (Government 
PrinUng Office, Washington, 1882). 

Gives rates of interest and price of issue of all United States loans from 
July 4, 1770, to June 30, 1880. 

Report of the New England Mutual Life Insurance Company, Bost<«n. 
1800. 

Gives rates realised by twenty representative insurance companies for 
ISbiMiS, aud for Hassaciiusetu savings banks tor 1877-«», and bank dlvi- 



1' 



i 



% 



:i* 






I J i 



t I 

it { 



422 



THE RATE OF INTEREST 



dends in Boston, New York «nd Philadelphia. The rates realized by the 
insurance companies tor the twenty years, 186»-88, inclasive, were 6.0, 6.9, 
6.1, 6.2, 6.5, 6.2, 6Ji, 6.1, 6.6, 5.1, 5.0, 4.8, 4.8, 6.1, 6.1, 4.7, 4.7, 4.9, 4.7, 4.6, 
respectively. These represent (if the writer mistakes not) the average rates 
earned on the par value of investments of all ages, some old, some new, 
some terminable soon and others having many years to run. For this 
reason they are of little or no use for the purposes of Chapter XIV. 

Lester W. Zartman, The Investments of Life Insurance Companies, New 
York (Henry Holt & Co.), 1906. 

Gives earning rate of real estate, mortgage loans and bonds and stocks 
of the principal life insurance companies of the United States 1860-1U04, 
and similar data for companies of England, Canada, Australia and other 
ccuntries. 

W. B. Hedge, " On the Rates of Interest for the Use of Money in Ancient 
and Modem Times. Part L" Association Magazine, Vol. 6 (1867), 
pp. 301-333. 

H. W. Famam, "Some Eflecta of Falling Prices," Yale Review, August, 
1896. 

F. M, Taylor, "Do wo want an Elastic Currency?" PolUical Science 
Quarterly, March. 1896, pp. 133-157. 

Gives diagram showing the relation of surplus reserves and rates of dis- 
count ; also seasonal variation of rate of discount. 

Carl C. Plehn, " Notes concerning the Rates of Interest In California," 
Publications American Statistical Association, Vol. VI (September 
1899), p. 350. 

R. M. Breckenridge, "Discount Rates in the United Stetes," PolUieal 
Science Quarterly, Vol. XIII (March, 1898), p. 119. 

R. H. Inglia Palgrare, Analysis of the Transactions of the Bank of Eng- 
land (London, 1874). 

Gives rates, 1844-72, and seasonal variation, 18i4.06 and 1867-72. Shows 
dependence of rate on ratio of reserve to liabilities. 

R. H. Inglis Palgrave, Bank Rate and the Money Market in England, 
France, Germany, Holland and Belgium, 1844-1900. New York 
(Dutton), 1903. 

Gives bank and market rates, with special reference to variability in 
England, France, Germany, Holland and Belgium. 

W. Stanley Jevons, Investigations in Currency and Finance (London, 

1884). 

Contains diagram for prices of consols and 3 p<T cent, stock from 17:<1, 
and minimum rate n( interest in London from lN'i4 ; also monthly varia- 
tion in rate of lnt«rt><<t, p. 10. The diagram for the price of consols shows 
that dnring the middle and flrst half of the elitht«enth rentnry the interest 
realized was almost as low as in the present generation. It is InMresting 
to note that this was a period of falling prices. 

Robert Giflen, Essays in Finance, second series (London, 1886), p. 37. 
Seasonal variations of inurest in connection with bank reserves, etc. 



STATISTICAL DATA 



423 



Gives Bank of England rates for 1691-1876. 
George Clare, Money Market Primer, 2d ed, (London, 1905). 

Diagrams for seasonal variations of Interest, bank reserves, etc. 
M. G. MuUhall, Dictionaru of StatUties (London, 1892), pp. 76 607 
^^Ives rates for countrle. of Europe by five and ten year periods since 

William Farr," On the Valuation of Railroads, Telegraphs " etc Joumni 

oftheBoyal Staliuical Society, September, 1876^p 464^0 
R^ of Ducount and Exchange, Banks of England," Franco,' Pruasia. 

Vienna, 1861-1886. Final Report Gold and silver Con.miss onTJ^ 

liamentary Blue Book, 1888, appendix, p. 207. 
Commercial and Financial StatiaUca of British India. fOovemment 

Printing Office, Calcutta.) I government 

Monthly Discount, Bank of Bengal, from 1861. and average quotations of 
government securities held In London. Huoiauons oi 

Tooke, Hittory of Prices, and 

Tooke and Newmarch, History of Prices from 179S to ISfiG 
J. Liegeois, Essai sur Vhistoire et la legislation de Vusure (Paris 18631 
Saugrain (Ga«ton), La baisse du taux de Vintc-et- causes et consequences 
(I'aris, Larose, 1800). <*»««<-« 

Boucher P. B., Histoire de Vusure ches les Egyptiens, hs (frees, les 

Homains, nos au citres et les Chinois (Paris, 1806, 1810). 
Alph. Courtoia, flls, Histoire des Banquet en France (Pari.s. 1881). 

Gives rate of interest at the Bank of France, 1800. 
Vtocomte 0. D'Avenel, Histoire iconomiqne de la propriete, des Salaires 

2i/^p^^l89%^":,.^^.^p.'^8;;^^ 

This work conuins also tables of the purchasing power of money. 
Dietionaire des Finances, Article "Interfit." 
Gives rates at which France has borrowed. 

"'"io' 1';?*'" ■^'" -'^'<'«'«'««'»*<"">««e ^nd Statistik, February, 1806, pp. 

B,?'"? ''v?'' ""* Tl^*^ '•'•■ '"' '^•""''"'' •'"'"• ""'"n. Amsterdam, 
ear" ""* " ''•'*'•'•"'«• ""l"* ^y <i'>cadt^, and 1881-1)6 by 

HanduOrterbufh der Staattwiuenscha/ten, Articles "Banken" and 
"Zlnafuas." 

Gives rates for Bank of PruMila and (Jermany. 1847 80 ; also for Bank 
of Austria, 1878-«); Switserlaad, 188»-88. 

Adolf Soetbeer, MateriaUen sur WUhrungsfl-age (Berlin, 1886), p. 78. 
Cover. IS3i-M f..r 0«i.ki. of England, France and Uennauy and market 
ratei of Hamburg and Vienna. 



1^4 



1- 



424 



THE RATE OF INTEREST 



GfuUv SchmoUer, Orundriu der Allgemeinen VolkatBirttchtifUlehre, 
Leipaic (Dancker und Hamblot), 1004, pp. 20&-208. 

Gives r&um€ of coqtm of interest rates from ancient to modem times. 
Also gives interest rates, London, Paris, Berlin, Amsterdam, Vienna, New 
York, and St. Petersborg. 

BUleter, Oesehichte dtB Zitufuues im Griechiseh-ItdmUchen Altertum bit 
a%^ Justinian (Leipsic, February, 1898). 

" According to the recent researches of Billeter, the normal rate of inter- 
est on good security during the period of greatest prosperity in Athens was 
about 12 per cent. ; while in Bome at the close of the Republic it had fallen 
to between 4 and 6 per cent. Starting in again during the early middle 
ages at a rate of 20 per cent, and 15 per cent., it gradually fell, until in the 
great financial centers of Holland towards the close of the eighteenth cen- 
tury it reached a rate of between 2 per cent, and 3 per cent." — From 
Principles of Economics, by Seligman, N.Y. (Longmans), 1905, p. 401. 

K. Laapeyres, Geschichte der volktuirthtchqftliehen Ansichten der Nieder- 
l&nder, Leipsic, 1863. (Preisschriften der f. Jablunowskischen Gesell- 
schaft, Bd. XI.) [ConUini Zins oder Wucher ; pp. 256 S.] 

Austrian Government, Tabellen tur Wdhrungsfrage (Vienna, 1892), 
pp. 204-206. (Second edition, 1896, and third edition, 1903, 4.) 

Covers rates since 1861 for banks of Italy, England, France, Germany, 
Austria, Belgium, and Holland, and market rates in Vienna since 1869. 

Wllhelm von Lucam, Die Oesterrtichische Nationalhank vodhrerui der 
Dauer des dritten Privilegiunu (Vienna, 1876). 
Gives rates for Bank of Austria, 1817-75. 
Theodor Hertzka, W&hrung und Handel (Vienna, 1876). 

Gives the number of weeks each rate lasted for the Banks of England, 
France, Germany, and Austria during 1844-73. 

G. Winter, "Zur Geschichte des Zinafuases in Mittelalter,'* Zeitsehrifl 
/Br Social und WirtsehajUgeMchichU (Weimar), 1875, IV, 2; 1806, IV, 

161. 
W. J. Streuber, Der Zinfu$$ hei den B&tnern, eine histortsehantiquarische 

Abhandlung (KaHel, 1857). 
J. Kabn, Geschichte des Zinfusaes in Deutsehland seit 1815 und die 

Ursachen seitier V^erdnderung. (Stuttgart, J. A. Cotta, 1893.) 
M. Newmann, Oesehichte des Wuchers in Deutsehland bis sur BegrUn- 

dung der heutigen Zinsgesetze (1664). Halle, 1865. 
Sombart : Der Modems Kapitalismus, I, 219. 

