The theory of prices a re examination of the central problems of monetary theory vol i

9 The place of "quantity equations" in monetary theory, ac-cording to Keynes's Treatise on Money, 9.. The place of "quantity equations" in monetary theory, according to Keynes's General

THEORY OF PRICES

VOLUME I

A Re-Examination

of the Central Problems of Monetary Theory

BY

ARTHUR W MARGET, Ph D.

PROFESSOR OF ECONOMICS, UNIVERSITY OF MINNESOTA

VOLUME I

REPRINTS OF ECONOMIC CLASSICS

AUGUSTUS M KELLEY· PUBLISHERS

NEW YORK • 1966

REPRINTED I 966 BY ARRANGEMENT

LIBRARY OF CONGRESS CATALOGUE CARD NUMBER

PRINTED IN THE UNITED STATES OF AMERICA

or to recommend their application, he should know what has been already undertaken, what has been accomplished, and what remains for discovery and elucidation The fol- lowing work gives sundry examples of the inconveniences resulting from the want of this information, by exhibiting able men engaged in the investigation of principles and the development of laws which had been previously estab- lished and traced, and putting forward speculations as original which had been long before the public.

-J.R McCulloch, The Literature of Political Economy

ARE we not justified in affirming that Political Economy represents, and that in a very eminent degree, one at least of those symptoms which M Comte has de- clared to be among the least equivocal evidences of really scientific conceptions-continuity of doctrine?

I VENTURE to assert that a more remarkable ample of continuity of doctrine, of development of seminal ideas, of originalaper,usextended, corrected, occasionally re-cast, of new discoveries supplementing, sometimes mod- ifying, the old-in short, of all the indications of progres- sive science-will not easily be found even in the history

ex-of physical speculation .

-J.E Cairnes, M Comte and Political Economy

masters to offend or embarrass us? Probably nothing save their docile modesty in instructing themselves in philos- ophy before setting out to further its progress They believed that philosophy could not possibly be the work of

a single man, no matter what his genius might be, but that

it progresses, like science, slowly, as the result of the tient collaboration of generations, each leaning on its pred- ecessors in order to surpass their achievement ' , We are like dwarfs," said Bernard of Chartres, "seated on the shoulders of giants We see more things than the Ancients and things more distant, but it is due neither to the sharp- ness of our sight nor the greatness of our stature; it is simply because they have lent us their own."

pa Etienne Gilson, The Spirit of Medieval Philosophy

T HE fundamental proposition from which this study

proceeds is that the Theory of Prices must be conceived

of as an organon, in the sense in which Marshall's Principles

may be said to be an organon The Theory of Prices, forthose who accept this view, is not a set of maxims of mone-tary policy, which can claim neither· the general validity northe authority that may be said to attach to a set of concep-tual tools N or is it a series of speculations as to matters

of fact, with respect to which the last word must be vided by investigations of the "facts" themselves Thereader, therefore, who expects a discussion of such matters

pro-as the wisdom of attempting to stabilize the price level, or

a "theory" of the business cycle, in the sense of a surmise

as to the facts of cyclical variation, is warned that he will

In-vii

There are, indeed, precedents for extended critiques of thework of an author of great eminence in his generation Thespirit of those parts of the present work which can be re-garded as a "critique" of Mr Keynes's writings, however,

is akin to that with which John Stuart Mill insisted that histwo-volume Examination of Sir William Hamilton's Philos- ophy was imbued "My subject," said Mill, "is not Sir

W Hamilton, but the questions which Sir W Hamiltondiscussed." The subject of this work is not Mr Keynes,but the questions which Mr Keynes has discussed It isthe importance of these questions, and not the importance

of Mr Keynes or any of his critics, which alone can justifythe length at which this book treats the questions constitut-ing its subject matter

I t follows, from the fact that by far the greater part ofsuch polemics as are contained in this study are polemics

on behalf of the Principle of Continuity as a maxim of trinal development, that the work as a whole is intendeddefinitely to be constructive; and I hope that it will be soregarded by all those for whom "construction" is not neces-sarily construction ex nihilo. I am aware, to be sure, thatsome of my readers will regret that the line of ·positiveanalysis may appear to be obscured by what will seem tothem an unnecessary degree of concern with the works ofother writers, including lVlr Keynes To this, my answer

doc-is twofold In the first place, it is my intention to followthis treatise with a publication which will be frankly in thenature of a textbook, and which should satisfy those whowould insist that it is the proper function of an author tostate only the conclusions which he himself believes· to besound, and not the reasons why he prefers these conclusions

to those reached by other writers

In the second place, I happen myself to be of the opinionthat if it is a vice to be concerned "excessively" with theviews of other writers, it is at least equally a vice to proceed

in complete disregard of what other writers have done orare doing One is reminded of the Cockatoo in Alfred

de MU8set's Histoired'un merle blanc, who attributed thedistaste of the public for his attempts at versifying to thefact that the public also read the works of poets other than

himself, and was "distracted" thereby I confess to thevice of opening myself to the danger of being "distracted"

by a consideration of the works of others, if it is a vice; andsince I am entirely prepared to forgive the trespasses ofthose who follow a procedure different from that which Ihave followed, provided only that the results that they reachare sound, I ask only that my own trespasses, if I havesinned in the opposite direction, may be forgiven also

I am aware that it will be objected that familiarity withthe work of other writers can be demonstrated in other waysthan by specific citation of, or discursive comment upon,the contentions of these other writers, and that it is notnecessary to bring into the exhibition gallery all the shavings

of the workshop To this I can reply only as follows: First,

in all honesty, not all the shavings of the workshop are herepresented; indeed, I am only too keenly aware that some

of my readers will feel that justice is not done to the specificcontributions which they have made or believe they havemade Second, there are various kinds of workshops, eachproducing its own kind of shavings A tortuous concernwith problems which the author himself ends by character-izing as side issues that do not strike the heart of the mattersurely results in a mass of "excess" shavings, particularlywhen no one but the author himself seems, to have beenbothered by these side issues, so that no citations to theworks of other authors are necessary It is at least argu-able that the fact that other writers can be cited wouldindicate that the matters under discussion are of interest tosome one besides the author Finally, I trust that I may

be permitted to lay at least part of the blame, if blame iscalled for, upon what were undoubtedly overgenerous com ments on some of my published articles in which much at-tention was paid to the existing literature on the subjectwith which they were concerned, in that these commentshave encouraged me to believe that there are others whoexperience the same pleasure that I do in viewing the results

of an adventure of exploration into the field of the history

of ideas

Familiarity with existing prejudices on the subject leads

me to fear, also, that most of the obloquy which maybe

directed against the form of exposition adopted in this studywill concern the number and volulne of the footnotes Thefootnotes are chiefly of three kinds: (1) page citations to thework of authors quoted or discussed in the text; (2) detailedspecification in support of a generalization advanced in thetext; and (3) supplementary comments designed to reinforce

or protect an argument stated in the text For the firsttype of footnote, I have no apology at all As for the sec-ond and third types, I ask the querulous reader to considerwhether it is not better, assuming that the material is to beincluded at all-and in this matter I can only refer again

to what was said above concerning the shavings of the shop-to put it where he need look at it only in case he feelsthe need of further supporting argument The same answer

work-is offered to those who may object to my adoption of thepractice-very common on the European continent, and be-coming increasingly common in English-speaking countrieswith the translation of continental works in which the devicewas employed-of putting into a smaller type, material of

an essentially supplementary character There is nothing

to force the reading of either footnotes or material printed

in smaller type by those who dislike such devices; and if Ihave erred in putting into footnotes or smaller type, mate-rial which a reader thinks should have gone into the maintext, or vice versa, I can only ask humbly to be forgiven forthe mistake in judgment

