CHAPTER VIII
THE "EQUATION OF EXCHANGE"
In Professor Irving Fisher's Purchasing Power of Money[130] we have the most uncompromising and rigorous statement of the quantity theory to be found in modern economic literature. We have, too, a book which follows the logic of the quantity theory more consistently than any other work with which I am acquainted. The book deals with the theory more elaborately and with more detail than any other single volume, and sums up most of what other writers have had to say in defence of the quantity theory. Professor Fisher's book has, moreover, received such enthusiastic recognition from reviewers and others as to justify one in treating it as the "official" exposition of the quantity theory. Thus, Sir David Barbour cites Professor Fisher as the authority on whom he relies for such justification of the theory as may be needed,[131] while Professor A. C. Whitaker declares that he adopts "without qualification the whole body of general monetary theory" for which Professor Fisher stands.[132] Professor J. H. Hollander has recently referred to Professor Fisher's work on money and prices as a model of that combination of theory and inductive verification which constitutes real science.[133] The American Economic Review presents as an annual feature Professor Fisher's "Equation of Exchange."
Not all, by any means, of those who would call themselves quantity theorists would concur in Professor Fisher's version of the doctrine—Professor Taussig, notably, introduces so many qualifications, and admits so many exceptions, that his doctrine seems to the present writer like Professor Fisher's chiefly in name. But there is no other one book which could be chosen which would serve nearly as well for the "platform" of present-day quantity theorists as The Purchasing Power of Money. Partly for that reason, and partly because the book lends itself well to critical analysis, I shall follow the outline of the book in my further statement and criticism of the quantity theory, indicating Professor Fisher's views, and indicating the points at which other expositions of the quantity theory diverge from his, setting his views in contrast with those of other writers. We shall find that this method of discussion will furnish a convenient outline on which to present our final criticisms of the quantity theory, and parts of the constructive doctrine of the present book.
First, Professor Fisher presents in the baldest possible form the dodo-bone doctrine. The quality of money is irrelevant. The sole question of importance is as to its quantity—the number of money-units.[134] I shall not here discuss this point, as a previous chapter has given it extended analysis, except to repeat that it is in fact an essential part of the quantity theory. If the quality of money is a factor, a necessary factor, to consider, then obviously we have something which will disturb the mechanical certainty of the quantity theory. Professor Fisher is thoroughly consistent with the spirit of his general doctrine on this point.
Second, Professor Fisher has no absolute value in his scheme. By the value of money he means merely its purchasing power, and by its purchasing power he means nothing more than the fact that it does purchase: the purchasing power of money is defined as the reciprocal of the level of prices, "so that the study of the purchasing power of money is identical with the study of price levels." (Loc. cit., p. 14.) In this, again, Professor Fisher is absolutely true to the spirit and logic of the quantity theory doctrine. The equilibration of numbers of goods, and numbers of dollars, in a mechanical scheme, gives prices—an average of prices, and nothing else. Any psychological values of goods or of dollars would upset the mechanism, and mess things up. They are properly left out, if one is to be happy with the quantity theory. Fisher, in discussion of Kemmerer's Money and Credit Instruments, has criticised the exposition of the utility theory of value with which Kemmerer prefaces his exposition of the quantity theory, as "fifth wheel." I agree thoroughly with Fisher's view in this, and would add that the only reason that it has made Kemmerer little trouble in the development of his quantity theory is that he has made virtually no use of it there! The two bodies of doctrine, in Kemmerer's exposition, are kept, on the whole, in separate chapters, well insulated. Coupled with this purely relative conception of the value of money, however, there is, in Fisher's scheme, an effort to get an absolute out of it: the general price-level is declared to be independent of, and causally prior to,[135] the particular prices of which it is an average. I mention this remarkable doctrine here, reserving its discussion for a later chapter.[136]
A further feature of Professor Fisher's system, to which especial attention must be given, is the large rôle played in it by the "equation of exchange." This device has been used by other writers before him, notably by Newcomb, Hadley, and Kemmerer, receiving at the hands of the last named an elaborate analysis. But Fisher, basing his work on Kemmerer's, has made even more extensive use of the "equation of exchange," and has given it a form which calls for special consideration.[137] The "equation of exchange," on the face of it, makes an exceedingly simple and obvious statement. Properly interpreted, it is a perfectly harmless—and, in the present writer's opinion, useless—statement. It gives rise to complications, however, as to the meaning of the algebraic terms employed, which we shall have to study with care. The starting point is a single exchange: a person buys 10 pounds of sugar at seven cents a pound. "This is an exchange transaction in which 10 pounds of sugar have been regarded as equal to 70 cents, and this fact may be expressed thus: 70 cents = 10 pounds of sugar multiplied by 7 cents a pound. Every other sale and purchase may be expressed similarly, and by adding them all together we get the equation of exchange for a certain period in a given community."[138] The money employed in these transactions usually serves several times, and hence the money side of the equation is greater than the total amount of money in circulation. In the preliminary statement of the equation of exchange, foreign trade, and the use of anything but money in exchanges are ignored, but later formulations of the equations are made to allow for them. "The equation of exchange is simply the sum of the equations involved in all individual exchanges in a year.... And in the grand total of all exchanges for a year, the total money paid is equal in value to the total value of the goods bought. The equation thus has a money side and a goods side. The money side is the total money paid, and may be considered as the product of the quantity of money multiplied by its rapidity of circulation. The goods side is made up of the products of quantities of goods exchanged multiplied by their respective prices."
Letting M represent quantity of money, and V its velocity or rapidity of circulation, p, p´, p´´, etc., the average prices for the period of different kinds of goods, and Q, Q´, Q´´, etc., the quantities of different kinds of goods, we get the following equation: