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1653 Eoit Morn St>Mt

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('16) 48J - 0300 - Phon.

(716) 288 - 5989 - fa.

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

THE RATE OF INTEREST

ITS NATURE, DETERMINATION AND

RELATION TO ECONOMIC

PHENOMENA

IRVING FISHER, Ph.D.

PR0FK880K OF POLITICAL ECONOMY, YALE UNIVERSITY

N(tD gorft
THE MACMILLAN COMPANY

1907

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

QTiie iUtmorg

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

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

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

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

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

61
63

68
71

CHAPTER V
Appreciatiok and Interest

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

77
78

ANALYTICAL TABLE OF CONTENTS

CHAPTER VI

Time-preference

PAOB

§ 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.

§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

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

§ 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

J 10.

$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

§2

§3

§4
§6

§6

§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

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

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.

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.

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

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

THE RATE OP INTEREST

[Chap. I

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

Sec. 2]

PRODUCTIVITY THEORIES

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.

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

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.

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

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.

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-

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

Sec. 6]

PRODUCTIVITY THEORIES

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.

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

Sec. 6]

PRODUCTIVITY THEORIES

+ $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.

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

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.

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.

§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

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

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

■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.

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

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/!

THE RATE OF INTEREST

[Chap. II

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.

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

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

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

I if

Hi I

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

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

THE RATE OF INTEREST

[Chap. Ill

I 1

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

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 '

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.

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

Sec. 5]

COST THEORIES

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.

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."

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

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.

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

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

I 1

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

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

§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-

/■

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

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.

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

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

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,

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

646

578

507

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.

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

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'\

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

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-

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

§ 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

■-i :

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

• 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

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

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

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.

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

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

1889

200

1890

280

3.3

1891

350

2.5

1892

«)0

2.2

1893

440

2.1

1894

470

1895

500

1.5

3.8

2.2

1.8

1.5

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

1.5

3.8

2.2

1.8

1.5

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

3.3

2.5

2.2

2.1

1.5

Reduced
Utility

5
3.8

1.8

1.5

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

1889

3.8

— BHB

1890

3.3

1891

100

2.5

2.2

220

1892

200

2.2

400

1893

280

2.1

1.8

504

1894

350

1.5

525

1895

400

1.5

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

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

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

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.

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

b
<

£.

1891

875

700

500

250

§0

1892

880

770

616

440

a ?■

1893

924

840

735

588

•^■J

1894

940

880

800

700

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

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.

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

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)

12.2

1.25 ii.4

1 1.8
!■■■

APPLIED I^A^1GE Inc

1653 tott Moin StrMi

Rochesttr, N«w York U609 USA

('16) ♦9J - 0300 - Phon.

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

1 1

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

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 : —

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

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

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.

11
It

liti

ill

fil

* i .
I I ■

? !

I I

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

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

THE RATE OF INTEREST

[Chap. IV

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 "

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

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.

-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

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

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

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]

THE RATE OF INTEREST

[Chap. V

■l\

'I J'i

■> i

§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

Sec. 4]

APPRECIATION AND INTEREST

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

III

;

I'-

i '

i'it

1 1 ■

f i

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

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.

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

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

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.

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

9
C

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

■f, i^mf^

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 'A \

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

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.

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

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.

■'

i 3

.1 f

f :■

- -I

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,

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

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

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

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-

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

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

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 ?

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

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

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 '

' 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.:

£•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.

Sic. B]

TIME-PREFERENCE

107

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.

112

THE RATE OF INTEREST

[Chap. VI

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

s c

z .i

I *" I «^ I -"

III ' I? ■ l^

3 Ji 5 r: -£

c * C = ^
•I * 2 *■ -I I

^ I

»•

■

I I

i 1

■v^

•

ail*

--s —

««

.«•

p»

■5

"5 :

■jt '

J ■

•■«

*■

«c

*
3
X

1'^

1 35

: jj

«i4

• «•

•S

, 1

r ti *

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!

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-

111'

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-

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

122

THE RATE OP INTEREST

[Chap. VII

Fio. 8.

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'

Sxc. 3]

FIRST APPROXIMATION

123

.B'

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-

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\

' ■^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.

§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

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

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.

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

'fi

> 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.

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-'

§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

.*■•■

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.

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?