I fear, finally, that even such merits as may be discovered

in this work will not reconcile those who have an implacablehatred for books that run to many pages Surely, however,the physical compass of a work is not a criterion for judgingits usefulness; it is something imposed by the nature of thetask which the author sets himself One of the tasks which

I have set myself in this book is the illustration of esses by which monetary theory has come to be what it is

theproc-In the nature of the case, this has involved a continuing anddetailed concern with the works of earlier writers, over thewhole of the field of the Theory of Money and Prices Onlythose who know the vastness and the richness of that fieldwill be aware of how much I have left out that I might haveput in; and it is their forgiveness that I beg, rather than

the forgiveness of those who will not be reconciled to fatbooks.

The physical dimensions of the work have recommendedits publication in two volumes rather than in one Thesecond volume, to which frequent references are made inthe volume now offered to the public, will contain the mate-rial dealing with the theory of the effect of money uponoutput; the theory of savings and investment as related tothe Theory of Prices; and a final evaluation, in the light ofthe received alternatives, of the Theory of Prices presented

in Mr Keynes'sGeneral Theory of Employment, Interest, and

Money-including such elements as Liquidity Preference, theMultiplier, the so-called Method of Expectations, and so on.The relegation of the material last mentioned to the secondvolume will, it is believed, commend itself to most readersafter the second volume will have appeared

Dr C O Hardy, who has read the first five chapters, hasgiven me the benefit of his support where he agrees with

me, and the much more valuable benefit of his frank cism on the points-suspiciously few, so far as these chaptersare concerned-on which he disagrees with me Professor

criti-E A J Johnson has read the whole manuscript with a gree of care far beyond anything that was imposed uponhim by his formal duties as editor of the series in which thework appears; and he has helped me greatly in matters ofpresentation I have been helped greatly in this respectalso by the editorial staff of Prentice-Hall, Inc Mr Harold

de-G Russell and his assistants on the staff of the University

of Minnesota Library have been extraordinarily helpful inmany ways Mr John K Langum of the University ofMinnesota was kind enough to read the galley proof andcaught several errors of content In other cases in whichspecific parts of the book-including parts of the manuscript

of Volume II~have been submitted to friendly critics, Ihave indicated, and desire here to express again, my sense

of profound gratitude to the persons involved

My obligations to the two to whom this book is dedicated,

on the other hand, do not lend themselves to specification,precisely because they are measureless The same thingmust be said of my obligations to my wife, who has helped

in so many ways that any attempt at particularization wouldlikewise represent an absurd minimization of her share inthe work.

ARTHUR W MARGET

CHAP'l'EU PAGE

I INTRODUCTORy 1

I An Apology for Polemics 1

II The "Theory of Prices" and Mr Keynes 2

PART ONE

"QUANTITY.EQUATIONS" AND THEIR MEANING

II "QUANTITY EQUATIONS" AND "THE QUANTITY THEORY" 9

I Quantity Equations and the Theory of Prices 9

II Keynes'sTreatiseand the Quantity Equations 13

III Quantity Equations versus the Quantity Theory 19

IV The Residuum of the Quantity Theory

V Quantity Equations and the Quantity Theory in Keynes'sTreatise . 27

VI Quantity Equations and Keynes'sGeneral Theory 29

VII Greek Gifts 33

VIII The Dead Shall Rise Again " . 35

III QUANTITY EQUATIONS AS "STATICAL IDENTITIES" 39

I The Quantity Equations as "Statical" Equations 39

II "Statical" Conditions as Stationary Conditions 40

III The "Truth" of the Quantity Equations 46

IV Methods of Correction: Insertion of Missing

V Methods of Correction: Redefinition of Terms 64

VI A Test Case from Keynes'sTreatise . 68

IV QUANTITY EQUATIONS AS "STATICAL IDENTITIES"

(Continued) . 72

I "Statical" Conditions as Equilibrium Conditions 72

II Quantity Equations and "Non-Statical" Analysis 78 III Quantity Equations and the Element of Change 81

IV The Quantity Equations and Monetary librium 85

Disequi-V The Quantity Equations as "Identities" 88

V THE "DYNAMICAL" EQUATIONS OF KEYNES'S

BEHIND THE "QUANTITY EQUATIONS"

GENERAL CONSIDERATIONS; THE QUANTITY OF

II A Simple Quantity Equation and its Justification III The Quantity of Money of Ultimate Redemption

THE QUANTITY OF MONEy-SUBSTITUTES, M'

I Bank Reserves and the "Creation" of Deposit

II The Role of the Rate of Interest III Bank-Rate and the Quantity Equations

IV The "Traditional" Theory of Bank-Rate

THE QUANTITY OF MONEy-SUBSTITUTES,M'

I Bank-Rate,M',and" Proportional" Price Change

Ill. M'and the Maintenance of a Low Bank Rate

THE QUANTITY OF MONEy-SUBSTITUTES, M'

I Interest as "Capitalization-" and "Cost-Factor"

II Wicksell on Interest as a Cost, andM' .

III The Argument Applied to Interest as

THE QUANTITY OF MONEy-SUBSTITUTES,M'

I Bank Rate and Keynes's Fundamental Equations

II "Capitalization," Interest as a Cost, and the

III. I - S as "Profits," and Bank Rate .

IV. I( -8)as "Investment" and Bank Rate

"VELOCITY OF CIRCULATION" (V) .

I The Concept of "Velocity" in Monetary Theory

II Attacks on "Velocity": Appearance and Reality III "Velocity" in Keynes'sTreatise THE "INCOME ApPROACH" TO THE THEORY OF

I Keynes'sTreatiseand the Income Approach

II Substance and Shadow in the Income Approach

VI The Influence of Wicksell and Wagner VII The Income Approach after 1909 "

PAGE

143143145154158158171178189206206212222231231247258268268269274279290290294298302302

306

311315324327

336

I Income, "Velocity," and the Quantity of Money

II Income versus Outlay from Income III Keynes'sTreatiseon Income and Velocity

IV The Concept of Income Velocity Examined

V "Income Payments" and Income Velocity

THE ALTERNATIVE TO "INCOME VELOCITY"

I Income Velocity as a "Hybrid Conception"

II Robertson versus Keynes on "Income Velocity" III Keynes and the Traditional Alternative to Income

IV Keynes's Alternative and the" Quantity

THE CASH-BALANCE ApPROACH • •

I Keynes and the Cash-Balance Approach, , ,

II The" MarshallianK" , , , , Ill Relevance and Irrelevance in the Cash-Balance

THE CASH-BALANCE ApPROACH (Continued) .

