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4. Prices and Consumption > 5. The Marginal Utility of Money

B. The Money Regression

It is obvious that this vitally important problem of circularity (X depends on Y, while Y depends on X) exists not only in regard to decisions by consumers but also in regard to any exchange decision in the money economy. Thus, let us consider the seller of the stock of a consumers’ good. At a given offered money price, he must decide whether to sell the units of his stock or whether to hold on to them. His eagerness to sell in exchange for acquiring money is due to the use that the money would have for him. The money would be employed in its most important uses for him, and this will determine his evaluation of the money—or its marginal utility of addition. But the marginal utility of addition of money to the seller of the stock is based on its already being money and its ready command of other goods that the seller will buy—consumers’ goods and factors of production alike. The seller's marginal utility therefore also depends on the previous existence of money prices for the various goods in the economy.

Similarly, for the laborer, landowner, investor, or owner of a capital good: in selling his services or goods, money has a marginal utility of addition, which is a necessary prior condition to his decision to sell the goods and therefore a determinant in his supply curve of the good for money. And yet this marginal utility always depends on there being a previous array of money prices in existence. The seller of any good or service for money, therefore, ranks the marginal utility of the money that he will obtain against the marginal utility of holding on to the good or service. Whoever spends money to buy any good or service ranks the marginal utility which keeping the money has for him against the marginal utility of acquiring the good. These value scales of the various buyers and sellers determine the individual supply-demand schedules and hence all money prices; yet, in order to rank money and goods on his value scale, money must already have a marginal utility for each person, and this marginal utility must be based on the fact of pre-existing money prices of the various goods.18

The solution of this crucial problem of circularity has been provided by Professor Ludwig von Mises, in his notable theory of the money regression.19 The theory of money regression may be explained by examining the period of time that is being considered in each part of our analysis. Let us define a “day” as the period of time just sufficient to determine the market prices of every good in the society. On day X, then, the money price of each good is determined by the interactions of the supply and demand schedules of money and the good by the buyers and sellers on that day. Each buyer and seller ranks money and the given good in accordance with the relative marginal utility of the two to him. Therefore, a money price at the end of day X is determined by the marginal utilities of money and the good as they existed at the beginning of day X. But the marginal utility of money is based, as we have seen above, on a previously existing array of money prices. Money is demanded and considered useful because of its already existing money prices. Therefore, the price of a good on day X is determined by the marginal utility of the good on day X and the marginal utility of money on day X, which last in turn depends on the prices of goods on day X – 1.

The economic analysis of money prices is therefore not circular. If prices today depend on the marginal utility of money today, the latter is dependent on money prices yesterday. Thus, in every money price in any day, there is contained a time component, so that this price is partially determined by the money prices of yesterday. This does not mean specifically that the price of eggs today is partially determined by the price of eggs yesterday, the price of butter today by that of yesterday, etc. On the contrary, the time component essential to each specific price today is the general array of yesterday's money prices for all goods, and, of course, the subsequent evaluation of the monetary unit by the individuals in the society. If we consider the general array of today's prices, however, an essential time component in their determination is the general array of yesterday's prices.

This time component is purely on the money side of the determining factors. In a society of barter, there is no time component in the prices of any given day. When horses are being exchanged against fish, the individuals in the market decide on the relative marginal utilities solely on the basis of the direct uses of the commodities. These direct uses are immediate and do not require any previously existing prices on the market. Therefore, the marginal utilities of direct goods, such as horses and fish, have no previous time components. And, therefore, there is no problem of circularity in a system of barter. In such a society, if all previous markets and knowledge of previous prices were somehow wiped out, there would, of course, be an initial period of confusion while each individual consulted his value scales and tried to estimate those of others, but there would be no great difficulty in speedily re-establishing the exchange markets. The case is different in a monetary economy. Since the marginal utility of the money commodity depends on previously existing money prices, a wiping out of existing markets and knowledge of money prices would render impossible the direct re-establishment of a money economy. The economy would be wrecked and thrown back into a highly primitive state of barter, after which a money economy could only slowly be re-established as it had been before.

