Chapter 4—Prices and Consumption (continued)
Some Fallacies Relating to Utility
A doctrine commonly held by writers on utility is that the consumer acts so as to bring the marginal utility that any good has for him into equality with the price of that good. To understand this thesis, let us examine the preference scale of Mr. Jones in contemplating the purchase of one or more suits (and we shall assume that each suit is of the same quality—the same “good”). Suppose his value scale is as follows:
And suppose also that the market price is 2.9 grains per suit. Jones will buy not one or three, but two, suits. He will buy up to the last unit at which the diminishing marginal utility that the suit has for him exceeds the increasing marginal utility of money. This is obvious. Now, if a writer couches the exposition in terms of highly divisible goods, such as butter, and in terms of small units of money, such as pennies, it is easy to leap unthinkingly to the conclusion that the consumer for each good will act in such a way as to equalize, at the market price, the marginal utility of the sum of money and the marginal utility of the good. It should be clear, however, that there is never any such “equalization.” In the case of the suit, the rank of the second suit is still considerably above the rank of the 2.9 grains. So there is no equalization. Even in the case of the most divisible of goods, there will still be a difference in rank, not an equalization, between the two utilities. A man may buy 11 ounces of butter at 10 cents an ounce, until there is nothing ranking between the 11th ounce and the 10cents on his utility scale; yet there is still no equality, but a difference in rank, with the last ounce bought ranking higher than the last sum of money spent. Of course, the consumer tries to spend his money so as to bring the two as close as possible, but they can never be equal.
Furthermore, the marginal utility of each particular good, after the purchases are made, differs in rank from that of every other. Thus, let us take one grain of gold as the monetary unit under consideration. Let us say that the given market-prices of various goods are as follows:
Now each individual will purchase each commodity until the last point at which the marginal utility of the unit exceeds the marginal utility of a grain of gold. For one man, this might mean the purchase of five pounds of butter, three loaves of bread, two bars of candy, etc. This would mean that either a sixth pound of butter or a fourth loaf of bread would have a lower marginal utility than a grain of gold forgone. However, the marginal utility of each good will still differ in rank from that of every other and will not be equal to that of any other.
Another, even more curious doctrine holds that in equilibrium the ratio of the marginal utilities of the various goods equals the ratio of their prices. Without entering in detail into the manner by which these writers arrive at this conclusion, we can see its absurdity clearly, since utilities are not quantities and therefore cannot be divided.
These fallacies stem from a related one: the idea that an individual will act so as to equalize the marginal utility that any good will have in each of its uses. Applied to money, this would imply that the marginal utility of a unit of money is equal for each field of expenditure for each person. This is incorrect, as we have just seen that the marginal utilities of the various goods are not equalized. Successive units of a good are allocated to the most desired end, then to the next most desired satisfaction, etc. If there are several uses for the good, each one involving many possible units, the marginal utility of a unit in each use continues to decline as the supply increases. As goods are purchased, the marginal utility of each good purchased diminishes, and a man may allocate his money first to one use, then to another, and then to the first use again. However, in no case is there any equalization of marginal utilities.
The dogma of the equalization of marginal utilities may best be illustrated in the following passage from perhaps the originator of this line of argument:
Let s be the whole stock of some commodity, and let it be capable of two distinct uses. Then we may represent the two quantities appropriated to these uses by xl and y1, it being a condition that xl plus y1 equal s. The person may be conceived as successively expending small quantities of the commodity; now it is the inevitable tendency of human nature to choose that course which appears to offer the greatest advantage at the moment. Hence, when the person remains satisfied with the distribution he has made, it follows that no alteration would yield him more pleasure; which amounts to saying that an increment of commodity would yield exactly as much utility in one use as in another. Let Du1, Du2, be the increments of utility, which might arise respectively from consuming an increment of commodity in the two different ways. When the distribution is completed, we ought to have Du1 = Du2 . . . The same reasoning . . . will evidently apply to any two uses, and hence to all uses simultaneously, so that we obtain a series of equations less numerous by a unit than the number of ways of using the commodity. The general result is that the commodity, if consumed by a perfectly wise being, must be consumed with a maximum production of utility.