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

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

WHAT THE

Forest Use

would have

Yielded

1st year

2000

000

2d year

1800

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

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

i^i

if
J

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- ■

■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

4i%

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;
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8bc. 6]

SECOND APPROXIMATION

149

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,

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150

THE RATE OJ? INTEREST

[Chap. VIII

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

*■'■--

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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

+ 110

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.

I
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I -4

■:f- %

1*1

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

I* i

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« •

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.

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.

:'M

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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

^!|l:

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(ANSI and ISO TEST CHART No. 2)

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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.

i I

1; * ^"

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.

■it'

§ 14

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

S I -I

.' f

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

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.

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

til

iil

4 I

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

* ,

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.

,: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^.

I: ,a

ll:

176

THE RATE OF INTEREST

! I

IH'

w ^ -

|BI

I^^Hr

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-

Sxc. 16]

SECOND APPROXIMATION

177

).|.|j|

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

t I I

'1*

i f

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-

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.

»,

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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.

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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

-O

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

■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

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

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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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.

1„

f J i n
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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

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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

» 'i

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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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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.

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.

i
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iV f. I

• J : I

CHAPTER X

INVENTIOK

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.

§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

200

THE RATE OF INTEREST

[Chap. X

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—

202

THE RATE OF INTEREST

[Chap. X

' It ^

4 # I I '!

' * if :-
't 1

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.

204

hr.

»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

•■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

r :

ft ■

I ' I

1 i I

t ■ I

• J

■|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

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

»«

[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

:jl:

kft
I)"'

Fa '

HI' .

: > J

' 3 ;

i I

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

' ■•' .;.-it
'i

'■4

?!'

'ii

'fl:

sir

? J « ;!

kill

ill

: r

,1 i 1 5

ii I

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 *

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.

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

^i>\

CHAPTER XII

BOLE OF INTEREST IN ECONOMIC THEORY

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

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.

i
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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

J ■!

—

I »'

5 M

I? * f
i I

i ^ V

« t

* il

« •!
» 1

Ji i
'I I I I p I

tit

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

232

THE RATE OF INTEREST

[Chap. XII

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

'Am

..tf^. ...V.^^'

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.

n,.>.

§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.

i.i

.-a

CHAPTER XIII

APPUCATION TO ACTUAL CONDITIONS

'? '•.

u!l^=l

§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 : —

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

.ill

'iA^

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238

THE RATE OP INTEREST

[Chap. XIII

f €

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

i I

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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

t r.

l»

■ ('■•

'^fi

.fi

242

THE RATE OF INTEREST

[Chap. XIII

7 I M f T 4.

[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.

11*

•

t. -

'%'

1 «. *

if *

III!

244

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.

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

Hi,

'SNP

246

THE RATE OP INTEREST

[Chaf. XIII

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

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

I',

I i.

^ 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

252

THE RATE OF INTEREST

[Chap. XIII

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'

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;:.

..^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

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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.

t«

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

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258

THE RATE OF INTEREST

[Chap, XIV

I *

'Hill

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

July, 1873

5.4

5.0

115.3

Jan., 1886

2.6

Jan., 1874

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

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

Jan., 1870 . .

7.1

6.3

2.1

July, 1870 . .

6.2

6.7

1.4

Jan., 1871 . .

6.7

6.3

1.3

July, 1871 . .

6.4

5.7

1.8

Jan., 1872 . .

5.9

5.7

1.3

July, 1872 . .

6.2

5.7

2.1

Jan., 1873 . .

6.5

6.2

2.0

July, 1873 . .

6.2

6.0

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

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 ' •

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

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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

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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

23.2

186S

4.3

4.0

23.0

1870
1871

4.3
4.1

4.0
3.8

23.6
23.2

1872

3.9

3.7

22.6

1873

3.9

3.7

22.4

1874

3.9

3.8

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

21.9

1876

4.1

3.7

20.5

1877

4.1

3.7

20.9

1878

4.2

3.9

20.2

1879

4.4

3.7

19.7

1880

4.3

3.6

20.0

1881

4.0

3.4

19.9

1882

3.9

3.5

19.5

1883

4.1

3.4

19.5

1884

4.1

3.3

19.5

1885

4.1

3.5

18.5

1886

4.1

3.5

17.5

1887

4.1

3.4

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

19.3

1891

3.8

3.1

17.1

1892

3.9

3.1

15.3

1893

3.9

3.0

15.0

1894

3.9

3.0

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.