Now the question may be raised: Granted that there is no circularity in the determination of money prices, does not the fact that the causes partially regress backward in time simply push the unexplained components back further without end? If today's prices are partly determined by yesterday's prices, and yesterday's by those of the day before yesterday, etc., is not the regression simply pushed back infinitely, and part of the determination of prices thus left unexplained?

The answer is that the regression is not infinite, and the clue to its stopping point is the distinction just made between conditions in a money economy and conditions in a state of barter. We remember that the utility of money consists of two major elements: the utility of the money as a medium of exchange, and the utility of the money commodity in its direct, commodity use (such as the use of gold for ornaments). In the modern economy, after the money commodity has fully developed as a medium of exchange, its use as a medium tends greatly to overshadow its direct use in consumption. The demand for gold as money far exceeds its demand as jewelry. However, the latter use and demand continue to exist and to exert some influence on the total demand for the money commodity.

In any day in the money economy, the marginal utility of gold and therefore the demand for it enter into the determination of every money price. The marginal utility of gold and the demand for it today depend on the array of money prices existing yesterday, which in turn depended on the marginal utility of gold and the demand for it yesterday, etc. Now, as we regress backwards in time, we must eventually arrive at the original point when people first began to use gold as a medium of exchange. Let us consider the first day on which people passed from the system of pure barter and began to use gold as a medium of exchange. On that day, the money price, or rather, the gold price, of every other good depended partially on the marginal utility of gold. This marginal utility had a time component, namely, the previous array of gold prices, which had been determined in barter. In other words, when gold first began to be used as a medium of exchange, its marginal utility for use in that capacity depended on the existing previous array of gold prices established through barter. But if we regress one day further to the last day of barter, the gold prices of various goods on that day, like all other prices, had no time components. They were determined, as were all other barter prices, solely by the marginal utility of gold and of the other goods on that day, and the marginal utility of gold, since it was used only for direct consumption, had no temporal component.

The determination of money prices (gold prices) is therefore completely explained, with no circularity and no infinite regression. The demand for gold enters into every gold price, and today's demand for gold, in so far as it is for use as a medium of exchange, has a time component, being based on yesterday's array of gold prices. This time component regresses until the last day of barter, the day before gold began to be used as a medium of exchange. On that day, gold had no utility in that use; the demand for gold was solely for direct use, and consequently, the determination of the gold prices, for that day and for all previous days, had no temporal component whatever.20,21

The causal-temporal pattern of the regression may be portrayed as in the diagram in Figure 38. Consecutive days are numbered 1, 2, 3, etc., and, for each period, arrows depict the underlying causal factors determining the gold prices of goods on the market. For each period of time, the gold prices of goods are fundamentally determined by the relative marginal utilities of gold and other goods on individual value scales, and the marginal utilities of gold are based on the gold prices during the preceding period. This temporal component, depicted by an arrow, continues backward until the period of barter, when gold is used only for direct consumption or production purposes and not as a medium of exchange. At that point there is no temporal dependence on preceding gold prices, and the temporal arrow disappears. In this diagram, a system of barter prevails on days 1, 2, and 3, and gold is used as a medium of exchange on day 4 and thereafter.

One of the important achievements of the regression theory is its establishment of the fact that money must arise in the manner described in chapter 3, i.e., it must develop out of a commodity already in demand for direct use, the commodity then being used as a more and more general medium of exchange.

Demand for a good as a medium of exchange must be predicated on a previously existing array of prices in terms of other goods. A medium of exchange can therefore originate only according to our previous description and the foregoing diagram; it can arise only out of a commodity previously used directly in a barter situation, and therefore having had an array of prices in terms of other goods. Money must develop out of a commodity with a previously existing purchasing power, such as gold and silver had. It cannot be created out of thin air by any sudden “social compact” or edict of government.