Gives the following table showing the rise iu price of a rent of one mark 
(in rent purchase) in Frankfurt a. M. : In 1304, 14-16 Marks ; i:U4-1315, 
16-17 Marks; 1323-1337, 18 Marks; 1333, 19 Marks; 13S8, 24 Marks. 

Rodbertus, " Ein Verauch, die Hiihe des antiken Zinafuaaea zu erklilren." 

Jahrb. f. Nat. Oek., Bd. XLII (Jena, 1884). 
J. Conrad, Politische Oekonomie, Jena (GuaUv Fiacher), 1906, p. 176. 

Gives rat« of discount 1871-1904 In London, Paria, Berlin, Vienna, and 
St. Petersburg. 






STATISTICAL DATA 425 

A. N. Kiaer, Om seddelbanker (Kriatiania, 1877) 
ha^^iTaS-TO*'""' °' ""•' ''"" " Kri.Uania; Stockholm, and KJoben- 

J. P. Norton, Statistical Studies in the New York \rn«.« tu t . ^r 
Haven (TutUe, Morehouse, and Taylor) "qS " '""*'"' ^""^ 

^"0^"''°°°'^"*'''"°""'°' •'*P'*"' '^°'^»' Government Print- 

%^ 
The following tables of index numbers are appended in 
order that the reader may verify the periods of Sg anS 
falling prices which have been discussed in Chapter XIV and 
SlMr^"^ nl^' "^^^ °^ '^^ '^^^''' °«*^bly those for In. 
r^era *" "°' ^'^ '^'"y ^''''''^^' to °»08t 

INDEX NUMBERS OF PRICES IN SEVEN COUNTRIES! 





Emu LAN II 


Okrmant 


FRAHri 


United 

Stater 


India 


JArAJi 


China 


1824 . . . 

1825 . . . 

1826 . . . 


105 
124 
108 
108 
97 
95 
97 
98 
93 
90 
93 
96 
103 
101 
101 
110 
104 
102 
90 
85 
83 
89 
89 
94 
82 
77 
77 
79 
78« 
95 
102 












• • • • 


1827 . . . 

1828 . . . 

1829 . . . 

1830 . . . 

1831 ... 

1832 . . . 

1833 ,. . 

1834 .. . 

1835 ., . 

1836 . . . 

1837 . . . 

1838 . . . 

1839 . . . 

1840 . . . 

1841 . . . 

1842 . . . 

1843 , . . 

1844 . . . 

1845 . . . 

1846 . . . 

1847 . . . 

1848 . . . 

1849 . . . 
1880 . . . 
1861 .. . 
1852 . . 
1863 . . . 
19*4 . . . 
1886 .. , 












. . . . 






98 ' 

98 

90 

84 

85 

88 

95 

93 

88 

83 

89 

99 

98 
105 
1U5 
109 







.... 


100* " 

102 

114 

121 

124 




1 




. . . . 






• • • » 


. . . ! ! 


. . . . 


101 




. . . . 



426 



THE RATE OF INTEREST 



INDEX NUMBERS OF PRICES IN SEVEN COUNTRIES — CondiMU 









Ekuland 


Obihany 


Fbaicck 


Ukitud 
8tati» 


Irdia 


Japan 


Chuca 


1856 . . . 


101 


123 




112 








1857 . . . 


105 


130 




114 








1858 . . . 


91 


114 




113 








1859 . . . 


94 


116 




103 








1860 . . . 


99 


121 




100 






.... 


1861 . . . 


98 


118 


100 


94 






.... 


1862 . . . 


101 


123 


118 


104 






.... 


1863 . . . 


103 


125 


127 


132 






.... 


1864 . . . 


105 


129 


129 


172 . 






.... 


1865 . . . 


101 


123 


112 


232 






.... 


1866 . . . 


102 


126 


115 


188 




• • > ■ • 


.... 


1867 . . . 


100 


124 


lUO 


166 






.... 


1868 . . . 


99 


122 


95 


174 






.... 


1869 . . . 


98 


123 


97 


152 . 






.... 


1870 . . . 


96 


123 


94 


144 






.... 


1871 . . . 


100 


127 


94 


136 






.... 


1872 . . . 


1()9 


136 


105 


132 








1873 . . . 


111 


138 


103 


129 


100 


104 




1874 . . . 


102 


136 


94 


130 


98 


104 


100 


1875 . . . 


96 


130 


87 


129 


95 


105 


103 


1876 . . . 


95 


128 


85 


123 


99 


102 


111 


1877 . . . 


94 


128 


82 


114 


121 


105 


101 


1878 . . . 


87 


121 


78 


105 


125 


114 


106 


1879 . . . 


83 


117 


76 


95 


119 


145 


111 


1880 . . . 


88 


122 


79 


105 


112 


160 


105 


1881 . . . 


85 


121 


76 


108 


99 


175 


110 


1882 . . . 


84 


122 


73 


109 


98 


159 


108 


1883 . . . 


82 


122 


73 


107 


96 


130 


103 


1884 . . . 


76 


114 


72 


103 


97 


116 


104 


1885 . . . 


72 


109 


70 


93 


95 


116 


105 


1886 . . . 


69 


104 


60 


93 


99 


107 


107 


1887 . . . 


68 


102 


71 


94 


101 


109 


105 


1888 . . . 


70 


102 


74 


96 


104 


112 


100 


1889 . . . 


72 


106 


80 


98 


107 


116 


105 


1890 . . 


72 


108 


83 


94 


103 


124 


104 


1891 . . . 


72 


109^ 


79 


94 


104 


123 


104 


1892 . . . 


68 


106 




89 


115 


124 


108 


1893 . . . 


68 


102 




89 


119 


129 


109 


1894 . . . 


63 


92 




81 


. . . 


132 




1895 . . . 


62 


91 




79 








145 








1896 . . . 


61 


91 




76 








133 


, , 






1897 . . . 


62 


92 




76 








173 


^ 






1898 . . . 


64 


93 




78 








159 


, , 






1899 . . . 


68 


111 




86 








175 


. . 






1900 . . . 


76 


110 




92 








165 


. . 






1901 , . . 


70 


103 




91 








160 


, , 






1902 . . . 


69 


99 




96 








165 


, 






1903 . . . 


69 


104 




96 










, , 






1904 . . . 


70 


104 




95 










^ , 






:905 . . . 


72 


107 




98 










, , 






1906 . . , 


77 

1 


i 


i 


103 






_'_ 


i 




_ 


_ 



STATISTICAL DATA 



427 

inclusive, and are taken from his^. inZi ! "^ ''°'" ^^-* *" '852 
n«.ce." Inorfer to m.iTS.e ubiel of i *" °"' I" '''^"*"°y »»'» *•*" 
ou.. Jevons's number for 18^2 ^^^2 ^sX^f'^'r' ""'*""" 
year) instead of 65, as given in th« • 7n„ V ' *'''""«>«<=k's for that 

numben.a.,r.i,edi;" Soof 8 to 65 Sf^i^^^^^^ "^^ "'*' '''''' 

commodities ; Sauerbeck's arB for forty five " ^^^ "" ^°' '""^ 

in the Aidrich "^t (T.'ST) flZlorSr^mlT-^' "''' «'^^" 
Conrad, as given in his ^«Ari«cAer 18M- S b^^r ,7"'"' '""" 
the ratio of 109 to 98 in order to mavl Ih. , *'* *" ""agn'fled in 

figure for 1891 is SJ^d Conri^ 2 T " 7"""°"^' ^'"'^^ »^'-'« 
Heinz cover 114 commoSues ' ' *'*"''"'^ °^ «"«'''««^ a«d 

-nie French numbers are from the Aidrich renort n ^«^ , ^ . 
.ttSrrtir ^ C;o«.™...„,.^„„,,, ,^, X:i^. -^Houmled^n 

ployed. -Siy L've l^^n SntZS aLrlsThv '"' "?°«'^ *"'"« «- 
Bulletin of the United Sta^s De^t™!.^! Tr I ""°^ ^^"^ ^'^^ «* ^^^ 
n.e flgu«s of this Crt^tJe a Kr^dldtn a% "^ '^• 

bring the initial flgurTfor 1891 intTcJirdd^nce l^'tt T '" ,"""" "" 
year, of the Aidrich report 94 «'"'"«ience with the figure, for that 

nomic Magazine Publishing Company '^ *^' ^"•'y° ^«=*^ 






■'■m^ 



¥ 

s 



iiit 



r 



INDEX 



Abstinence theory of interest, 43- 
61 ; crude form of agio theory 
contained in, 54. 
Accommodation paper, 244. 
Aceumtilation of wealth, process and 
causes of, 231-236, 290; cycles 
of, and distribution, 233. 
Agio theory of interest, 43, 340-341 ; 
Bohm-Bawerk's theory called, 
63 {tee Bdhm-Bawerk) ; early 
forms of, in abstinence theories, 
and in Rae's, Jevons's, Sax's, 
and Launhardt's works, 54; 
author's version of, 87-88. 
Agriculture, annual cycle in income- 
stream in connection with, 
314, 384-386. See Farming. 
"Aldrich Report" cited, 274, 319 n.> 

*27. 