I Money "in Circulation" and the Cash-Balance

II "Savings Deposits," Cash Balances, and

III Investment, Borrowing, and" Cash Facilities"

IV Forces Determining the Relative Size of Cash

THE "VOLUME OF TRANSACTIONS" CPT); THE

"PLURALITY" OF PRICE LEVELS ,

II "Consumers' Goods" Equations and the Plurality

of Price Levels III "Consumers' Goods" Equations, Plural Price Lev-

IV Fisherine Equations and the Price Level of Output

V The Case for a "Total Transactions" Equation

THE "VOLUME OF TRANSACTIONS" (Continued)

I Keynes's Treatise and "Non-Output"

II Output versus Transactions in Output III Goods Produced versus Goods Intended for Sale

IV The Velocity of Circulation of Goods

V Keynes'sTreatiseand the Velocity of Circulation

PAGE

344344354356364

374

388388

398

402409414414415420459459466470478484484

485

509514518525525

538544

548564

CHAPTER PAGE

XIX THE "VOLUME OF TRANSACTIONS" (Continued) 569

I The Price Level of "Services" and the Fisherine Equation 569

II The Role of Transactions in Securities 576

III The "Volume" and the "Value" of Transactions

in Securities . 588

IV, Keynes's Treatise on Transactions in Securities

and the Price Level of Output 595

V The Role of Output in the Theory of Prices 599INDEX 603

CHAPTER PAGE

I INTRODUCTORy 1

Mr J M Keynes on the present status of the "Theory of Prices," 1 An apology for polemics, 1 Reasons for the selection of Mr Keynes as a case in point, 3,

PART ONE

"QUANTITY EQUATIONS" AND THEIR MEANING

II "QUANTITY EQUATIONS" AND "THE QUANTITY THEORY" . 9

The place of "quantity equations" in monetary theory,

ac-cording to Keynes's Treatise on Money, 9. tions versus "The Quantity Theory," 19 The residuum

Quantityequa-of the "quantity theory" controversy, 22 The confusion

of "Quantity Equations" with" The Quantity Theory" in

the Treatise, 27. The place of "quantity equations" in

monetary theory, according to Keynes's General Theory of Employment, Interest, and Money, 29 Reasons, neverthe-

less, for continued concern with the argument of the Treatise,

30 The confusion of "Quantity Equations" with "The

Quantity Theory" in the General Theory, 33.

III QUANTITY EQUATIONS AS "STATICAL IDENTITIES" 39

Keynes's charge that the older "quantity equations" are

"statical" in character, 39 "Statical" conditions as tionary" conditions with respect to the variables included

"sta-in the Quantity Equations, 40 When the charge is lated to mean that the equations a -,sume the presence of stationary conditions with respect to relations not given specific notation in the equations themselves, it reduces to the charge that" Quantity Equations" are not under all cir- cumstances true equations, 46 History of the latter charge: statistical, considerations, 46 Analytical cOllsid- erations: the "incompleteness" of the equations as lists of variables affecting prices, 49 Recognition of the issues in- volved by Newcomb and others, 51 The first method for meeting the difficulty: the insertion of the missing factors,

trans-55 Examples from the practise of Newcomb, Fisher, and others, including Keynes himself, 56 Usefulness of the method, 59 The second method for meeting the difficulty: redefinition of the terms, 64 Invalid objections to this method, 65 Examples of the method as applied by New- comb and others, 66. A crucial passage in Keynes's T1'eatise

tested in the light of the considerations developed in this chapter, 68.

The validity and usefulness of the" Quantity Equations" for non-staticalanalysis, 79. The Quantity Equations and analysis with respect to the causes and the process ofchange

in prices and in the variables determining prices, 81 The Quantity Equations and analysis with respect to the nature and causes of monetary" disequilibrium/' 85 The Quan- tity Equations as "identities," 88 The charge viewed in the light of the historical development of the" equation of exchange," 90; and in the light of the results obtained by the use of Quantity Equations which are true by definition, 99.

V THE "DYNAMICAL" EQUATIONS OF KEYNES'S

Treatise on Money 101

Reasons for dealing with the problem: the claims of the

Treatise itself, and tile subsequent challenge, 101. founded criticisms of the Fundamental Equations as being

Un-supposedly "statical" in character, 102 The case oi namic equilibrium," 103 The theory of output presented

"dy-in the Treatise is not inherent in the Fundamental

Equa-tions themselves, and therefore does not invalidate those equations for the case of "dynamic equilibrium," 103 The same thing is to be said with respect to the argument of the

Treatise concerning the conditions for" equilibrium" other

than an equality between costs and prices, and between

"savings" and "investment," 107 The Fundamental tions, as such, do not assume an independent relation be- tween the level of earnings and the rate of interest, 110 Nor do they necessarily lead to an argument for the sta- bility of general prices, and therefore to an assumption that the level of costs remains unchanged, 113 Sound criti- cisms of the validity of the Fundamental Equations under changing conditions: the relation of the costs of production

Equa-of capital goods and consumers' goods, respectively, 115.

"Short period" and "long period" analysis as a statement

of the relation between the older quantity equations and the fundamental equations of the Treatise, 118. Keynes's reply to the criticism in question, 120 The decisive ob- stacle to the utilization of the Fundamental Equations un- der changing conditions, 124 The twofold purpose of the Equations, 124 The truistic character of the expression

P R =E - S could be defended only at the cost of a series

of tortuous constructions with respect to the meaning of

"savin~" and "investment," 125 But even these tions did not justify the identification of "cash earnings available for outlay" with" costs," under changing condi- tions, 126 Not all "costs" are associated with equivalent cash payments, 127 The identification of "earnings avail- able for outlay" with "costs of production" is impossible when account is taken of the time relations involved, 130 The result is to destroy the claim that the Equations per-

V THE "DYNAMICAL" EQUATIONS OF KEYNES'S

Treatise on Money (Cont.)

form the twofold purpose assigned to them under changing conditions, 133. Keynes's comment, in the General Theory,

on the Fundamental Equations of the Treatise, and its

in-terpretation, 138.

PAGE

PART Two

BEHIND THE "QUANTITY EQUATIONS"

MONEY OF ULTIMATE REDEMPTION 143

Relation of the topics treated to the writings of Mr Keynes,

144 Justification of this procedure, 144 A Quantity Equation of the general Fisherine form, 145 The criteria

on which it is based, 145 The treatment ofuvelocity," 148 Meaning of Uthe quantity of money," 148 "Money of ultimate redemption" and its relation to Umoney in circu- lation" and the quantity of money-substitutes, 150 A brief summary of the theory with respect to the forces de- termining the quantity of money of ultimate redemption, 154.