The chief errors here consist in conceiving utility as a certain quantity, a definite function of an increment in the commodity, and in treating the problem in terms of infinitely small steps. Both procedures are fallacious. Utilities are not quantities, but ranks, and the successive amounts of a commodity that are used are always discrete units, not infinitely small ones. If the units are discrete, then the rank of each unit differs from that of every other, and there can be no equalization.
Many errors in discussions of utility stem from an assumption that it is some sort of quantity, measurable at least in principle. When we refer to a consumer’s “maximization” of utility, for example, we are not referring to a definite stock or quantity of something to be maximized. We refer to the highest-ranking position on the individual’s value scale. Similarly, it is the assumption of the infinitely small, added to the belief in utility as a quantity, that leads to the error of treating marginal utility as the mathematical derivative of the integral “total utility” of several units of a good. Actually, there is no such relation, and there is no such thing as “total utility,” only the marginal utility of a larger-sized unit. The size of the unit depends on its relevance to the particular action.
This illustrates one of the grave dangers of the mathematical method in economics, since this method carries with it the bias of the assumption of continuity, or the infinitely small step. Most writers on economics consider this assumption a harmless, but potentially very useful, fiction, and point to its great success in the field of physics. They overlook the enormous differences between the world of physics and the world of human action. The problem is not simply one of acquiring the microscopic measuring tools that physics has developed. The crucial difference is that physics deals with inanimate objects that move but do not act. The movements of these objects can be investigated as being governed by precise, quantitatively determinate laws, well expressed in terms of mathematical functions. Since these laws precisely describe definite paths of movement, there is no harm at all in introducing simplified assumptions of continuity and infinitely small steps.
Human beings, however, do not move in such fashion, but act purposefully, applying means to the attainment of ends. Investigating causes of human action, then, is radically different from investigating the laws of motion of physical objects. In particular, human beings act on the basis of things that are relevant to their action. The human being cannot see the infinitely small step; it therefore has no meaning to him and no relevance to his action. Thus, if one ounce of a good is the smallest unit that human beings will bother distinguishing, then the ounce is the basic unit, and we cannot simply assume infinite continuity in terms of small fractions of an ounce.
The key problem in utility theory, neglected by the mathematical writers, has been the size of the unit. Under the assumption of mathematical continuity, this is not a problem at all; it could hardly be when the mathematically conceived unit is infinitely small and therefore literally sizeless. In a praxeological analysis of human action, however, this becomes a basic question. The relevant size of the unit varies according to the particular situation, and in each of these situations this relevant unit becomes the marginal unit. There is none but a simple ordinal relation among the utilities of the variously sized units.
The tendency to treat problems of human action in terms of equality of utility and of infinitely small steps is also apparent in recent writings on “indifference maps.” Almost the entire edifice of contemporary mathematical economics in consumption theory has been built on the “indifference” assumption. Its basis is the treatment of large-sized classes of combinations of two goods, between which the individual is indifferent in his valuations. Furthermore, the differences between them are infinitely small, so that smooth lines and tangents can be drawn. The crucial fallacy is that “indifference” cannot be a basis for action. If a man were really indifferent between two alternatives, he could not make any choice between them, and therefore the choice could not be revealed in action. We are interested in analyzing human action. Any action demonstrates choice based on preference: preference for one alternative over others. There is therefore no role for the concept of indifference in economics or in any other praxeological science. If it is a matter of indifference for a man whether he uses 5.1 or 5.2 ounces of butter for example, because the unit is too small for him to take into consideration, then there will be no occasion for him to act on this alternative. He will use butter in ounce units, instead of tenths of an ounce. For the same reason, there are no infinitely small steps in human action. Steps are only those that are significant to human beings; hence, they will always be finite and discrete.