America, increasing income-streams 

exemplified in, 304-306; cycle 

of income-stream fluctuations 

and rates of interest in, 316. 

iSee United States. 

Andrews, Benjamin, quoted, 286 n.'. 

Annuities and the waiting theory of 

interest, 46-48. 
Appreciation, influence of m^ letary, 
on rate of interest, 78 ff., 358 ff. ; 
relation between rate of, M>d 
rate of interest illustrated, oO- 
81 ; of monetary standard, con- 
cept of, 257 ff. ; of gold during 
period of paper inflation, 259- 
265; theory of, applied to 
periods of rising and falling 
prices, 270-286 ; rates of interest 
and, in London, Berlin, Paris, 
and New York, 272-276; in 
India, Japan, and China, 276; 
of gold as compared with silver 
as shown by rates of int< rest on 
Indian ioaiis, 206-270; uistory 
of theory of, and interest, 356- 
368. 

429 



Aristocracy, rise of an, trac-d, 
232. 

Aristotle, ground of opposition of, 
to interest-taking, 4, 22. 

Australia, loans and rates of interest 
in, 309-310. 

Average production period postu- 
lated by Bdhm-Bawerk, 65; 
discussion of, 56-58. 

B 

Bacon, N. T., cited, 294. 

Bagehot, Walter, cited, 304, 333. 

Baldwin, cited, 333. 

Bank of England, the, 240. 

Bank loans, imperfect foresight 
and, 286 n.'. 

Bank reserves and rate of interest, 
322-324. 

Banks, function of, 262-253. 

Basis of security, 210-211, 337. 

Baxter, Robert, quoted, 280-281. 

Bayley, R. A., cited, 421. 

Berlin, rates of interest in, relative 
to rising and falling prices, 273, 
319, 418-421. 

Betterments, repairs which may bo 
called, 188. 190. 

Billeter, cited, 424. 

Bimetallists, 287. 

Bland Act of 1878, 269. 

Bloch, cited, 292. 

Bdhm-Bawerk, Eugen von, 4 n.', ', 
12, 16, 38, 39; on "indirect 
productivity theories," 13 n. ; 
quoted on exploitation theory 
of interest, 40; on abstinence 
or waiting theory of interest, 43- 
46,49; deservedly high esteem 
for work of, 63 ; at one point de- 
fect ive, 53; consideration of 
theory of, 63-74; summary 
of theory of, 64-66; quoted 
on importance of his " tech- 
nical" theory, 73; author's 
tribute to, 74; theory of, mar- 



430 



INDEX 




P.-- t 







ginal rate of return on sacrifice 
and, 163 tl. ; on consumption 
loana, 241 ; mathematical 
refutation of theory of, 351- 
355 ; cited, 45 n., 84, 88, 92 n., 
93, 98, 103, 383, 384. 

"Bohm-Bawerk on Rae," Mixter'g, 
54 n.'. 

Bondholders, 125 ; freedom of, from 
element of risk, 215-216, 245, 
256 ; and war loans, 239 ; position 
of. as typical creditors, 288. 

Bonds, explicit and implicit rates of 
interest on, 10; selling value 
dependent on expected income, 
15; risk element and the price 
of, 216 ; issue of, for war loans, 
239; for public improvements, 
240 ; mortgage, of corporations, 
245 ; explicit and implicit inter- 
est of income, 255 ; golil, vs. 
currency or coin bonds, 259-261 ; 
rupee, 266. 

Bond tables, 10, 260. 

Borrowing, on part of United States, 
305. 

Borrowing and len<ling, in form a 
transfer of capital, in fact a 
transfer of income, 113; equali- 
zation of preference rates by, 
117-118, 231; modification of 
income-stream by, 120-125; ef- 
fect on capital of modification of 
income-stream by, 231 ft. ; 
theory of, exemplified by issue 
of bonds for public improve- 
ments, 240; influence of un- 
equal foresifjht on, 285-287; 
high rate of interest sometimes 
neutralized by, 289-290. See 
Loans. 

Bortkiewicz, L. von, cited, 58, 68; 
criticism of Bohm-Bawerk 's the- 
ory by, 72. 

Boston, Franklin fund in, 238. 

Boucher; P. B., cited, 297, 423. 

Breckenridge. R. M., cited, 422. 

Brough, William, quoted, 275 n.». 

Brown, Mary \V., cite<l, 298 n.». 

Bullock, C. J., citml, 88. 

Busine>!s loans, 236, 240 ff. ; con- 
traste<l with con.sumption loans, 
246-250. 

Buying and selling, modification of 
income-stream bv, 125-127, 145, 
174-175, 176, 231; elTt-cl on 
capital of modification of in- 
come-stream by, 231 ff. 



Calcutta, rates of interest in, in rela 
tion to price-movements, 276 
319; yearly average rates o 
interest in, 418-421. 

California, income-stream of, anc 
rate of interest, 307. 

Call loans, 211, 244, 275, 357 n.'. 

Calvin, right and wrong interest 
taking according to, 5. 

Canals as subject of investment 
196-197. 

Cannan, Edwin, cited, 230, 231. 

Capital, interest viewed as repre- 
senting productivity of, 3 (»«« 
Productivity theory, etc.) ; rela- 
tion between income and, 14-15 
229; income produces, not viet 
versa, 15 ; how productivity of, 
affects rate of interest, 28; 
waiting forms an increase of, 45 
rate of interest not dependent 
on, but on income, 109-113; 
modifying income-sticani by 
changing use of, 137 ff. ; rate of 
interest is the ratio between 
income and, 216 n. ; effect on, 
of modification of income-stream 
by borrowing and lending or 
bu>'ing and selling, 231 ff. ; 
acc'unulation of, 290; dissipa- 
tion of, 290; definition of, 
337. 

Capitalistic method of production, 
191-193, 337; and the rate of 
interest, 196-197. 

Capitalists, socialists' view of, as 
robbers of laborers, 38—40 ; how 
laborers might become, 41 ; not 
robbers, but labor-brokers, 41- 
42 ; entrepreneurs, landlordn, 
and laborers as, 230; pr<K'et(.s 
of rise of, trace<l, 231-235. 

"Capital seeking investment," the 
phrase, 126. 

Capital-value, effect of income-value 
on, 13; is discounted income, 
110; determination of, through 
rate of interest, 229. 
Capital-wealth, production of future 
income-services by present, 
14. 
Carver, T. N., cited, 124 n., 126 n., 

159, 181, 184, 214, 357 n.'. 
Casscl, cited, 196. 

Caution, coefficient of, defined, 337, 
338. 



INDEX 



431 



Chance, options of, 178; element of, 
and ita effect on rate of interest 
207 ff. ; defined, 337-338. 
Chattel mortgages, 300. 
China, rates of interest and appre- 
ciation for, 276 ; effec. of charac- 
teristic qualities on rate of 
interest in, 292; small income- 
stream and high rate of interest 
wi, 300; index numbers of 
prices in, 425-426. See Shann- 
hai. ^ 

•Choice, among optioral uses of capi- 
tal, 137 ff. ; will fall on income- 
s»» which has maximum 

...■ luh.i 139, 152, 389^ 397. 
two i.'. .;- of, of income, 145; 
'•>;;• ; for individual by 
' •? f ii;.' tit, but for society 
I • ;; >ieni t • of interest is in- 
.. f.ho...l 1 ^ 146-149; three 
.■<(n! •I^-n,- 01 condition deter- 
' . iir : Hween options, 156; 
". ' t o. nge of, on rate of 
: '' isf, 'j8-175; practical ef- 
!<■ ! ': -ange of, 175-177, 329- 



Corporations, mortgage bonds of, 245. 
»^o«t, interest viewed as representing 

Cost-of-production theory of value, 

Cost theory of interest, rate of in- 
terest sought in ratio between 
income from capital and cost of 
that capital, 29; labor cost, 
33 n. ; abstinence or waiting 
theory, 43-51; summary of 
conclusions regarding, 51-62 

Courtois, Alp., fiU, cited, 423. 

Credit cycles, 285. 

Creditor, position of bondholder as 
the typical, 288. 

Crop liens, 242-243, 253-254, 315. 

Crump, Arthur, cited, 423. 

Currency, depreciation of, and rat« 
of interest, 259. 

Currency bonds, 259-261. 

Cycles of accumulation and distribu- 
tion of wealth, 233. 



D 



^ Int.", m< itgages on, 245. 
' Whr , ..per money and rate of 
interest during, 259. 280. 
Clare, George, cited, 324, 423 
Clark, J. B., cited, 189, 357, 359. 
Clearing-house certificates, 325 
Clothing, effect of rate of interest on 

price of, 226. 
Coefficient of caution, 337, 338. 
Coefficient of probability, 338. ' 
Coefficient of risk, 338, 342. 
Coin bonds, 259-261. 
Colorado, interest rates of early 307 
Commercial paper, 243. 
Commodities, definition of, 338. 
Commodity interest, 277-280. 
Commutation, rate of, and rate of 

interest, 216 n. 
Composition ' incor stream in- 
oa^^^ ' "^ ti. -rreference, 

Conant, Charies A. cited, 3a3 

(onrad, J., cited, 42';, 427 

Consumption loans, 8o-callc<l, jw 
opposed to "productive loans," 
24^248' ^''""'P'''*''*""" °f. 