VII THE QUANTITY OF MONEy-SUBSTITUTES, M' 158

The size of bank reserves and their ratio to the quantity of money-substitutes, 158 The" creation" of bank deposits,

160 The mechanism of changes in general prices quent upon changes in the quantity of money of ultimate redemption, 171 The role of the rate of interest, 173 Bearing upon the relation between monetary theory and

conse-"value theory," 176 The relation of Bank-rate to the Quantity Equations, 178 Wicksell on Bank-rate and the

quantity of M', 183 The argument of Keynes's Treatise

on this point, 188 The" invariability" of the association between Bank-rate and changes in M': Tooke's supposed

"refutation" of the classical position, 189 The irrelevance

of this type of empirical argument, 190 The argument of

Keynes's Treatise and the classical position, 191. The trasting case of Wicksell, 195 The" Gibson Paradox," 196.

con-Market rate and "natural rate" in Keynes's Treatise, 199 The meaning of the "natural rate" in Wicksell's Interest and Prices, 201. The present positi on of the theory of the

"natural rate," 204.

VIII THE QUANTITY OF MONEy-SUBSTITUTES, M'

Bank-rate,M',and" proportional" changes in general prices,

206 The "Quantity Theory" versus the Quantity tions, again, 206. The" six points" of the Treatise with re-

Equa-spect to "The Relation of Bank-rate to the Quantity of Money," 208. The "order of events" in the modus operandi

of Bank-rate, 212 Relation of the argument to the tity Equation," 214; to the "second strand" in the "tra- ditional doctrine," 216; and to the "priority" of changes in

"Quan-Bank-rate with respect to changes in quantity of M', 217 The interpretation of the argument of Keynes's Treatise on

CHAPTER PAGEVIII THE QUANTITY OF MONEy-SUBSTITUTES,M' (Cont.)

this point, 220 The" effectiveness" of Bank-rate in the absence of a change inM',222 The case of the" rationing"

of credit, 223 The "fringe of unsatisfied borrowers," 224 Keynes on the" traditional doctrine," Wicksell and Cassel

with respect to the relation between the quantity of M' and

the maintenance of a low Bank-rate, 228.

IX THE QUANTITY OF MONEy-SUBSTITUTES, M'

(Con-tinued) '.' 231

The argument of Keynes's Treatise with respect to interest

as a "capitalization factor," 231 The traditional doctrine

on the subject, 233 Limits to the application of interest

as a "capitalization factor" in tracing the modus operandi

of Bank-rate, 233 Bearing of the argument on the

expo-sition in the Treatise, 234. The market rate of interest versus the rate of "capitalization," 237 Wicksell and Keynes on the point in question, 237 Relation of the argument to the question as to the relation between the short-term and the long-term loan market, 239 Interest

as a "Capitalization Factor" in relation to interest as a

"Cost Factor," 240 The importance of interest as a

H cost," 244. The interpretation of the Treatise on this

head, 244 Wicksell's argument with respect to the" direct" influence of changes in the rate of interest upon prices, 247 General versus "relative" prices, 248 The argument of Tooke with respect to interest as a "cost," and Wicksell's rebuttal, 249 The case of rising interest costs, 249 Bear- ing of the discussion on the question of the "priority" of

changes in P and in M ', 252 The case of falling interest

costs, 253 The relation of Wicksell's argument to that of Ricardo, 256 Application of the Wicksellian argument to the treatment of interest as a "capitalization" factor, 258.

The relation of this part of Keynes's Treatise to the

tradi-tional doctrine, 259.

X THE QUANTITY OF MONEy-SUBSTITUTES,M' tinued) 268 Reasons for examining the problem, 268 The Fundamen- tal Eql.lations and interest as a" capitalization factor," 269 The Equations and interest as a "cost factor," 270 The treatment of interest costs in the Fundamental Equations,

(Con-270 "Profits" in the Fundamental Equations and the

modus operandi of Bank-rate, 274 The relation of I

-B(= Q) to the "natural rate," 275 The "price premium,"

276 Aggregate versus marginal costs, 277 The factor

of "anticipations," 278 The decisive objection to the use

of the "profits" (Q) of the Fundamental Equations for a tracing of the modus operandi of Bank-rate, 279. (l - S)

as a summary of the forces leading to a change in the mensions of the stream of money expenditure, 280 The meaning of "Investment," 280 Wicksell and the place of

di-"investment" in the modus operandi of Bank-rate, 283.

Keynes on "speculation" versus "investment," 283 The forces determining the amount of entrepreneurial spending,

285 Keynes on the relation of the "third strand" in the

CHAPTER

X THE QUANTITY OF MONEy-SUBSTITUTES,M' (Cont.)

"traditional doctrine" to the" first strand," 285 His plies to Robertson and Hayek, 286 The subsequent steps

re-in the modus operandi of Bank-rate, 287. The re-emergence

of the Quantity Equations, 288.

.

XXI

PAGE

XI "VELOCITY OF CIRCULATION" (V) 290

State of the subject, 290 That the confusion is less than

it appears to be becomes evident when account is taken of the varying qualifications of the disputants, 295; of the true nature of the relation between the" cash-balance approach" and the concept of velocity, 296; and of the initial uncer- tainty to be expected in the exploration of uncharted fields,

297. The treatment of "velocity" in Keynes's Treatise on Money, 298.

XII THE "INCOME ApPROACH" TO THE THEORY OF

PRICES: ITS HISTORY 302

The argument of Keynes's Treatise as an example of the

"income approach," 302 Shortcomings of existing tories of that approach, 304. The various components of

his-the" income-approach" are to be found far back in economic literature, 306 Irrelevancies introduced by historians of the "income approach": the "nature" of money, 308; the

"marginal utility of money-income," 309; the "passiveness"

of prices, 309 The relation of Tooke to the" income proach," 311 Tooke's influence on Adolf Wagner, 315; and on Rnut Wicksell, 323 The influence of Wicksell, 327; and of Wagner (and N Johannsen), 329 F von Wieser,

ap-336, and his influence on Schumpeter, 338; and on Aftalion,

339 R G Hawtrey and the "income approach," 340 The concept of "income-velocity": Foster and Catchings, and "circuit velocity," 341; Robertson and Pigou, and "in- come velocity," 342 The "income approach" contains so many heterogeneous elements that it is best handled as part

of the discussion of the analysis "lying behind" each of the variables of our" Quantity Equation," 342 The Genealogy

of the "Income Approach," 343.

XIII THE "INCOME ApPROACH" AND "VELOCITY":

IN-COME VELOCITY 344

"Velocity" as an element of "superfetation," according to certain "income-theorists," 344 The supposed antithesis between emphasis upon a "stream" of money and emphasis upon the stock of money is an ancient one, 345 The reso- lution of this antithesis, however, instead of making it pos- sible to dispense with the concept of "velocity," demands the inclusion of "velocity" among price-making forces, 345 The income approach "versus" the "quantity theory," 346 The introduction of the "quantity of money" into the "in- come theory" becomes necessary as soon as we ask why the level of money incomes is higher at one time than at another, 348 History of doctrine on this point, 349 Re- lation to the question as to the place of "velocity" in an

"income" equation such as that of Aftalion,352 "Income" versus" outlay from income," 354 Bearing of the distinc-

CHAPTER PAGE

XIII THE "INCOME ApPROACH" AND "VELOCITY":

IN-COME VELOCITY (C ont.)

tion upon the place of "velocity" in an "income-equation,"

356. The position of Keynes's Treatise on the issues thus

far discussed, 356 The concept of "income-velocity" and its history, 357 Motivation underlying the concept of

"income-velocity," 364 A judgment as to the usefulness

of the concept of "income velocity" is best undertaken by comparing it with the concept of "virtual velocity," 366 Objections to the latter concept, 367 The same type of objection applies to the concept of "income velocity,' 368 The problem of "velocity" versus the problem of the mag- nitude and composition of total monetary transactions, 369.