268

THE RATE OF INTEREST

[Chap. XIV

RATES OF INTEREST REALIZED FROM DATES NAMED
TO MATURITY OR IN PERPETUI.'Y— Conduded

Rupee

Gold

Differ-
ence

EXCRANOE ON

India
Pence per Rupee

1895

3.4

2.8

13.4

1896

3.3

3.1

14.3

1897
1898

3.5
3.7

3.1
3.2

.4
.5

15.1
16.0

1899

3.6

3.2

16.1

1900

3.7

3.4

16.0

1901

3.7

3.5

16.0

1902

3.6

3.5

16.0

1903

3.5

16.0

1904

3.6

3.7

-.1

16.1

1905

3.6

16.1

1906

3.6

3.2

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.

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

.-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.

■*

,^|:

.^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

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

- 1.4

APPRtCIA- VlF-.TfAt.

TIO.V or I.VTEREAT I N

Mo.VET IX CoMHCDrTIEil

CoJiMODiTiE.^ .'P.arik,

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

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

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)

]

;

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

-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

6.0

188.5-1891

—

0.1

-0.2

4.9

1892-1897

—

4.6

^.5.6

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

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 !

15
5

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*

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

V.tH.

■"•tandafi

-T*tion,

No.

PXKIOD*.—

Market

I-VTSaEST

ViRTT

Inter;

LocdoQ ....

1 ", !

.S.S

.■i.U

Beriin ....

; \

.56

2.^'}

New York .

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

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

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

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

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

8.2'

5.1

4.5

Appreciation or

Money in

Commodities

-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

1 ir

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.

§ 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

If'

kS^

3 J

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

.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,

•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

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

§ 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

' t ■-

: •■ -•;■

is. i

ii. i:

Ifl

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

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»

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.

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.

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.

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.

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

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.

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

1 1

. ;

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.

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

§ 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

i'L

318

THE RATE OF INTEREST

fCkAP.XVI

s' 'i

hi u

[S :

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

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

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

■1

. t:

322

THE RATE OF INTEREST

[Chap. XVI

^H i'JM

K'"^

^H -n

K f

^H ^Wm

H ^

^^m -Me

Hi If

^^^^^B . «^B

^E .^

^^H ' ^B

'B s

^^^H jHili

•§|p tI

^^B ^B

SS'^s

^H ^uLS

3vi "*

■ i»W

ft''

K .^M

C:i

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.

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

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.

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.

f';

1'^ t

% f i

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

CHAPTER XVII

§ 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;-

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 ^

§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 '

H I

I s .

i ;
1

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^ ■
I

tiJ

■'#ii

ill

!■* I

ff- •,

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.

■ ■I t

ft.

' ^1

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.

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

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. /.

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

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

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.)

*•!

S ': :

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: '*■'

TflP

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^mt

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■

.Mgl't

iflB.

ffi^

13L

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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

:,-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"

(1+0*

m — l

■(1+0*

+ 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

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

§ 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,

(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,

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

'I-

^'11

MKatocorv kisoiution tbt chait

(ANSI and ISO TEST CHART No. 2)

/APPLIED IIVMGE I

1653 £a>l \ta.n Slr«.t

*'oc^•«^tf. New Yorh U609 US*

(716) »8J - 0300 - Phon.

("6) JM - i989 - ra>

"tl

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 = °'"^"*"^"*

(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
■♦.I

^k|

wii'.

■1

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.

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

300

250

320

loo

300

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

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

*,«

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.

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.

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

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

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,

1
J

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

\\% *

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 +

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 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 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

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 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 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."

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

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

(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: —

(1.2026)

40
(1.2026)'

= 16.631 millions

(1.2026)3
10

= 27.659 millions

= 17.250 millions

= 4.781 millions

(1.2026)*
Total = 66.321 millions

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)

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

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

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-

,.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 = '•

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.

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

ngs

ext

his

)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

■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.)

— 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 "

= F,(c,'-hx,',tV'+x,")

ti > V

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.

+ ... = 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

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'\

.t;=?^^.+?^)....=o.

'.i.

4.1

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'

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

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

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,

„ desir.Ax'^ ,,desir. Ax'' ,,
Or-^-^_ Ax'+— ^-^„-- Ax" »0,

Am., a (/

— -, Ax' -I- —--7, Ax"
Ax' A x"

A u _Au

A ''" ' x'Ax

Ax" : -Ax' =NS:MS

ifij

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.

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

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

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-

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

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

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.'"-'),

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

.iiii

402

APPENDIX TO CHAPTER VIII

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

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 +

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

•!