Contmuous reckoning of interest, 82, 

Contractual intercbt. See ExpUcit 
mterest. 



Day, Clive, cited, 232, 292 n > 
D'.\venel, Viscomte G., cited, 423. 
IJebent ires of corporations, 245. 
Debtor, position of stockholder as 

the typical, 288. 
De Haas, 270 n.>. 
Delay, interest-taking justified by, 

by metlia'val wTiters, 5, 54. 
Del Mar, Alexander, theorv of in- 
terest of, 22 ; marginal" rate of 
return on sacrifice and ■ heory of, 
ICl-163; theory of, that Na- 
ture should be reproductive, 
does not hold, 186. 
Depreciation, influence of monetary, 
on rate of interest, 78 ff. ; rela- 
tion between rate of, and rate of 
interest, illustrated. 80-81 ; of 
monetary standard, concept of. 
257 ff. ^ ' 

Depression, periods of, due to in- 
e<iuality of foresight, 285-287. 
Desirability, concept of, 88, 338. 
Di.scount curve, defined, .3,{8. 
I)i.scov,.ries, effect of, on rate of 

interest, 203-204. 
Disservice, definition of, 338. 
Dissipation of capital. 290. 
DistribuUon of wealth, application 
of rate of in'orest to theory of, 
229 ff. ; wha. la meant bv the 
phrase, 2.30; classical theory of, 



432 



INDEX 



W 



abandoned, 230; eauaes of in- 
equality of, 231-23S ; effect of 
habit on. 232-234; cyclea of 
accural; 'tion and, 233. 

Doney, cited, 291. 

Douglass, William, quoted, 356. 

rhirability of instrumenU, and the 
rate of interest, 1S7-188, 196, 
290; changes in regard to, in 
Amenca, 305-306. 

Dwellings, effect of rate of interest 
on price of, 225-22«. 



E 



Electricity, enlargement of range of 

choice by discovery of, 201. 
ElUott, E. B., statistics by, 283 n., 

419 n. . 

England, tendency in, of distribu- 
tion of wealth to remain un- 
changed, 234; effect of indi- 
vidual characterintics on rate of 
interest in, 291 ; expenditure on 
railways in, 291 ; loans of, in 
China, and effect on rate of 
interest, 293; postal savings 
banks in, 298; income-»treara 
and rates of interest in, 300, 310 ; 
cycle of income-stream changes 
and rates of interest in, 316; 
index numbers of prices in, 425- 
426. See London. 
Entrepreneurs, and cost theory of 
interest, 42-43; power exerted 
by, on character of income- 
stream of society, 194-196; as 
capitalists, 230. 
Europe, infre<juency in, of changes 
in distribution of wealth as com- 
pared with Unit'Hl 8t«ies, 234. 
Exchange, definition of, 330. 
Exchange brokerage firms, if 3. 
ExpecUtion, rate of interest is base<l 

on, 213. 
Expectation of life, effect of, on tune- 
preference, 105-106. 
Explicit interest (contractual in- 
terest), defineil, 6-«, 340; effect 
of risk on hnplirit and, 211; 
shown to differ from implicit, in 
degree rather than in kind, 256. 
Explioil rate of interest. See under 

hitertftl, rate of. 
Exploitsliim, period of, relative to 

invenlionB. 203-204. 
Exploitation theory of intcrent, 3M-40. 

Extraction, rale of, in mining, 1H6. 



F 



Falkner, cited, 427. 
Farmers, fluctuations in income- 
stream of, 315. 
Farming, intensive, degree of, de- 
termined by rate of interest, 167, 
161. 
Fanna, mortgages on, 244-245, 308- 

309, 361-362, 363. 
Famam, H. W., cited, 422. 
Farr, William, cited, 423. 
FaBhl3n, force of, 333. 
Fecundity of plants and animaU, 
interest viewed as representing, 
3, 22-23; examination of the 
theory, 23-27. See George, 
Henry. 
Feilbogen, translation by, of Bohm- 
liawerk's Recent Literature on 
Intereet, 3 n. 
Fetter, F. A., criticism by, of Dohm- 
Bawerk's concept, 58; quoted 
on Bohm-Bawerk's theory, 73; 
cited, 88, 128, 184, 194. 
Fines as a subterfuge for interest- 
taking, 5, 54. 
Fisher, Irving, The Nature of Capital 
and Income by, cited, '.0, 11, 12, 
17, 20, 26, 26, 30, 39 n.», 40, 46, 
51, 77, 82 n.', 83, 88, 90, 91, 9<i, 
127. 138, 141, 142 n.«, 141, 154, 
168, 189, 216, 217, 225. 226, 231 
241, 202, 348, 404: articles by 
cited, 85, 131, 184, 276, 332, 367 
389, 416. 
Flow, defined, 339. 
Food, price of, not sensibly affectet 
by rate of interest, 226; eff*-*' 
of scarcitv or abundance, oi 
rate of interest, 301-3O2. 
Foreitight, effect of, on rate of time 
preference, 103 fl. ; as appUed I 
falling and rising prices, 267 
268, 284 ; periods of speculatioi 
ad depression due to inequal 
ity of, 28.'S-287 ; effect of, on rat 
of intert-st, 291 ff.. 3.14; effer 
of presence or lack of, in variou 
nations and races, 291-294 
partly natural and i>artl.. a< 
quiretl, 207-299 
Forestry policy, Europ«'an and Ame 

lean, 27. 
France, effect of foresight, self roi 
trill, and regard for jMwtrrity c 
rate of interest in, 2tU ; eff'- 
of iiic oiiie-stream on rate 



:jrm~f: 



INDEX 



433 



interest in, 300 ; index numben 
of prices in, 425-426. <Se« Paris. 

Franklin funds, 238. 

Fund, deBnition of, 339. 

Furniture, effect of rate of interest 
on price of, 226. 



Oeorge, Henry, tlieory of interest of, 
22-23; marginal rate of return 
on sacrifice and theory of, 161- 
163; tlieory of, that Nature 
aiiould be reproductire, does not 
hold, 186. 

Oermany, maintenance of rate of 
interest in, 313-314; index 
numbers of (Hices in, 425-426. 
5se Berlin. 

Oibbs, H. H., 271. 

Qiffen, Robert, 271 ; cited, 310, 311, 
422. 

Oold, appreciation and depreciation 
of, 258-261, 335; rate of in- 
terest on, compared with rate 
on silver, 285-270. 

Oonner, E. C. K., cited, 235. 

Ooodbody, Robert, cited, 301, 357. 

Ootha Mutual Insurance Company, 
rates of interest made by, 313- 
814. 

Orasiani, cited, 358. 

Greenback BUI, 264. 

Oraenbaeks. Sss Paper moaey. 

Qrewie, Darid I., 357 n.*. 



Hmm, Jaeob de, cited, 367. 

Habit, effect of, on rate of time- 
preference, 105; effect of, in 
distributLin of wealth, 232-234. 

Hadley, A. T., cited, 216. 

Uara, lehi, compilation by, 41B n., 
427. 

Hedge, W. B., cited, 422. 

Uaiai, aUtiaties by, 319 n.>. 427. 

Heredity, error ia laying stress on 
importanee of, as compared with 
environment, 208. 

Hertska, Theodor, cited, 424. 

Highways, American, 306-306. 

Hitomi, compilation by, 419 n., 427. 

Holland, qualities of foresight, M>ir- 
rontroi, and regnnl for posterity, 
and the rate of intcrnit in. y.H . 
pffect of Inromp-ntrpain <>n rnir 
of interest in, 300. 
3 V 



Holmes, George K., on productive 
and consumption indphtednpfts 
in United States, 240-241 ; 
cited relative to mortgage nta- 
tistics, 244 ; cited in relation to 
statistics of negro and Russian, 
294. 

Holt, n.vron W., editor of The Gold 
Supply and Prosperity, 288, 
358 n.'; cited, 301, 33.% 357. 

Horace, philosophy of, 100. 

Homrr, method of obtaining averaRo 
rate of interest, 262 n.», 372. 

House, prire of a, the discountnl 
value of it» future inoonip, ((1. 

Howell, Price, cited, 201. 

Hume, David, 8. 

Huribert, H. B., quoted, 302-303. 



Implicit interest (natural interest), 
defined, 6, 340 ; effect of risk on 
explicit and, 211 ; differs in 
degree rather than in kind from 
explicit interest, 255. 

Improvements, and the rate of in- 
terest, 190-191, 195-106; loans 
for public, 240; railroa<l, 245. 

Improvidence, loatu to offset, 230, 
237, 246-248. 

Impure rate of interest, 212-213, 
218-219. 