An algebraic demonstration, 369 Importance of the tinction for a study of the mechanism of price change, 371 Its importance for the study of movements in "velocity," properly so called, 372 The methodological implications

dis-of the "cash-balance approach," 373 Further illustrations:

"income measured in money>' versus "income payments," 375; payments" into" income, and payments" out of" in- come, 379 The distinction has been concealed by certain definitions of "income," 379; but is of the greatest impor- tance for an evaluation of the concept of "income velocity,"

381. The problem of payments out of income, when related

to money income received, is properly a problem of

"ve-locity," 382; but the problem of payments into income is

a much broader problem, 382 An algebraic formulation

of the point at issue, 383 The argument against the cept of "income velocity" is not that it necessarily leads to analysis that is erroneous, but that it is not of sufficient precision for use in the central problems involved in the Theory of Prices, 385.

con-XIV THE ALTERNATIVE TO "INCOME VELOCITY" 388

Keynes's attack on the concept of "income velocity," in the

Treatise, 388. The reply of D H Robertson, 388 The test as to whether the concept of "income velocity" is

"hybrid" in character, 389 Pigou's argument with respect

to "income velocity" as a "genuine physical magnitude," judged in the light of the methodological implications of the cash-balance approach, 390; and of the difficulties raised by the notion of "physical" movement, 391 Other unsatis- factory defences of the concept of "income velocity" against the attack of Keynes, 393 Keynes on the notion of "true" velocities, 394 In what sense "income velocity" is not a

"true" velocity, 395 Results of a failure to recognize its

"hybrid" character, 396 D H Robertson on "income velocity" again, 398 The case of integration of industry,

399 Bearing of the argument on "income velocity," 399 Robertson's main criticism of Keynes's position with re- spect to "income velocity" rested upon a misunderstanding

of that position, 401 KeYnes's attack on "income-velocity" reviewed, 402 The concept of "income-velocity" does not date from "the earliest literature on our subject," 403 Its present standing, 403 The antecedents of Keynes's alter- native to "income velocity," 404 The analysis of R G Hawtrey, 407 Relation of Keynes's alternative to the

"Quantity EquatioDS," 409.

CHAPTER PAGE

xv. THE CASH-BALANCE ApPROACH 414

Keynes and the cash-balance approach, 414 The" shallianK"and its relation to "velocity," 415 The impli- cations of the expressionK = 1/V,417 The shortcomings

Mar-of the concept Mar-of "income-velocity" are not to be uted to the cash-balance approach, 420 The use of the latter should not be confined to the case of cash balances held against payments out of income, 422 The H price- level" involved in "cash-balance" equations need differ in

attrib-no wise from the "price-level" involved in equations of the Fisherine type, 424 An algebraic demonstration, 427 The argument of D H Robertson with respect to the con- cept of "latent money" and its bearing upon the relation between "cash-balance" equations and equations of the Fisherine type, 431 The cash-balance approach finds its unequivocal justification only in its use in the explanation

of changes in the velocity of circulation of money, 433 It

is therefore not fair to criticize the approach in question because it is not well-adapted for the solution of other prob- lems, 434 Misunderstandings of the claims which are properly to be advanced on behalf of the cash-balance ap- proach are probably to be attributed to certain" real bal- ance" variants of this approach, 436 Keynes on the rela- tion between "cash-balances" and "real balances," 437 The nature of the connection between the "cash-balance approach" and "general value theory," 440 The cash- balance approach and" utility analysis," 442 The" abso- lute" and the "relative" demand for cash balances, 444 It

is a mistake to insist upon the adoption of the" real balance" variant on the ground that variants of this type are de- manded by the postulates of "general value theory," 450 XVI THE CASH-BALANCE ApPROACH (Continued) 459 Corollaries of the cash-balance approach: money" in circu- lation" and money "out of circulation," 459; money as a

"store of value" and "bearer of options," 463 "Savings deposits," and their relation to "velocity," 466 Invest- ment and borrowing opportunities in relation to the size of cash balances held relative to outlay, 470 Keynes's" cash- facilities," 472 The forces determining the size of cash balances held relative to outlay, according to Keynes's

Monetary Reform, 478. "Habits" as an explanation, 479.

A summary statement of the forces determining the size of cash balances held relative to outlay, 482.

XVII THE "VOLUME OF TRANSACTIONS" (PT); THE

"PLURALITY" OF PRICE LEVELS 484 Keynes on the T of the "Fisher equation," 484 Alleged uselessness of the latter as a guide to the" purchasing power

of money," 485 History of the suggestion that pur major concern must be with the prices of consumers' goods, 486 The suggestion has not always been accompanied by an adequate supporting argument: Tooke's treatment, 487; Wicksell's treatment, 489 Relation of the suggestion to ('utility analysis," 490 The argument for a "consumers' goods" equation is in reality an argument for a "plurality

of price-levels," 495 History of the latter argument, 496 Keynes's "plurality of price-levels," 506 Relation of a

CHAPTER PA.GE XVII THE "VOLUME OF TRANSACTIONS" (PT); THE

"PLURALITY" OF PRICE LEVELS (Cont.)

"consumers' goods" equation to equations of the general

Fisherine form, 510. Examples, 511 Relation of tions of the general Fisherine form to the use of a "plurality

equa-of price-levels," 512 Relation of these equations to an equation for the price level of "output," 514 Equations

of the "total transactions" type are capable of telling us as much as equations dealing solely with the price level of output, but they also tell us more, 518 The role of "inter- mediate transactions," 519 Mises versus Wieser, 520 The conclusion stated in terms of a composite demand for cash balances, 521.

XVIII THE "VOLUME OF TRANSACTIONS" (Continued) 525

The argument developed thus far applied to the debate tween Robertson and Keynes on the relation of the latter's separate price levels to each other, and to the price level for

be-"output as a whole," 525 The key to the dispute lies in the treatment of "non-output" transactions, 527 Corol- laries: the alleged "independence" of the separate price levels, and its relation to the question as to the functions

of "partial" and "general" equilibrium analysis, tively, 531 The Keynes-Robertson debate in the light of the concept of "real balances," 534; and of the concept of

respec-"income-velocity," 537 The "volume of output" versus the "volume of transactions in output," 538 "Output" versus" goods produced for sale," 540 Relation of the dis-

tinction to certain distinctions made in the Treatise, 542;

and to the question as to the formal validity of the mental Equations under all conditions, 544 "Goods pro- duced for sale" versus "goods intended for sale," 544.