On the other hand, it does not follow from this analysis that if an extant money were to lose its direct uses, it could no longer be used as money. Thus, if gold, after being established as money, were suddenly to lose its value in ornaments or industrial uses, it would not necessarily lose its character as a money. Once a medium of exchange has been established as a money, money prices continue to be set. If on day X gold loses its direct uses, there will still be previously existing money prices that had been established on day X – 1, and these prices form the basis for the marginal utility of gold on day X. Similarly, the money prices thereby determined on day X form the basis for the marginal utility of money on day X + 1. From X on, gold could be demanded for its exchange value alone, and not at all for its direct use. Therefore, while it is absolutely necessary that a money originate as a commodity with direct uses, it is not absolutely necessary that the direct uses continue after the money has been established.

The money prices of consumers’ goods have now been completely explained in terms of individual value scales, and these value scales have been explained up to the point of the content of the subjective use-valuations of each good. Economics is not concerned with the specific content of these ends, but with the explanation of various phenomena of action based on any given ends, and therefore its task in this sphere is fully accomplished by tracing these phenomena back to subjective valuations of useful goods.22

  • 18. It is true that
    he who considers acquiring or giving away money is, of course, first of all interested in its future purchasing power and the future structure of prices. But he cannot form a judgment about the future purchasing power of money otherwise than by looking at its configuration in the immediate past. (Mises, Human Action, p. 407)
  • 19. ee Mises, Theory of Money and Credit, pp. 97–123, and Human Action, pp. 405–08. Also see Schumpeter, History of Economic Analysis, p. 1090. This problem obstructed the development of economic science until Mises provided the solution. Failure to solve it led many economists to despair of ever constructing a satisfactory economic analysis of money prices. They were led to abandon fundamental analysis of money prices and to separate completely the prices of goods from their money components. In this fallacious course, they assumed that individual prices are determined wholly as in barter, without money components, while the supply of and the demand for money determined an imaginary figment called the “general price level.” Economists began to specialize separately in the “theory of price,” which completely abstracted from money in its real functions, and a “theory of money,” which abstracted from individual prices and dealt solely with a mythical “price level.” The former were solely preoccupied with a particular price and its determinants; the latter solely with the “economy as a whole” without relation to the individual components—called “microeconomics” and “macroeconomics” respectively. Actually, such fallacious premises led inevitably to erroneous conclusions. It is certainly legitimate and necessary for economics, in working out an analysis of reality, to isolate different segments for concentration as the analysis proceeds; but it is not legitimate to falsify reality in this separation, so that the final analysis does not present a correct picture of the individual parts and their interrelations.
  • 20. As we regress in time and approach the original days of barter, the exchange use in the demand for gold becomes relatively weaker as compared to the direct use of gold, until finally, on the last day of barter, it dies out altogether, the time component dying out with it.
  • 21. It should be noted that the crucial stopping point of the regression is not the cessation of the use of gold as “money,” but the cessation of its use as a medium of exchange. It is clear that the concept of a “general” medium of exchange (money) is not important here. As long as gold is used as a medium of exchange, gold prices will continue to have temporal components. It is true, of course, that for a commodity used as a limited medium of exchange only a limited array of prices has to be taken into account in considering its utility.
  • 22. Professor Patinkin criticizes Mises for allegedly basing the regression theorem on the view that the marginal utility of money refers to the marginal utility of the goods for which money is exchanged rather than the marginal utility of holding money, and charges Mises with inconsistently holding the latter view in part of his Theory of Money and Credit. In fact, Mises’ concept of the marginal utility of money does refer to the utility of holding money, and Mises’ point about the regression theorem is a different one, namely, that the marginal utility-to-hold is in itself based on the prior fact that money can exchange for goods, i.e., on the prior money prices of goods. Hence, it becomes necessary to break out of this circularity—by means of the regression theorem. In short, the prices of goods have to exist in order to have a marginal utility of money to hold.
         In his own theory, Patinkin very feebly tries to justify circularity, by saying that in analyzing the market (market “experiment”) he begins with utility, and in analyzing utility he begins with prices (individual “experiment”), but the fact remains that he is caught inextricably in a circular trap, which a methodology of cause-and-effect (in contrast to a mathematical type of mutual determination) would quickly reveal. Don Patinkin, Money, Interest, and Prices (Evanston, Ill.: Row, Peterson & Co., 1956), pp. 71–72, 414.