Income, relation of, to capital, 14- 
16; produces capital, not capital 
income, 15; waiting is not, 4.'>- 
48; time-preference the prefer- 
ence for early over late, 89 ff. ; 
definition of, 90-91, 339-340 ; di>- 
pendence of time-preference for 
each individual on his, 109; rate 
of time-preference and conse- 
quently rate of interest depenil- 
ent OD, 100 ff. ; relation be- 
tween time-preference and, repre- 
sented by iiche<Iule, ll.l-llS; 
Immediate and reniote, consti- 
tutes difference between spend- 
ing and investing, 125-126; 
enjoyable following on inter- 
mediate, 141 ; net, is difference 
between total gross income nnd 
outgo, elements of both of wliirti 
are dependent on rate of in- 
terest, IfW ff . 241 . 3.TO ; effect of 
invention anil discovery cm. \',>H- 
2tl« ; rstc iif interest i-itlii' ratio 
between capital and, 2\iS n. , 



434 



INDEX 



- • t^5S 



u fi 



loans made to ofTaet fluctuations 
in, 236, 237-238; public loans 
to offset fluctuations in, of 
govemmento, 239-240. 
Innome-concept, 88. 
Income-services, production of fu- 
ture, by present capital-wealth, 
14. 
Income-stream (or Income), defini- 
tion of, 90-91, 339, 340; de- 
pendence of time-preference on 
future, 92; elements which 
constitute, 93-94; modification 
of, by borrowing and lending, 
120-12S, 231 ; graphic repre- 
senUtion of, by curves, 121- 
124; modifying by method of 
sale, 125-127, 146, 174, 176, 231 ; 
modifying by changing the use 
to which capital is put, 137 (I.; 
the total final, 141 ; capitalistic 
method of production requires 
an ascemling, 191-193; effect 
on, of invention, 198 ff. ; regu- 
lation of, by loans, 236 ff. ; loans 
for rpgulntiiig fluctuations in 
privatp, 237; in public, 238- 
240; effect on rate of interest 
of character of (sise, «hape, 
composition, and probabiUty), 
209 ff. 
Income-streams, option among, and 
choip«%f onehaving maximumdc- 
sirability, 1.3» ff., 389, 397 ; choice 
among <liff«rpnt optional, shown 
to di'i>ciid on rate of interest, 145- 
149; priirtiral effect of existence 
of large number of, on rate of 
interest, »» lialance wheel, 175- 
177; differint canes of optionai, 
178 ff. ; rate of interest high with 
increasing, low with decreasing, 
.HM-30« 
Income-value. effjTt of, on capital- 
value, 13. 
India, rates of interest on loans of, 
in gold and in Kilver. 266-270. 
rates of interest and appreciation 
for. .'7(1. effert of lack of fore- 
sight anil negligence on rate of 
intercut in, 'Jil- low incom«'- 
strentn ami logli rale of interest 
in. 3(M»; InMeK lUiinlxTs of 
price- III, 4'I'> <2'> 
Indians, etTwt of i Imrm ti m-.Uih of, 

on ml. ..f irlcre«» -•'IJ, Mi 
Imlirci I |,i.«lii.tiMiv •!i"mi- lit n 
lu>liir«>'ineiit. rink redin<<l l.\ 'JIS 



Industrials, mortgages on, 24S. 
Inequalities of distribution of wealth, 

causes of, 231-235. 
Inostranieta, cited, 292. 
Instrument, definition of, 340. 
Instruments, CAdrability of, 290. 
Insurance, effect of, on value of 

capital subject to risks, 217. 
Insurance company investments, 308- 
309, 313 ; references for, 421-422. 
Intensive farming, degree of, de- 
pendent on rate of interest, 156- 
157, 161. 
Interactions (intermediate services), 
30, 90, 141, 168, 340: not the 
cause but the result oC value, 
39 n.'; value of, derived from 
succeeding future services, 91-92, 
226 ; how rate of interest affects, 
226-227 ; real object of buniness 
operations obscured by, '24\. 
Interest: definition of, 3, 340; vari- 
ous theories of, 3-4 ; early his- 
tory of practice of taking, 4-6; 
explicit and implicit, denned, 
5-6, 236, 340 ; expl= " dejien.l- 
ent upon iinplic f|Uestion 

of what determine ..iplicit, 0; 
processes of nature an<l, 22-28; 
theories of, based on cost, 29 ff.; 
labor-saving theory of, 35-36; 
socialists' view of, as extortion, 
38-39, 41, 52; abstinence or 
waiting theory of, 43-51 ; agio 
theory, 43 ; Ii<>hm-Itawerk's agio 
theory of, 51 ff. ; B6hm-Ha- 
werk's theory of, discussed, 53- 
74; relation between apprecia- 
tion or depreciation and, 77 ff. ; 
distinction l)etween interest in 
terms of money anil interest 
in terms of gooiU, 84 ; futilif v of 
laws against, I27-I2K; existence 
of. because of "nlowness of 
Nature," 185-186; cliowii to 
\>o, not a part, but the whole, of 
income, 229; rent, profits, and 
wages iiieludml in, aW-i-W; 
llieorv of, OH applied to lojiiu, 
•J.1«l ff application of theory to 
rroji liens, 242-243; roiiiniereiiil 
l>»l»-r, 243, ttccomniiMlalion pa- 
per, 244 ; explicit and implicit. 
differ III ilegr<-<- rather than in 
kind. 2,5.5. miIohI. 277-2HU; 
commoility. 277 -2811 , historv of 
llienrv of apprermtion niul, .'l">li 
•!.-,H. 



t 




INDEX 



^A "^^ "'" ^^^ °f- « an 
index m a given coramunitv of 
preference for a dollar of preient 
over a dollar of future iS^"e 

t:^J.' ..'"PP'y and demand" 
explanation of, 6-7; "use of 
money" explanation of, 7-9' 

m circulation governg, 8; cm- 

tion between impliciv and ex- 
Pcit, louu; exwtence of ira- 
pUcit ,n bonda, notes, land, etc 

l^rfl .i'^'T"*"'* °f '^''alth, 
^m the value of .very capital: 
K«M. I»-ll ; cannot bo deduced 
from ratio of income from capital 
to value of that capital, 14-15 
utility of raisins, by' raising 
pr.Hluctivity of capital, \a-Ui- 
•e «ame objectioim apply in 
the uw" theories, lo" fT 
20""' *'':"'-B''''« «l'">rip, ahoui.' 
f" -*•■ "Pwed a* consimting in 
the average rate of gr,„vtl? of 
animala and plants. 23; conclu- 
"l""" ''"ncerning pr.Kluctivitv 
tLooryand. 28; how prmluctiv:. 
>ty <.f capital doe« affect 28 
cost theory of, define) 2fl 
viewe^l a.s„ wage for the labor 
of producng capital (exploita- 
t.onfh..,ry), ,38-40: relation be- 

i^wP' .""'' """"■'»'■>■ "»:indar,l 
in which it m oxpresxcl. 77 ff . 
relation iwtween rate of gnnre-' 
ciation or depnviation and, 
.llu,tr«,e.l. 80-81 ; the numbe; 
expre«.ng depend, „n stand- 
ard of value in which pre«.nt| 
an.l future good, arc expressed. 

ard .„ which ,.x,ir.^„.d, 84 no I 
alwolute standard of vaj,,,. f,,, i 
r..k„ni„g. 84-8«; determining 
I"'. 87 ff. ; l««,H „f, „„ ,i„ . 
I>ref..renc.., 88 („, Tinie.,,refer- 
J-n--) ; ronsideration of relation 
H-t wej.„ rates of prcferenc, an. I ' 
"' n ; four conditions win, =, i 
•letcrmin... I32-1;M; ch„i...i 
•""""« optional income-»freams i 
K"v..rn,.l 1„ ir., change in. 
result, ,n ,h«„gc „r Hioice of ' 
income-streamn, 14(1 ifw ff i 
(letcrm.nes choice „f ,ndivi.l„a| j 
among optional iiiconie-Mrcani^ 
but for .ociety a» !»rge i* innu- 



435 



I4«-149; s-x conditions whi^ 
rfetermino, l.SO; choice of option 
whose marginal rate of return on 
sacrifice im e(|ual to, 1.58 159- 
effect on, of range of choice be-' 
tween options, 1(>8-17.5 effect 
of, OD *af<fs of lal>or, 1«9-170 
change in. will affect all income-' 
streams (lowing from (;i,.pn 
instruments of capital 1 71 • 
practical effect on. of range of 
choice, 175-177; effect of. on 
"peculation, 17i»-180; arising 
from "slowness of Nature,'- 
1«S; waterworks, .anals, im- 
ga ion system... improvement of 
railways etc., h„,|, njo^igy. 
effiH-t of invention on, I9S (T • 
tcmiH.rary nature of effect of 
invention on. 203-204 ,.|e 

anT'oTir "'"■••[•""">■ "' income 
in.1, 207 ff. ; base,l „„ exiwta- 

tioM, 213; and rate of commuta- 

on, 2IBn.; r6le plaved In . in 

tlie theory of prices. 225 ff • 

influence on, of change., in the 

monetary stan.lard. 257-288 

•«•> ff.; tables showing com-' 

parative rates renli.ed on g„|d 

and currencv bonds. 20O 262- 

comparison of rates on gold and 

on silver. 20.5-270 ; jn-riocls of 

270-2^5; relativ,.|y high when 
prices are ri.sing, |„w when fall- 
jog. 277 : loans as an offset to 
hiRh, 289-290; manner in «' ,1, 
nature of the individual indu- 
I "'?;■ 2',''>-^«": effect of fore, 

sight, s.'lfH.„ntrol, and regard for 
■ P"H»<;rit.v on, 2t.I ff. ; eff,,^, „„ 

"f .Imriuter .,f income-stream' 
(■■<i«', HhaiH-, r.mijwsition, and 
probability ^ 299 ff. ; inductive 
rcf_iitati«n of m-.ney theorv of 