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.

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.

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.

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.

APPENDIX TO CHAPTER XI

ft.

p II

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.

'Mi

Ai PENDIX TO CHAPTER XIV
Statistical Data

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

■tf
5?

a>9>5S

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

LoiiDoa

Beklim

Pa«i«

New Toiik

Ualcutta

TulLTO

5UAMUIIAI

4.1

4.5

6.6

M
i

1855

4.7

2.0

9.3

9.7

^ ,

• .

1856

5.0

6.1

4.0

5.5

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

• •

. ■

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

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

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

4.1

2.5

6.0

10.8

0.1

6.0

18.

12.

1870

3.1

4.5

4.8

4.0

5.1

8.1

7.2

6.7

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.

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.

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.

1879

1.8

2.5

2.7

3.7 2.2

2.6

6.0

6.3

11.

16.

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.

1882

3.4

4.1

3.0

4.5

3.4

3.8

5.7

6.6

10.

17.

1883

3.0

3.6

3.1

4.1

2.6

3.1

6.6

6.8

7.9

11.

1884

2.6

3.0

2.0

4.0

2.4

3.0

6.2

6.4

12.

16.

1885

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

1887

2.4

3.3

2.3

3.4

2.4

3.0

6.7

6.6

9.0

8.8

6.5

1888

2.4

3.3

2.1

3.3

2.8

3.3

4.9

6.5

10.

9.7

6.0

1880

2.7

3.6

2.7

3.7

2.6

3.1

4.8

7.0

10.

6.2

1800

3.7

4.5

3,7

4.5

2.6

3.0

6.0

5.8

11.

7.2

1891

2.5

3.3

3.0

2.6

3.0

6.7

3.1

9.4

0.4

3.6

1892

1.5

2.5

1.8

3.2

1.8

2.7

4.3

3.5

8.3

8.4

6.0

1893

2.1

3.1

3.2

4.1

2.2

2.6

7.1

4.9

7.8

6.9

1804

1.0

2.1

1.7

3.1

1.8

2.5

3.4

5.4

9.3

0.4

3.8

1805

2.0 , 2.0

3.1

il.6

2.1

3.8

4.3

9.6

2.8

fi.r)

1S«>6: 1.4

2.5 3.0

3.7

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

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)

. . .

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*^'

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-

: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

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
105
1U5
109

....

100* "

102

114

121

124

. . . .

• • • »

. . . ! !

. . . .

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 . . .

114

113

1859 . . .

116

103

1860 . . .

121

100

....

1861 . . .

118

100

....

1862 . . .

101

123

118

104

....

1863 . . .

103

125

127

132

....

1864 . . .

105

129

172 .

....

1865 . . .

101

123

112

232

....

1866 . . .

102

126

115

188

• • > ■ •

....

1867 . . .

100

124

lUO

166

....

1868 . . .

122

174

....

1869 . . .

123

152 .

....

1870 . . .

123

144

....

1871 . . .

100

127

136

....

1872 . . .

1()9

136

105

132

1873 . . .

111

138

103

129

100

104

1874 . . .

102

136

130

104

100

1875 . . .

130

129

105

103

1876 . . .

128

123

102

111

1877 . . .

128

114

121

105

101

1878 . . .

121

105

125

114

106

1879 . . .

117

119

145

111

1880 . . .

122

105

112

160

105

1881 . . .

121

108

175

110

1882 . . .

122

109

159

108

1883 . . .

122

107

130

103

1884 . . .

114

103

116

104

1885 . . .

109

116

105

1886 . . .

104

107

1887 . . .

102

101

109

105

1888 . . .

102

104

112

100

1889 . . .

106

107

116

105

1890 . .

108

103

124

104

1891 . . .

109^

104

123

104

1892 . . .

106

115

124

108

1893 . . .

102

119

129

109

1894 . . .

. . .

132

1895 . . .

145

1896 . . .

133

, ,

1897 . . .

173

1898 . . .

159

, ,

1899 . . .

111

175

. .

1900 . . .

110

165

. .

1901 , . .

103

160

, ,

1902 . . .

165

1903 . . .

104

, ,

1904 . . .

104

^ ,

:905 . . .

107

, ,

1906 . . ,

103

_'_

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^

iiit

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.

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.

^ 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

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«.

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.

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.

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

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 '.

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

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.

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

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.

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.

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.

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.

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.

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