Funda-"Old" goods, 545; and their relation to the argument of the

Treatisewith respect to the sources of a discrepancy between

"Savings" and "Investment," 547 "Goods intended for sale" versus" goods sold," 548 The" velocity of circula- tion of goods," 548; and its components: the number of middlemen's sales," 554; and the rate" of sale" of goods, 563.

The treatment of these elements in Keynes's Treatise, 564.

XIX THE "VOLUME OF TRANSACTIONS" (Continued) 569 The case for the segregation of a price level of "services,"

569 The difficulty of "non-specifiable prices," 572 tion of the argument to equations of the" total transactions" type, 574 History of discussion of the rOle of "security transactions" in the Theory of Prices: Sismondi, 576; Tooke, 577; and Hawtrey, 579 The strength of the latter's argu- ment, 581; its weaknesses, 581 The" composite demand for cash-balances," again, 584 Application to the problem

Rela-of the "absorption" Rela-of "purchasing power" by the market, 585 Hawtrey's argument with respect to the role

stock-of "security transactions" further considered: the "volume" versus the "value" of "security transactions," 587 Haw- trey's real argument has to do with the merging of the price indexes of dissimilar things, 591; and not with the justifica- tion for the inclusion of "security transactions" in the equa- tion of exchange, 593 The conclusions of these chapters

XIX THE "VOLUME OF TRANSACTIONS" (Cont.)

applied to the argument of Keynes's Treatise, 595 pI as

the" price-level of new investment goods" versus pi as the

"price-level of securities," 596 The "Financial tion," 598; and its relation to an equation of the "total

Circula-transactions" type, 598 The place of "output" in such an equation, again, 599.

THEORY OF PRICES

VOLUME I

I

AN ApOLOGY FOR POLEMICS

I N THE opinion of Mr.J M Keynes, the "more cated" of recent discussions of the "Theory of Money andPrices" have brought it about that we seem, in this field, to

sophisti-be "lost in a haze where nothing is clear and everything ispossible."I From many points of view, undoubtedly,the best method of demonstrating the unfairness of Mr.Keynes's statement would be to continue to use, in signifi-cant and fruitful ways, precisely that received apparatusfor dealing with the "Theory of Money and Prices" whichseems to its detractors little more than a "haze"of con-fused analysis In the long run, indeed, this is the only way

to demonstrate it

There can be little doubt, however, that a principal son why something less than the maximum use is made oftools lying ready to our hand is that many of those whoshould be using them refrain from doing so only becausethey are not aware of the fact that the nature of these toolshas been misrepresented by writers who are themselves not

rea-in sympathy with received tradition Whenever such representation is made, surely ordinary scruples of scholar-ship would demand that the misrepresentation be corrected.There are those, to be sure, who, rightly impressed withthe futility of so much of polemical discussion, would insistthat it is better to pass over the misrepresentations insilence, and proceed to consider the "positive" contributions

mis-of those who are unsympathetic to the older body of

doc-1The General Theory of Employment, Interest, and Money (1936), 292.

The specific context in which the statement appears will be discussed at greater length in Volume II of this study.

1

trine That this is the wise procedure in many cases, onecannot deny Yet it must be obvious that, in other cases,such a procedure may easily do more to retard the progress

of our subject than would any conceivable amount ofpolemics

For, in the first place, it is clearly impossible to determinethe significance of "positive contributions" unless we areclear as to whether these contributions represent an accre-tion to, or an overthrowing of, the main body of receivedtradition In either case, discussion is obviously impossibleunless we are agreed as to the substance of the traditionwith respect to which the "contribution" in question is to beadjudged an accretion or an antithesis

The same proposition holds for any attempt to judge thesignificance of "positive contributions," when these "con-tributions" are regarded neither as avenues to results whichdemonstrate the fallaciousness of previous results obtained

by the use of old techniques, nor as techniques for handlingnew types of problem, but are regarded rather as alternativetechniques for dealing with familiar problems It is clearlynecessary, in such cases, that we should be in a position todecide whether the techniques in question are in fact su-perior to received techniques for dealing with those prob-lems This again,however, is impossible unless we arefully conversant with the substance of the techniques whichthe newer devices are designed to displace Whether welike it or not, therefore, there are occasions when polemicsbecome necessary, not only in the interest of accurate schol-arship, but also in the interest of the advancement of oursubject

II

THE "THEORY OF PRICES" AND MR KEYNES

It will be iplmediately obvious, from the pages which low, that this book, despite its title, is concerned with only apart of what should properly be included under the head of

fol-"The Theory of Prices"-namely, that part which has to do

with the effect of money upon prices in a "closed" economic

system The title has been chosen in conscious imitation of

the practice indicated by Mr Keynes in his latest book.2The reason for this is simply that both the form and thesubstance of this book-and indeed the fact that it was writ-ten at all-are due to the writings of Mr Keynes.

It would be an injustice to Mr Keynes to suggest that theappearance of confusion characterizing the "Theory ofMoney and Prices" at the present time is due solely to theimpact upon contemporary monetary theory of the Treatise

on Money and The General Theory of Employment, est, and Money. Yet there can be little doubt that this ap-pearance of confusion became really pronounced· only afterthe publication of the Treatise. Nor can there be anyserious doubt that the principal reason for this was l\1r.Keynes's insistence, both in the pages of theTreatiseand inthe discussion which followed its publication, not only thathis analysis represented a clear break with most of what hadgone before, but also that any attempt to restate the.· sub-stance of his argument in terms suggested by the olderanalysis could lead only to an obscuring, rather than to aclarification, of that argument.3

Inter-It is, therefore, only reasonable that a book representing

an attempt to defend the substance of received tradition onthe subject of the "Theory of Money and Prices" against itsdetractors should center its interest upon the arguments of

Mr Keynes The selection of Mr Keynes for thispurpose~however, can be justified by reasons other than the mere factthat it is he who is largely responsible for the feeling thatthe Principle of Continuity does not apply as a maxim ofscientific procedure at the present stage in the development

of monetary theory

The first of these additional reasons is that Mr Keynesholds a very distinguished place in contemporary economics.When a distinguished historian charges economists with

2 See especially Chapter XXI of the General Theory ;

3 See for example, Keynes's "Reply to Dr Hayek,"

Economica,Novem-ber, 1931, 6: "Those who are sufficiently steeped in the old point of view simply cannot bring themselves to believe that I am asking them to step into a new pair of trousers, and will insist on regarding it as nothing but an embroidered version of the old pair which they have been wearing for years." For examples of passages in the Treatise itself which are relevant

to a judgment as to Mr Keynes's understanding of the relationship of the apparatus presented in theTreatiseto the older analysis, see below, pp 13 ff.

having allowed their subject to fall into "utter confusion,"

or when an equally distinguished chemist sneers at the ventions and half-truths that pass for economics," we areamused, perhaps, or mildly annoyed, but hardly deeply con-cerned.4 The invasion of barbarians into fields utterlystrange to them is, after all, a phenomenon to which econo-mists, above all others, have by this time become accus-tomed Mr Keynes, however, is no barbarian He hasbeen called, rightly, "the most famous of living econo-mists";5 no one could dispute his claim to the position of one