;"*:•'-,"' •'*'''^- "'■ '" '■elation 
♦'• high and low prircM 319- 
'l>mntily of n,..„,.v and, .Xt)-' 
•'--; bank refers.., ,„,,), .S22- 
•«.^; definitio,, „f i„ ,,„,i,„,., 
«-nse-. MO -341 : formula con- 
necting rv,.M ,n two .liverging 
utandar.N, ;j.58 Wo ve,.rlv aver- 
age rates in London, Merlin 
lati'., etc . 41«~»21 
""Tfflt fHk.„p. ..Hrly laws ,Md nr.<... 
lice, nncermng. 4-fl , not' pre- 



436 



INDEX 



1 



a. 




rented by prohibitinc lo*" 0°' 
tracts, 127. 
Intermediate ■ervioee. Sae Inter- 
actions. 
Invention, economic effect of, 198 ff. ; 
temporary nature of effect of, 
on rate of interest, 203-204; 
the ba*i of progress in civiliia- 
tion, 208; conditions for most 
rapid multiplication of, 205- 
206 ; speculation following, 212- 
213 ; effect of, on time-shape of 
income-streamn, 313; progress 
of, and its bearing on rate of in- 
terest, 3:14. 

Inventors, tribute to, 206. 

Investing, defined as purchase of 
right to remote enjoyable in- 
come, 125-126, 341. 

Investment, peritnl of, in connection 
with inventionn, 2()3-2(H ; effect 
of risk on rate nf interest in 
casex of unsafe. 212-213; in 
cases of safe, 21.3-215. 

Investments of iimuranof companies, 
308-309. 313-314, 421-422. 

Irelanil. small inrome-slream and 
high rate of iiiterist in, 300-301 . 

Irrigation works, as Mubjert of in- 
vitttnient, 1U7. 



.lurncwiii, iimiular rc|>ort of. 427. 

Japan, rate* of interest and apprecia- 
tion for, 27(! ; jH-ace loan for. 
313; yi-arly avi-rage rates of 
inlcrcMt in. 41H-430; index 
uumlH"r« of priri"* in, 425—426. 

Java, debt wrvilude in. 2.32; rate of 
interci<t in, as affe«'ttil by lack 
of f(>r»"mglit anil neKligence, 292. 

Jevons, W. HtHnli-v, agio theory in 
work of, 54. 74 ; liiihin-Hawerk 
on, 73; rit«l. .'.VJ, ■«»l-.-»02, 330, 
432. 427 ; I)p llBas' rritirium of, 
270 n' . tablw of, 277. 3H» n.' . 
i|Uot('(l, 281. 

Jews, iiit<'ri>)it-takinB l»rtween. for- 
liidili-ii liv MoMuir laws. 4 ; rfTert 
of rliiiraclenslir i|imlities on 
rate of iiiti-rent among, 21M ; 
low |irrfiTi-iirf rate uiitonK. 21)5 : 
iiiitural and tratlitioiial tendi'ii- 
cieit of, jniX. 

JolmMoii. Jo-«'|!li K . ciletl, 358. 

Jones, Si-nalor, :i!i7 11 '. 

Jufia', nted. 28© n.' 



Kabn, J., cited, 4M. 
KeUogg. Dr- ^ H., 2M n.>. 
KeUoK, Mrs. J. H., 298 n.>. 
Kemmerer, E. W., cited, 301. 
Kiaer, A. N., cited, 425. 
Kinley. David, cited, 239, 
Klondike, high intereat rata* in the, 

307. 
Korea, effect of risk-alement on rate 

of interest in, 302-303. 



Labor, cost of, an important ele- 
ment in inoom»-«eeounts, 169- 
170 ; bearing of, on choice be- 
tween uses of capital affording 
immediate and those affordiiii; 
remote returns, 193-195; wagon 
of, as affected by rate of intercNt, 
228-229; defined as outgo in 
tlie form of human exertion, 
341. 
Labor cost, in cost theories of in- 
terest, Xi n. 
Laborers, rate of interest and wagcK 
of, 169-170, 228 ; may be siiinll 
capitalists, 230. 
Labor-saving theory of interest, S.'i- 

36 
Land, as an instrument of wcallli, 
implies a rate of interest, U; 
in Tiirgol'!" explanation of im- 
plicit interest. 11-12; view of. 
as source of all human reviun'. 
12; degree of intensivene«»< i>f 
cultivation of, governed by rat^- 
of interest, 157. 101 ; speculate >i, 
in, and effect of rate of intcn-t 
on, 180 ; effect of rate of inlcn ~! 
on price of. 225; mortgHges .■n. 
244-245, .■J0«-30»; define.1 u« 
wealth which w part of il ■• 
earth's mirfare, .'Mt. 
l^uidlords as capitalistx, 2.30. 
I^nd in.rt>tgage«. 244-245. .«« .to'i. 
3<V1 ; reference for informntH.ii 
on. 421. 
Landrv. Adolphc, cost theorv "f 
intirsst of, 37 .HH, 161 ; criticism 
of Holun-Hawt-rk's theory liy, 
72; cited. H4, 1(2 n , 15fl, ISl 
Lanin, K H . <ite<l. 292. 
I,a«i|ieyn'i, K., cited, 424. 
Ijkunhanlt. agio theory in work <!'. 
54, 74; Itolim-Hawerk on vu^^■^ 
of, 7» 



INDEX 



I*w of decrewing retumg for luldi 
tioniJ sacrifice, 33, 157 

Le Bon, cited, 333 

Lending li^iuti„„ „f, rf„e e„ H^k. 

l»n^ i"" Borrowing and 

lending and I.oana 
Levy, B. K. O., cited, 322 
L-exin, citeil, 58. 
I'iegeoia, J., cited, 423 
Life, expectation of, and t™^ 
preference. IO6-167. *'""^ 

tjfe insurance, 1 08 
Life insurance companies, Western 
in vestment, of, 308-3;)9 "* 

ixjans (loan contracts), a means nf 
equalising rate of' timt^^'fer! 
enre and rate of in.eres.Ml 

enect of risk on, 2M-2I2 
clamification of 23« • .^ » 
237 01a L,. ' **• Pnvate, 

237-238; public, 238-240; pub: 
be, f„ offset fluctuation in 
«venue and expe„«,, 239-24^ 
«or public improvements, 240 

b^n«'«.240ff.;producti;ea«d 
o-^umptiori. 240-24I ; short or 
P^odir, 242-244; long-time 
or permanent, 244-245; con 
^P:;2"-2-»«-348;pr«,Uv"e. 
rr: ■; '"^kerage concerns 
for handling (f,ank.. trust com! 
l-'iOH, etc.), 253; s^U'ot 2M 

effect on rate „f i„,cre«t, 293 

*«. low rate on safe. Ma 
^te" on. in new VVeslern farm-' 
mgc,m„,ne,, 308-:m; cv.scd 
Dv miHfnrt li I M 3 1 1 -1 1 .» . _ 
Jl^-J13; ,,«,„<., 324-.J28 

London, r.,«. „f i„,^, ; 

4iT^2r "' """^^-' '" 

Longfield. cite«l. 3<)i 
L«>wry, iHigUl M. cit«l, '..•.. „ 
Luram, H. von, cifnl. 42i 
Lumbenng eommunit<«., cycle of 

interest rates in, 308 * 
Luxury, habit of, 233 



437 



M 



Managing, cost of, 42-43, 61 
Manufacturers, fluctuations' in i„. 
come-stream of, 315. 

„ 2«7'n..'^^.3^"«:'„T«'. ^' 
Monger Karl, cited, 212. " 
Metchnikoff, cited, 106 

tTrL.^"''l""« •^'^ ""'w of 
interest in, 308. 

Sii2-^'°^'-'23«- 
M'll. J. 8., cited, 324, 357 
Mining, rate of extraction in, 185 
Mining cmnmunitios, rates of nt^rcst 

•n, 306-308 •««« rest 

248-251 ; public loans to off^-t 
Mixtlr'r °r'i'*-='39. 3.2-3,3 ' 
•iixter C \V ,, editor of Rae's So- 

37 n.', .54 n ' 74 "^ ^"P^"'. 

*^°"de''„'n::"';"''*"'*' "PP^^i'tion and 
<lepreciation <if, 257 ff 

Money, ,heor>- that quantity of in 
r.rculation. governs rate .^ j " 
«erest, 8. 14. 19, 320-322 • ,he 
r*'::^':^' value usually ch Jen 
to express rate of interest, 77- 
.nfluence of apprecia.io,,' ,.; 

depr^.at.onof.„nra,e.,nnter- 

; '; .'" " ; reprewnu capital. 

.««1 income, 122;, he ....M^sala. 

ble..f,,r„,«^ie,, a,2;i„,,„c,i"e 

Mormon, ., laboren, who became 
•■apitalis,,. 41 Became 

Mortgage companies. 253 

*, *• /«3; chattel, 300- 
reference for informatiok con- 
cerning land mwtgage, 421 

Mullhall. M. <i, citetl. 423 



Natural Jn.ere... ^,, ,,„,.,i^i^ ,^ 

N»<ure, »|,.w„e*< .,f, »,„, ^„ 

exut.i.c. of interest, 18ft-18a 
P-';-iv..y of. .„d i„.ere^: 



438 



INDEX 




Negroes, effect of eh«i«eterietica of, 
on rate of interest, 292, 294; 
reversal of characteristics by 
training, 298. 

Net income, deBned, 168 ff., 241, 339. 

Nevada, cycle of rates of interest in, 
308. 

New England Mutital Life Insurance 
Company, report of, cited, 421. 

Newmann, M., cited, 424. 

Newmarch, cited, 284 n., 423. 

New Yoric, rates of interest in, rela- 
tive to rising and falling prices, 
275, 283, 319; yearly average 
rates of interest in, 418-421. 

Norton, John P., cited, 335, 358, 
425. 

Notes, explicit and implicit rates of 
interest on, 10. Sm Bonds and 
Mortgages. 



O 



Offspring. See Regard for posterity. 

Ophelimity, 88 n.*. 

Options, among various income- 
streams, 139 ff., "11; rate of 
interest determines, for indi- 
vidual, but for society at large 
existence of optiona influences 
rate of interest, 14A-149 ; eligible 
and ineligible, 150, 397 ; condition 
determiningchoice between, 156; 
choice among, where indefinite 
in number, 156-158 ; three chief 
kinds of, 178; of versatility, 
178; of ehance,178-179; special 
rnne uf trade, the ordinary use 
of the word "option," 179; 
consideration of, among em- 
ployments of capital which differ 
in sise and time-sha|)e, 170 fT. ; 
special cases of, applying to 
durable instruments of wealth, 
180 ff. ; when quantity of in- 
come is definitely fixe<l, 180- 
184 ; when income is fixed, but 
comes slowly, 185-186 ; of mak- 
ing renewals and repairs, 188- 
19«): of betterments, 190-191 ; 
different methotls of production 
and, 191-193; involving human 
capital, lalior, 193-105; certain 
untouched, beyond the margin 
of rhoire (waterworks, canaln, 
railwHys, etc.), 196-197; intro- 
• liirtiou of new. by invention ami 
diM-nvsriss, 10ft ff. 



Orchard, as an example of capital- 
value, 13. 

Outgo, waiting is not, 45-48 ; defined 
as negative income, 341. 



Palgrave, R. H. I., cited, 316, 422. 

Panics, financial, 324-326. 

Paper money, and rate of interest, 
259; rates on, compared with 
rates on co^n, 260-265. 

Paraguay, lack of foresight among 
Indians of, 294. 

Pareto, curves of distribution of 
income of, 231. 

Paris, rates of interest in, relative to 
rising and falling prices, 274, 
319; yearly average rates of 
interest in, 418-421. 

Partial payments, considered in rela- 
tion to appreciation and in- 
terest, 361-363. 

Patents, 198, 206. 

Pawn shops, 209-210, 300. 

Peasantry, process of decline of 
individuals into a, 232 ; personal 
characteristics of, and effect on 
rate of interest, 292, 294. 

Perishability of instruments, 290. 

Personal equation, influence of, on 
time-preference, 103 ff. 

Philadelphia, Franklin fund in, 238. 

Philippines, small income-streams 
and high rate of interest in, 300- 
301. 

Physiocrats, 12. 

Pigou, A. C, cited, 84 n.». 

Plehn, Carl C, quoted, 307; cited, 
422. 

Poor, debtor-class not composed of 
the, 288 ; borrowing among the, 
299-300. 311-312. 

Population, effect of increase of, on 
time-preference, 108. 

Postal savings banks, Knglish, 298. 

Posterity, influence of regard for, un 
time-preference, 107-109; bear- 
ing of regard for, on rate of 
interest, 200-299, 334. 

Poverty, effect of, on time-prefer- 
ence, 94-95 ; high rate of inter- 
est iluc to, 204-295. 

Powers, H. II., 357 n.». 

Preference rate, equalisation of. by 
borrowing and li-nding, or buying 
and selling. 117-118, 126-127, 
231 : definition of, 342. 



INDEX 



^PM»tory service, BO. 

£«ce, Bonmmy, qtioted, 281-282 

Pnce., rflle played by raU of jnfere-t 

tiof*27^t '^''',°' *PP"«i- 

low di8-32o ; mdex number, of 
Pri JLT •? cintrie,, 425-4M 

Pninogeniture, l,w of, and effect „„ 
dj.tnbu,ion of wcahh fsT *"* 

Ptt>UbilUy, element of in h™^ 
preference. 94, 99^ 02 . cTm 
cient of, 338 coem- 

"""^S-Z^""^' "^'"«'' 240 ff.. 

"^det^rW^'-' -^ value. 
Productivity theory of interest 1- 

•peciesof. 12; confusion bv of 
S-:;"^»':^"«=t|vityandvX 
^y^kt t"' ^'"' '>verl«,ked 
ti^' I.„V "T P^xluee. capi- 
tal not capiui income. 14-15. 

^"ct of chMgc of productivitv 
.^ii?ibe«Se^' 

.5roS--2i^^-r1; 

ncom. from capital and va^Tro" 
that capit^. 29; mathematl 
Pr«fl» ?^ ~°"dered, 347-350. 
Profita^mduded in "interest, " 229- 

Property, 89. 341. 

"»IWty.right, valuation of everv 

involve, interest, 127 icoS; 
and partial, defined, 341 "^ 
"««Penty, periods of no^alled 2«W 

'^""2ir2?9. °' '"•-*• ^-^-i 

Pub^mprovemrnts, lo.^ for, 236. ' 



439 



R 



Q-'«'-t*tv ..f ,„,.,„.v ami ra,^ ..f ,„. 
'"•^>'.S, 14, Ifl, 317, .J20-322 



37-38. 74. 159; Bohm-Bawerkiw 
comments on. 64 n.'; quot^ «! 
8»rding foresight, 104 „w[!r 

tTm.^irV''''^*^"-""^ 
time-preference, 106-107; de- 

ectinanaly^i, of inter^tot 
ii'f n.; on fime-preferenp«i Jit 
mdividual, and r^ation^ate 
of interest, 117; treatment by 
of subject of economic effect of 

«venMon,203:con,ributirnof 
to subject of philoHophical thl' 
ory of distribution, 23'^^^qu„*S^ 
concerning the Dutch, 291-^ 
on the Chinese, 292-M3. „ ' 
d'-regard for posterity o^^'cie^t 
I^ans of dogene^te days 

s^n ^= "" '"'•'' °' ''"rableT' 
S' m" •?„.^'"^"«"'' 3<«-3oS; 

''•gwet. Currency and Banki^ k 
quoted, 25fi^ «"'*"^ by, 

R^'ways. improvement of 197. 

««'way securities, reference fordata 
concerning, 421. '"^ oata 

2«>«e of choice, 168 ff., 329-331 
««te of commutation, 2Ifi n. 
Hate of extraction in mining, 185 
H*te^of interest. S,e InteTekt. rate 

R«te^of preference. 5«, P,efc^,, 

Rate of return on sacrifice. 163 ff. 

Real-.;:. °""«'"*'' '««. 159. 342. 

3^ 4.?'""5"^' 244-245, 30a- 

Reese. Michael, 307 
flcgsrd f„r posterity, and time-pref- 
en>n«-c 1 07-1 no- 1 • ^"^t"^"'- 
V ' '"^ ■ '>earing of, on 
rat,- of mterest, 296-299 33^ 
«<•"«,. H.pen.l,.„ce of. .,„ ^ate'^f 
TZr'^:"^- ""'^'"'ledin'-il 
Rent purcha* J.^v.^. .,f lag 

nf laterest, 195-lBe. 



440 



INDEX 



Ratum on aaerifiec, rate of, 153 ff., 
342 ; marginal rat« of, 158, 159. 

Bieardo, and the fallacy that value 
of the product equals its coat, 39. 

Risk, influence of, on time-preference, 
99-103; Umitotion of lending 
due to, 117 ; effect of element of, 
on rate of interest, 207 ff., 302- 
304 ; the greater the, the higher 
the bams on which security will 
■ell, 210-211 ; effect of, on im- 
pure rate of interest (i.e. rate 
on unsafe investments), 212- 
218 ; effect on safe investments, 
213-215; assumption of, by 
stockholders in corporations, 
215, 250; insurance and its 
effect on capital subject to, 217 ; 
effect of speculation in reducing, 
217; stunmary of disturbance 
caused by introduction of ele- 
ment of, 217 ff. ; influence of, on 
difference between explicit and 
implicit interest, 255-256; con- 
stitutes real difference between 
stocks and bonds, 250; coeffi- 
cient of, 338, 342. 

