Appendix A: The Diminishing Marginal Utility of Money

Some writers, while admitting the validity of the law of diminishing marginal utility for all other goods, deny its application to money. Thus, for example, a man may allocate each ounce of money to his most preferred uses. However, suppose that it takes 60 ounces of gold to buy an automobile. Then the acquisition of the 60th ounce, which will enable him to buy an automobile, will have considerably more value than the acquisition of the 58th or of the 59th ounce, which will not enable him to do so.

This argument involves a misconception identical with that of the argument about the “increasing marginal utility of eggs” discussed in chapter 1, above.41 There we saw that it is erroneous to argue that because a fourth egg might enable a man to bake a cake, which he could not do with the first three, the marginal utility of the eggs has increased. We saw that a “good” and, consequently, the “unit” of a good are defined in terms of whatever quantity of which the units give an equally serviceable supply. This last phrase is the key concept. The fourth egg was not equally serviceable as, and therefore not interchangeable with, the first egg, and therefore a single egg could not be taken as the unit. The units of a good must be homogeneous in their serviceability, and it is only to such units that the law of utility applies.

The situation is similar in the case of money. The serviceability of the money commodity lies in its use in exchange rather than in its direct use. Here, therefore, a “unit” of money, in its relevance to individual value scales, must be such as to be homogeneous with every other unit in exchange-value. If another ounce permits a purchase of an automobile, and the issue is relevant to the case in question, then the “unit” of the money commodity must be taken not as one ounce, but as 60 ounces.

All that needs to be done, then, to account for and explain “discontinuities” because of possible large purchases is to vary the size of the monetary unit to which the law of utility and the preferences and choices apply.42 This is what each man actually does in practice. Thus, suppose that a man is considering what to do with 60 ounces of gold. Let us assume, for the sake of simplicity, that he has a choice of parceling out the 60 ounces into five-ounce units. This, we will say, is alternative A. In that case, he decides that he will parcel out each five ounces in accordance with the highest rankings on his utility scale. The first five ounces will be allocated to, or spent on, the most highly valued use that can be served by five ounces; the next five ounces to the next most highly valued use, and so on. Finally, his 12th five ounces he will allocate to his 12th most highly valued use. Now, however, he is also confronted with alternative B. This alternative is to spend the entire 60 ounces on whatever single use will be most valuable on his value scale. This will be the single highest-ranked use for a unit of 60 ounces of money. Now, to decide which alternative course he will take, the man compares the utility of the highest-ranked single use of a lump sum of 60 ounces (say, the purchase of a car) with the utility of the “pack-age”—the expenditure of five ounces on a, five ounces on b, etc. Since the man knows his own preference scale—otherwise he could never choose any action—it is no more difficult to assume that he can rank the utility of the whole package with the utility of purchasing a car than to assume that he can rank the uses of each five ounces. In other words, he posits a unit of 60 ounces and determines which alternative ranks higher on his value scale: purchase of the car or a certain package distribution by five-ounce (or other-sized) units. At any rate, the 60 ounces are distributed to what each man believes will be its highest-ranking use, and the same can be said for each of his monetary exchange decisions.

Here we must stress the fact that there is no numerical relation—aside from pure ordinal rank—between the marginal utilities of the various five-ounce units and the utilities of the 60-ounce units, and this is true even of the package combination of distribution that we have considered. All that we can say is that the utility of 60 ounces will clearly be higher than any one of the utilities of five ounces. But there is no way of determining the numerical difference. Whether or not the rank of the utility of this package is higher or lower than the utility of the car purchase, moreover, can be determined only by the individual himself.

We have reiterated several times that utility is only ranked, and never measurable. There is no numerical relationship whatever between the utility of large-sized and smaller-sized units of a good. Also, there is no numerical relationship between the utilities of one unit and several units of the same size. Therefore, there is no possible way of adding or combining marginal utilities to form some sort of “total utility”; the latter can only be a marginal utility of a large-sized unit, and there is no numerical relationship between that and the utilities of small units.

As Ludwig von Mises states:

Value can rightly be spoken of only with regard to specific acts of appraisal. ... Total value can be spoken of only with reference to a particular instance of an individual ... having to choose between the total available quantities of certain economic goods. Like every other act of valuation, this is complete in itself. ... When a stock is valued as a whole, its marginal utility, that is to say, the utility of the last available unit of it, coincides with its total utility, since the total supply is one indivisible quantity.43

There are, then, two laws of utility, both following from the apodictic conditions of human action: first, that given the size of a unit of a good, the (marginal) utility of each unit decreases as the supply of units increases; second, that the (marginal) utility of a larger-sized unit is greater than the (marginal) utility of a smaller-sized unit. The first is the law of diminishing marginal utility. The second has been called the law of increasing total utility. The relationship between the two laws and between the items considered in both is purely one of rank, i.e., ordinal. Thus, four eggs (or pounds of butter, or ounces of gold) are worth more on a value scale than three eggs, which in turn are worth more than two eggs, two eggs more than one egg, etc. This illustrates the second law. One egg will be worth more than a second egg, which will be worth more than a third egg, etc. This illustrates the first law. But there is no arithmetical relationship between the items apart from these rankings.44

The fact that the units of a good must be homogeneous in serviceability means, in the case of money, that the given array of money prices remains constant. The serviceability of a unit of money consists in its direct use-value and especially in its exchange-value, which rests on its power to purchase a myriad of different goods. We have seen in our study of the money regression and the marginal utility of money that the evaluation and the marginal utility of the money commodity rests on an already given structure of money prices for the various goods. It is clear that, in any given application of the foregoing law, the money prices cannot change in the meantime. If they do, and for example, the fifth unit of money is valued more highly than the fourth unit because of an intervening change in money prices, then the “units” are no longer equally serviceable and therefore cannot be considered as homogeneous.

As we have seen above, this power of the monetary unit to purchase quantities of various goods is called the purchasing power of the monetary unit. This purchasing power of money consists of the array of all the given money prices on the market at any particular time, considered in terms of the prices of goods per unit of money. As we saw in the regression theorem above, today’s purchasing power of the monetary unit is determined by today’s marginal utilities of money and of goods, expressed in demand schedules, while today’s marginal utility of money is directly dependent on yesterday’s purchasing power of money.45

• 41See chapter 1, pp. 73–74.
• 42Cf. the excellent discussion of the sizes of units in Wicksteed, Common Sense of Political Economy, I, 96–101 and 84.
• 43Mises, Theory of Money and Credit, pp. 46–47. Also see Harro F. Bernardelli, “The End of the Marginal Utility Theory,” Economica, May, 1938, pp. 205–07; and Bernardelli, “A Reply to Mr. Samuelson’s Note,” Economica, February, 1939, pp. 88–89.
• 44It must always be kept in mind that “total” and “marginal” do not have the same meaning, or mutual relation, as they do in the calculus. “Total” is here another form of “marginal.” Failure to realize this has plagued economics since the days of Jevons and Walras.
• 45For further analysis of the determination of the purchasing power of money and of the demand for and the supply of money, see chapter 11 below on “Money and Its Purchasing Power.”