"con-of the most eminent "con-of living monetary theorists; and hisutterances have naturally exerted an influence correspond-ing to this position of eminence An attempt, therefore, tomeet Mr Keynes's strictures upon the present state ofmonetary theory can hardly be regarded as an unnecessaryconcern with the type of inconsequential criticism to whichtraditional economics has always been subjected, but whichit·has always managed somehow to survive

Nor is this all Mr Keynes himself has been chargedwith what ought to be regarded as the most serious of crimesagainst scholarship, and would be so regarded if there werenot so many who would stand convicted if the record werecarefully kept: the crime, namely, of charging a group,vaguely described as "economists" generally, with havingheld notions which it is in many cases very difficult to showthat any important group of economists ever did hold.6 Itwould ill· become the defenders of the tradition which isunder such vigorous attack to adopt a similar set of tactics,and content themselves only with vague references to "thecritics" of that tradition The selection of Mr Keynes atleast makes it possible'to cite chapter and verse, so that thereader himself may judge whether the position of the attack-ers is as seriously misrepresented by the defenders as thelatter believe their position to have been misrepresented bythe former

4The quotations are taken from Charles A Beard, The Open Door at Home (1935), 125, and Frederick Soddy, The Role of Money (1935), 4 f.

IISo H D Henderson, in The Spectator, February 14, 1936, 263. .

8See, in this connection, the comment of Professor Pigou, in Economwa,

May, 1936, 116, n 1.

The purpose of the discussion that follows, then, is therestatement of the subject matter of received doctrine uponthe subject of the "Theory of Money and Prices," withspecial reference to the criticisms levied against that doc

to be regarded as important is the restatement and the de fense, rather than 5uch incidental counterattack upon alter natives of the type proposed by Mr Keynes as may be asso

lows is certainly intended in no sense as a critique of all parts

thing, as Professor Pigou has put it, Mr Keynes has gone

"on a sniping expedition in a large village"; and it is doubt ful whether it would be wise, even if one had the patience, toattempt to "track down the course of his every bullet."7The most that can be claimed for the present work is that itproceeds on the assumption that something is to be said fordividing up the village into important sectors, and for allow ing different individuals to trace the bullets that have fallenwithin the particular sector in which they are interested.The sector to which this study is alone devoted is that which

Mr Keynes himself has demarcated under the heading ofthe "Theory of Prices."

IfIbid., 116.

"QUANTITY EQUATIONS" AND THEIR MEANING

"Quantity Equations" and

"The Quantity Theory"

I

QUANTITY EQUATIONS AND THE THEORY OF PRICES

IT is fair to say that, prior to the publication of Mr

Keynes's Treatise on Money, little objection would have

been raised to the proposition that any attempt ·to explainthe determination of general prices must, implicitly or explic-itly, start with a "quantity equation" in some form -that is,with a formulation with respect to the forces determining

"prices" in which the quantity of money was given an

unmis-takable place.1 When, therefore, the analytical apparatus

presented in the Treatise for dealing with the problem of the

determination of prices was interpreted in some quarters asdispensing once and for all with the necessity for the familiar

"quantity equations," the effect could not have been wise than disturbing For, in substance, we were beingasked to turn our backs upon a type of reasoning which goesback at least as far as the time of Jean Bodin; although alge-braic "quantity equations" embodying this reasoning hadnot begun to appear extensively in economic literature prior

other-to the middle of the nineteenth century or, at best, the latterpart of the eighteenth.2

1 The only instances that might be adduced as significant exceptions to this generalization would be represented by those cases in which (1) it was suggested that acceptance of an "income approach" to the problem of the value of money involved a rejection or supersession of the older "quantity equations," and (2) there were objections to the use of certain "quantity equations" either because of their supposedly "truistic" character, or- paradoxically-because of their "untrue" character On the first, see below,

pp 344 ff., and on the second, pp 88 ff and 46 ff.

2 Some writers have insisted that the type of reasoning involved goes back

to the Gemeine Stimmen von der Muntz of the Albertine-Ernestine troversy (1530); others that it goes back to Julius Paulus (ca. 200 A.D.);

con-9

Our knowledge with respect to the history of algebraic "quantity tions" has been considerably extended in recent years Attention has been called, for example, to a crude formulation, containing no term for

equa-"velocity of circulation," which was presented by Henry Lloyd in 1771 3

It has also been shown that at least three algebraic formulations of the Uequation of exchange" in essentially the "Fisherine" form were presented

in the 1850's, namely, those of Roscher (1854), Bowen (1856), and seur (1858).4 More recently, attention has been called to the fact that

Levas-K H Rau presented a "Fisherine" equation in 1841-i e., some thirteen years before Roscher 1S This last discovery has led to the suggestion that what has been called throughout this study, in conformity with current practice, the "Fisherine equation" should be called henceforth the "Rau- Fisher equation." 6 The danger of desiring prematurely to rechristen a given doctrine or analytical device in the light of the latest discovery

as to its "origin" has, however, more than once been demonstrated in the history of economic doctrine; and in the present instance it has already been demonstrated by the fact that it is now possible to cite more than and still others that it goes back to· Chinese writers of 500 B.C.! No fur- ther justification for the selection in the text of Bodin, however, is needed, for the purpose in hand, than is offered by the fact that.he provided what was probably the most influential among the earlier examples of a recog- nition of the importance of changes in the supply of metallic money for the determination of the general level of prices It will be noted that I have not characterized Bodin as the "founder" of "the quantity theory."

Cf what is said on this matter below, p 96, n 54.

3Cf.myarticle in the Zeitschrift fur N ationalOkonomie, IV (1932), 197 n The general neglect of Lloyd's book by later English writers-a matter

commented upon by Jevons (The Theory of Political Economy, p xlii of

the 4th [1924] edition)-prevented these writers from even considering,

to say nothing of developi;ng further, his formula The formula was sidered, however, by Lloyd's Italian contemporaries and their successors See, e g., the "Estratto del saggio sulla teoria della moneta del general Lloyd, stampato in Londra nel 1771," as appended by "the mathema- tician Paolo Frisi" to the sixth (1772) edition of Pietro Verri's M editazioni

con-8ulla economia politica (reprinted in Custodi's Scrittori classici di economia p.olitica, parte moderna, XVII [1804], 375 ff.,and, more recently, by M.

Fasiani in Annali distatistica e di economia, V [Genoa, 1937], 271 ff.) Frisi's discussion of Lloyd was copied almost verbatim by F Fuoco, in the latter's "Applicazione dell' algebra all' economia politica" (1827), 108 ff (173 ff.of Professor Fasiani's edition, Annali di statisticae di economia, V).

4Seethe Journal of Political Economy, XXXIX (1931), 574, n 11 (the

reference to Levasseur's La Question de l'Or there, given should be p. 150

instead of p 148).