Bobbins, G. P., compilation by, 283n., 
419 n. 

Rodbertua, 40 ; cited, 424. 

Romans, interest-taking between, 
prohibited by Roman law, 4; 
disregard for posterity among 
ancient, of degenerate days, 
107-108, 290-297. 

Roecher, illustration borrowed from, 
33. 

"Roundabout process," Bohm-Ba- 
werk's, 55, 66, 71-78, 163-164. 

Rupee paper, 266. 

Russia, rate of interest among peas- 
antry of, 232, 292, 294. 



8 



Baeriftce, rate of return on, 158 ff. ; 
law of decreasing returns for 
additional, 157 ; marginal rate of 
return on, 158, 169; definition 
of, 342. 

Bailors, influence of risk on time- 
preference of, 102. 

8akata, translation by, 419 n., 
427. 

Sale, method of. Sm Huying and 
selling. 

SalmiuiuH, attempted explanation nf 
interest by, 6. 



San Francisco, mortgage rata 

307; earthquake in, and 1 

arising from, 312. 
Sauerbeck, tables of, 319 n.>, 41 

427. 
Saugrain, Gaston, cited, 423. 
Saving, phenomenon of, 126. 
Sayings banks, function of, 

253; postal, in England, 29 
"Saving capital out of income,' 

phrase, defined, 126. 
Sax, agio theory in work of, 54 
SchmoUer, GusUv, cited, 424. 
Scotch, natural and acquired 

deneiee of, 298. 
Scotland, foresight, self-contrtd, 

regard for posterity, and thi 

of interest in, 291. 
Scott, translation by, of B 

Bawerk's Recent LiUmtur 

Intereal, 3 n. 
Seaman, J. F., 419 n. 
Seasons, changes in inoome-st 

due to succession of, 314-3 
Securities, investments in. 

Stocks and Bonds. 
Self-control, effect of, on ral 

time-preference, 105 ff. ; p 

natural and partly aoqi 

297-299 ; influenoe of, on n 

interest, 334. 
Seligman, £. R. A., cited, 

quoted, 424. 
Selling. See Buying and sdU 
Senior, abstinence theory irf, 5 
Services, 89; two kinds of, i 

mediate and final, 226; 

of rise or fall of rate of int 

on, 226-227; enjoyable < 

tive, defined, 342 ; intermei 

••• Interactions. 
Shanghai, rate of interest in, in 

tion to price-movements, 

293, 319; yearly average 

of interest in, 418-421. 
Skvman Act of 1890, 260. 
"Shirt sleeves to shirt slec 

adage, 233. 
Slver, appreciation and d«p 

tion of, 258 ; rate of intere 

compared with rate on 

265-270. 
Simcox, quoted on rate of inter 

China, 293. 
Single-tax advocates, 4 n.'. 
Smart, WiBiam, translation of 1: 

Bttwerk'H Cnpilal ami U 

by, 3. 



INDEX 



;ag« mtrs in, 
in, And loans 

10 n.>, 418 n., 

id, 423. 
of, 136. 
ion of, 252- 
igland, 208. 
t income," the 

arii of, 54, 74. 
ed, 424. 
•cqiMred ten- 

If-contitd, and 
y, and the rate 
I. 

jr, of B6hnj- 
LUtntun on 



inoome-etream 
of, 314-315. 
Its in. iS«e 
I. 

r, on rate of 
06 ff. ; partly 
rtly acquired, 
e of, on rate of 

., cited, 207; 

and adling. 
wry of, 64. 
inda of, inter- 
A, 226; effect 
ate of interest 
joyaMe objec- 
; intermediate, 

rest in, in rela- 
ivementa, 276, 
average rates 
k421. 
,268. 
ihirt sleeves " 

and depreeia- 
' of interest on, 
rate on gold, 

\ie of interest in 

4 n.«. 

lation of liohm- 

l and Intrrrft 



Socialists, and the view of rate of 
interest as a wage for labor of 
producing capital (exploitation 
theory). 38-40, 52; where mis- 
take IS made by, 235. 
Soetbeer. AdoK, statistics by, 273 
„ 319 n.', 423, 427. ' 

Sombart, cited, 424. 
SpecuUtion effect of rate of interest 
on, 179-180; following new 
inventions, 212-213; effect of 
m reducing risks, 217; use of 
oans m, 244; period, of, due 
to^inequality of foresight, 285- 

Spending, defined as purchase of 
right to immediate enjoyable 
income, 126, 342 
Spruce timber, two acres of. for one 

eaition of newspaper, 27 
Standard deviation of rates of inter- 
est, 279, 283. 
Standard of value, no absolute, ex- 
^pt^for a particular individual. 

Standardising of income, 17-18 
Stockholders, office of. as "risk 

•n cases of loans bv coroorn 

th°e"r' '*',= r.! ** P^«^nSe 
the typical Uebtow, 288. 

Stocks explicit and implicit rate of 
interest on. 10; gelling value 
dependent on expected income! 
of,'2l'"6 "^ •""* "•" P"«« 

Streubir, W. J., cited. 424. 
oumner. cited. 259, 286 n « 
Supply and demand. expUnation of 

'?'' °[ '"/*'"** ^y- 8-7; que,. 

tion of what constitutes. 9 ; in 
Turgots' explanation of implicit 
interest, 11-12; dependence of 
rate of wages on. 228. 



441 



Tarde, G., cited, 333 

Tau«8iR, F. w., cite<i;58 

^8yl»r,^^. M.. compilation by, 418 n., 

Technical superiority of present 
goods. Hohm-Hawerk'H theory 
of, 66, 58-74; business loans :;^ 
down as due to, 241 

Hawerk's, marginal rate of re- 
turn on sacrifice and, 159. 



Thrift, habit of, 233; bearing of. on 

rate of interest, 334 
Tmi^preference in theory of interest. 

Bawerk's terms approximating 
to, 88 ; summed jp «, a prefer- 
ence for eariy over late in- 
come 89; four elements on 
which dependent. 94; depend- 
ence of, on 8i«. of income, 94- 

7: '"""^nce on, of distribution 
Of income in time, 95-98 ; influ- 
ence of composition of income- 
stream on, 98^; influence of 
ri8ko„,9^j02; dependence of, 
onincome. 10.3, 109; effect on 
of foresight, self-control, habit 

expectation of life, and interest' 
n the liv«, of other persons, 103- 
1<»; relation between, and in- 
^°^^' '^PT^^nted by schedule. 
lld-115; law of, 331-332. 

98, 342-343; modification of 
by borrowing and lending, li»J 
1^4; impress on, of choice 
among income-streams, 141 flf • 

SrS"^^ °' "■"** °^ ^*''"*« "n." 

Tokyo, rates of interest in. in relation 

lo pnce-movements, 276 319. 

^4^^^^'^ "**« "^ •-««-♦' 
Tooke. cited, 282, 284 n., 423 
1 rade options, 178-179 
Training, influence of, on habits of 

fwssight, self-control, etc., 298- 

Trust companies, function of, 253 
Tsuboya Zenshiro, history of Japan 
ny, 419 n. 

Turgot, attempted explanation of 
implicit interest by, 11-12. 23. 



U 



Uncertainty of income and the rate 

Lmtci States, c.vcliral movement of 
accumulation and distribution of 
wealth in, 233-2.34 ; increaHine in- 
come-streams in, .W4-30fi ; index 

..?• 'V'"'™™ of prices in, 425-426 
'Ise- theory of interest. 3. 4 ,,« 
7-9, 16-20. 

Isurv. futility of medieval laws 
againNt. !28. 

rtilit y, 88 n », .•J38. 



442 



INDEX 






rri 





Value, defined, 343. 

Variability, mean, of rates of interest, 

279, 283. 
Versatilitv, options of, 178. 
Virtual interest, 277-280. 

W 

Wages, effect of rate of interest on, 
169-170, 228-229; included in 
"interest," 229-230. 

Waiting, cost of, 4, 60. 

Waiting theory, 43-51 ; crude form 
of agio theory contained in, 54. 

War loans, 238-239, 312-313. 

Waterworks, loans for, 240 ; as sub- 
ject of investment, 196. 

Wealth, 89, 343. 

Weighted arithmetical mean, Bohm- 
Bawerk's, 56-58, 351-352. 



Wheat, speculation in, 180; 

of, and rate of discount, 

302,361. 
Williams, F. W., 419 n. 
Winter, G., cited, 424. 
Wood-pulp, 23-27. 



Vearlv average rates of interest 
421. 

Years' purchase, a rate of ir 
implied by sale of land on 
of a number of, 11; in Tt 
explanation of implicit in 
11-12. 

Z 

Zartman, L. W., Investmenta o 
Insurance Companiei by, 
309, 310, 314, 422. 



in, 180 ; price 
discount, 301- 



)f interest, 418- 

'at« of interest 
)f land on baais 
11 ; in Turgot's 
nplicit interest, 



fstmerUa of Life 
inte< by, cited, 
,22.