Irving Fisher on Equation of Exchange - Dictionary of Arguments

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Equation of Exchange: The Equation of Exchange, MV=PQ, represents the relationship between money supply (M), its velocity (V), the price level (P), and output (Q. It shows how money circulates in an economy, highlighting the link between monetary policy and economic activity. See also Quantity theory, Irving Fisher. _____________ Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

> Fisher, Irving	> Equation of Exchange	Irving Fisher on Equation of Exchange - Dictionary of Arguments Rothbard III 830 Equation of Exchange/Fisher/Rothbard: The classic exposition of the equation of exchange was in Irving Fisher's Purchasing Power of Money.⁽¹⁾ Fisher describes the chief purpose of his work as that of investigating "the causes determining the purchasing power of money." Money is a generally acceptable medium of exchange, and purchasing power is rightly defined as the "quantities of other goods which a given quantity of goods will buy.“⁽²⁾ He explains that the Iower the prices of goods, the larger will be the quantities that can be bought by a given amount of money, and therefore the greater the purchasing power of money. Vice versa if the prices of goods rise. Rothbard III 831 RothbardVsFisher, Irving: This is correct; but then comes this flagrant non sequitur: "In Short, the purchasing power of money is 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.“⁽³⁾ Rothbard: From then on, Fisher proceeds to investigate the causes of the "price level"; thus, by a simple "in short," Fisher has leaped from the real world of an array of individual prices for an innumerable list of concrete goods into the misleading fiction of a "price level," without discussing the grave diffculties which any such concept must face. >Price level/Fisher. Rothbard III 832 Def price level/Fisher/Rothbard: The "price level" is allegedly determined by three aggregative factors: the quantity of money in circulation, its "velocity of circulation" - the average number of times during a period that a unit of money is exchanged for goods - and the total volume of goods bought for money. These are related by the famous equation of exchange: MV = PT. M - Money supply V - Velocity of circulation P – Price level T - Expenditures This equation of exchange is built up by Fisher in the following way: Def price level/Fisher: First, consider an individual exchange transaction - Smith buys 10 pounds of sugar for 7 cents a pound.⁽⁴⁾ An exchange has been made, Smith giving up 70 cents to Jones, and Jones transferring 10 pounds of sugar to Smith. From this fact Fisher somehow deduces that "10 pounds of sugar have been regarded as equal to 70 cents, and this fact may be expressed thus: 70 cents = 10 pounds multiplied by 7 cents a pound.⁽⁵⁾ RothbardVsFisher: This off-hand assumption of equality is not self-evident, as Fisher apparently assumes, but a tangle of fallacy and irrelevance. Value/equality/valuation: Who has "regarded" the 10 pounds of sugar as equal to the 70 cents? Certainly not Smith, the buyer of the sugar. He bought the sugar precisely because he considered the two quantities as unequal in value; to him the value of the sugar was greater than the value of the 70 cents, and that is why he made the exchange. On the other hand, Jones, the seller of the sugar, made the exchange precisely because the values of the two goods were unequal in the opposite direction, i.e., he valued the 70 cents more than he did the sugar. Exchange/RothbardVsAristotle: There is thus never any equality of values on the part of the two participants. The assumption that an exchange presumes some sort of equality has been a delusion of economic theory since Aristotle, and it is surprising that Fisher, an exponent of the subjective theory of value in many respects, fell into the ancient trap. Equality: There is certainly no equality of values between two goods exchanged or, as in this case, between the money and the good. Is there an equality in anything else, and can Fisher's doctrine be salvaged by finding such an equality? Obviously not; there is no equality in weight, length, or any other magnitude. But to Fisher, the equation represents an equality in value between the "money Side" and the "goods side"; (…). Rothbard III 833 Fisher: „[T]he 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.... The goods side is made up of the products of quantities of goods exchanged multiplied by respective prices.