I See K F Maier, Goldwanderungen (Jena, 193.f~), 9 n., where the fourth

(1841) edition of Rau's Lehrbuch der politischen Okonomie, Vol.I siUze der Volkswirtschaftslehre) , p 305, is cited The equation does not appear in the corresponding passage of the French translation (1839) of the third (1837) edition of Rau, which is the only example of the editions of Rau prior to that of 1841 which I have been able to consult.

(Grund-880 F Lutz, "Vber die Umlaufsgeschwindigkeit des Geldes," in

Jahrbil-cher fur N ationalokonomie und Statistik, CXLIV (1936), 387 The erine" equation has, of course, also been called the "N'ewcomb-Fisher equation." See,on this practice, my comments in the Journal of Political

"Fish-Economy, XLIII (1935), 149, n 10.

one instance prior to Rau In 1813, for example, the Italian economist Cagnazzi published an equation of the general form MV = [P]G'v-

i.e., an equation identical with that published forty-three years later by Bowen; and in 1819 Samuel Turner presented an equation which was virtually identical in form with that presented by Roscher some thirty- five years afterward 7 Still more striking is the case of Sir John W.

Lubbock, who, in a work published anonymously in 1840, wrote, as the first of his "'equations of condition, which connect the quantities which occur in the theory of currency," ~a(%+E= lD+mB+nC-an equation which, when rewritten in more familiar symbols, becomes noth- ing more nor less than ~pq+E= M'V' +.M"V"+MV, in which

"Spq, MV, and M'V' have essentially the meanings given to them by Fisher; M"V" is the volume of bills of exchange used as money, times

IfFor Cagnazzi's formulation, see the extracts from his Elementi di

eco-nomia politicaincluded by Fasiani in the latter's admirable "Note suisaggi

economici di Francesco Fuoco," Annali di statistica e di economia, V~ 112

ti., especially p 113 The "defect" which Fasiani attributes to Cagnazzi's formula M c= DC, in which c represents the "[velocity of] circulation of

money," D the "quantity of commodities," and C their "[velocity culation"-namely, that it does not include a term for "prices"-is at worst

oflcir-a merely formoflcir-al one; for Coflcir-agnoflcir-azzi, who regoflcir-arded his equoflcir-ation oflcir-as oflcir-a lation of the conditions for "the equilibrium of· the· two circulations [of money and of goods, respectively] ," obviously considered a change in prices

formu-to be the criterio:l of "disequilibrium." Even formally, moreover, he wasno more at fault than Bowen, who, though he regarded himself as translating into algebraic terms John Stuart Mill's enumeration of the forces deter- mining the "value of money," likewise did not bother to include a special

term for "prices." For Turner's formulation, see his LeUer Addressed to

the Right Honorable Robert Peel, etc., etc., Late Chairman of the mittee of Secrecy,· Appointed to consider of the State of the Bank ofEng- land, with Reference to the Expediency of the Resumption· of Cash' Pay- ments at the Period fixed by Law (2d ed., London, 1819), 12 if. The a of Turner's "algebraic statement" a=bc, in which b was "the quantity of

Com-the precious metals circulating" in a country (i e.,M),arid c was the culating power, or the number of times thatb changes hands" within a given period of time (i ·e., V), was defined as the "value of the· commodi" ties exchanged in a given portion of time, as a year." It was, there- fore, the exact equivalent of Roscher'suin the equationu= ms,in which

"cir-m is the equivalent ofM and sis the equivalent ofV in the' ordinary

"equa-tion of exchange"-u being in fact defined as the "amount of annual

ex-changes" (Anzahl der jiihrlichen Umsiitze) for money The case of Turner

is cited by Professor Viner (Studies in· the Theory of International" Trade

[1937], 249, n 23) along with that of Henry Lloyd and the anonymous

author of The Theory of Money JOT, A Practical Inquiry~ntothe Present State of the Circulating Medium, etc., (London, 1811), as having 'provided

"algebraic (or arithmetic) formulations of the' equation of exchange in which the velocity of circulation of the means of payment·· had been expressly provided for." The citation of Lloyd in this context, however,· is a slip, since, as we have seen, his algebraic formulation did not include a term for velocity; and the formulation of the author of The Theory of Money

(pp 41 ti.) is perhaps better regarded as an arithmetic illustration ofa algebraic formulation of the equation of exchange For an earlier example

non-of such a non-algebraic formulation, see the reference to Beccaria' (1769) in

my "Leon Walras and the Cash-balance Approach," Journal of Political

the "velocity of circulation" of such bills; and the termEhas a purpose not greatly dissimilar from that assigned to the tennRin M A Cope- land's formulation of the equation of exchange asPT+R ==1\JV 8

It is this type of formulation, we were told, which Mr.Keynes had, in the Treatise, "definitely abandoned infavour of the 'savings and investment' analysis."9 It is ofcourse true that certain commentators upon Keynes's argu-ment differed from this interpretation of its drift; but I havenot been able to find any cases in which the commentators inquestion supposed that, in so doing, they were stating Mr.Keynes's own intention In some instances, for example,their position seems to have been simply that Mr Keynes'snew 'equations could not be regarded as having supersededthe older quantity equations so long as it remained true that,

in the absence of a clear demonstration of the falseness orthe uselessness of the older equations, the conclusions

reached by Mr Keynes through the use of these new

equa-tions were subject to continued check by the use of the olderequations, which, therefore, could hardly be said to havebeen "abandoned."10

To say, in any case, that some commentators upon the

Treatisesought to demonstrate that the use of the new

equa-8 See [John W Lubbock], On Currency, iv, n.; also 4, 6, 24, 37, and 43.

(Lubbock's equation is reproduced by Viner,Studies, 249, n 23; but, through

some error, X appears in place of Lubbock's 4.) On some of the pages cited from Lubbock, the term which we have/written lD appears as A,

representing "the amount of checks drawn." Cf., however, pp 24 and 43

of Lubbock's book On the relation of Lubbock'sE to Copeland'sR, see below, pp 57 f.

980 R C Mills and E R Walker, Money (1935), 96; cf also J H.

Williams, "The Monetary Doctrines of J M Keynes," Quarterly Journal

of Economics, XLV (1931), 549 These authors, and others that could be

cited in this connection, use the expression "the quantity theory" in place

of "quantity equations," which is what is called for by their context: a usage which, as must be obvious from section iii of this chapter, is copied from

Mr~ K'eynes himself.

10 The pointed remarks of Mr D H Robertson, to which reference is made below, pp 15 f., may be taken as typical, in this connection When, for example, Robertson characterized the first of the "Fundamental Equa- tions" of theTreatiseas being based upon "that rigorous Fisherine concept

of a certain flow of money in a given time-interval meeting a: certain flow

of goods in the same time-interval" (Economic Journal, XLI [1931], 400,

he was presumably to be understood as having argued that, unless the first equation was so interpreted, and unless the argument based upon it was translated into the terms of equations of the general "Fisherine" form, we run the danger of obtaining results which are either wrong, or in conflict with Mr Keynes's supposed desire to avoid the charge that the older equa- tions would, under certain circumstances, lead us to wrong results.