“⁽⁶⁾ Rothbard III 834 Equation of exchange: Fisher considers that this equation yields the significant information that the price is determined by the total money spent divided by the total supply of goods sold. RothbardVsFisher: Actually, of course, the equation, as an equation, tells us nothing about the determinants of price; thus, we could set up an equally truistic equation (…) This equation is just as mathematically true as the other, and, on Fisher's own mathematical grounds, we could argue cogently that Fisher has "left the important wheat price out of the equation." We could easily add innumerable equations with an infinite number of complex factors that "determine" price. Solution/Rothbard: The only knowledge we can have of the determinants of price is the knowledge deduced logically from the axioms of praxeology. ((s) I.e. from subjective valuations in the course of human action.) >Praxeology/Rothbard. Rothbard III 835 Determinants of price/Fisher: If we consider the equation of exchange as revealing the determinants ofprice, we find that Fisher must be implying that the determinants are [e.g.,] the "70 cents" and the "10 pounds of sugar." RothbardVsFisher: But it should be clear that things cannot determine prices. Things, whether pieces of money or pieces of sugar or pieces of anything else, can never act; they cannot set prices or supply and demand schedules. All this can be done only by human action: only individual actors can decide whether or not to buy; only their value scales determine prices. >Value/Rothbard, >Price level/Fisher. Rothbard III 839 Weighted average/Solution/Fisher: Fisher's more complicated concept of a weighted average, with the prices weighted by the quantities of each good sold, solves the problem of units in the numerator but not in the denominator: P = pQ + p’Q‘ + p‘‘Q‘‘ / Q + Q‘ + Q‘‘. RothbardVsFisher: The pQs are all money, but the Q's are still different units. Thus, any concept of average price level involves adding or multiplying quantities of completely different units of goods, such as butter, hats, sugar, etc., and is therefore meaningless and illegitimate. Even pounds of sugar and pounds of butter cannot be added together, because they are two different goods and their valuation is completely different. And if one is tempted to use poundage as the common unit of quantity, what is the pound weight of a concert or a medical or legal service?⁽⁷⁾ Equation of Exchange/RothbardVsFisher: It is evident that PT, in the total equation of exchange, is a completely fallacious concept. While the equation E = pQf or an individual transaction is at least a trivial truism, although not very enlightening, the equation E = PT for the whole society is a false one. Neither P nor T can be defined meaningfully, and this would be necessary for this equation to have any validity. We are left only with E = pQ + p'Q', etc., which gives us only the useless truism, E =E.⁽⁸⁾ >Velocity of circulation/Fisher. Rothbard III 840 Rothbard: In fact, since V is not an independently defined variable, M must be eliminated from the equation as well as V, and the Fisherine (and the Cambridge) equation cannot be used to demonstrate the "quantity theory of money." And since M and V must disappear, there are an infinite number of other "equations of exchange" that we could, with equal invalidity, uphold as "determinants of the price level." Thus, the aggregate stock of sugar in the economy may be termed s, and the ratio of E to the total stock of sugar may be called "average sugar turnover," or U. This new "equation of exchange" would be: SU = PT, and the stock of sugar would suddenly become a major determinant of the price level. Or we could substitute A = number of salesmen in the country, and x = total expenditures per salesman, or "salesmen turnover," to arrive at a new set of "determinants" in a new equation. And so on. >Quantity theory. 1. Fisher, Irving, Purchasing Power of Money, 2nd ed. New York: Macmillan, [1913] 1926. Reprinted as volume 4 of The Works of Irving Fisher, William J. Barber and James Tobin, eds. Pickering, 1997. especially pp. 13 ff. 2. Ibid., p. 13. 3. Ibid., p. 14. 4. We are using "dollars" and "cents" here instead of weights of gold for the sake of simplicity and because Fisher himself uses these expressions. 5. Fisher, Purchasing Power of Money, p. 16. 6. Ibid., p. 17. 7. For a brilliant critique of the disturbing effects of averaging even when a commensurable unit does exist, see Louis M. Spadaro, "Averages and Aggregates in Economics" in on Freedom and Free Enterprise, pp. 140-60. 8. See Clark Warburton, "Elementary Algebra and the Equation of Exchange," American Economic Review, June, 1953, pp. 3 58-61. Also see Mises, Human Action, p. 396; B.M. Anderson, Jr., The Value of Money (New York: Macmillan & Co., 1926), pp. 154-64; and Greidanus, Value of Money, pp. 59-62. _____________ Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.	F.M. Fisher I Franklin M. Fisher Disequilibrium Foundations of Equilibrium Economics (Econometric Society Monographs) Cambridge 1989 Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977

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