The error in reasoning on the basis of “indifference” is the failure to appreciate the fact that a problem important in the field of psychology may have no significance in the realm of praxeology, to which economics belongs. Psychology deals with the problem of how or why the individual forms value scales, and for this question it is relevant to consider whether the individual is decisive or inclined to be “indifferent” between various alternatives. Praxeology, however, is a logical science based on the existence of action per se; it is interested in explaining and interpreting real action in its universal sense rather than in its concrete content. Its discussion of value scales is therefore a deduction from the nature of human action and not a speculative essay on the internal workings of the mind. It is consequently irrelevant for praxeology whether a man, in having to decide between alternatives A and B, makes a choice firmly and decisively, or whether he decides by tossing a coin. This is a problem for psychology; praxeology is concerned only with the fact that he chooses, for example, A rather than B, and that therefore A ranked higher in his preference scale than B. Utility theory is not concerned with psychology or the internal operations of the mind, but is part of a separate science based on the logical consequences of the simple existence of action.
Neither is praxeology based on behaviorist psychology. In fact, in so far as praxeology touches on psychology, its principles are the reverse of those of behaviorism. As we have seen, far from simply observing action in the same way as we observe and record the movements of stones, praxeology is based on a fundamental distinction between human action and the motion of inorganic matter, namely, that human action is motivated toward the achievement of certain ends. Means and resources are used for the achievement of these ends. Far from leaving mind out of the picture, praxeology rests fundamentally on the basic axiom of action, action caused and put into effect by human minds. However, praxeology is not concerned with the content of these ends, the manner of arriving at them, or their order; it is concerned with analysis of the logical implications of the existence of these ends.
Some writers, in their artificial separation of value scales from real action, have actually gone to the length of attempting to discover people’s indifference maps by means of questionnaires. These attempts, besides being open to the stricture that indifference is not praxeologically valid, fail to realize that value scales can and do change continually and that therefore such questionnaires have no relevance to the business of economics. Economics is interested not in value scales professed in response to questionnaires, but in the values implied by real action. As Ludwig von Mises states, with regard to all attempts to separate value scales from action:
. . . the scale of value is nothing but a constructed tool of thought. The scale of value manifests itself only in real acting; it can be discerned only from the observation of real acting. It is therefore impermissible to contrast it with real acting and to use it as a yardstick for the appraisal of real actions.
Since indifference is not relevant to human action, it follows that two alternatives for choice cannot be ranked equally on an individual’s value scale. If they are really ranked equally, then they cannot be alternatives for choice, and are therefore not relevant to action. Hence, not only are alternatives ranked ordinally on every man’s value scale, but they are ranked without ties; i.e., every alternative has a different rank.
The famous illustration used by the indifference theorists to demonstrate the relevance of indifference to human action is the case of Buridan’s ass. This is the fable of the ass who stands, hungry, equidistant from two equally attractive bales of hay, or, thirsty, equidistant from two water holes. Since the two bales or water holes are equally attractive in every way, the ass can choose neither one and must therefore starve. This example is supposed to prove the great relevance of indifference to action and to be an indication of the way that indifference is revealed in action. Compounding confusion, Schumpeter refers to this ass as “perfectly rational.”
In the first place, it is of course difficult to conceive of an ass or a person that could be less rational. He is confronted not with two choices, but with three, the third being to starve where he is. Even on the indifferentists’ own grounds, this third choice will be ranked lower than the other two on the actor’s value scale. He will not choose starvation.
If both the left and right water holes are equally attractive, and he can find no reason for preferring one or the other, the ass or the man will allow pure chance, such as a flip of a coin, to decide on either one. But on one he must and will decide. Again, we are interested in preference as revealed through choice and not in the psychology of preferences. If the flipped coin indicated the left water hole, then the left water hole was finally placed higher on the actor’s value scale, as was revealed when he went toward it. Far from being a proof of the importance of indifference, the case of Buridan’s ass is an excellent demonstration of the fact that indifference can play no part whatever in an analysis of human action.
Another way of attempting a justification of the indifference analysis is to suppose that a man, Jones, chooses each of two alternatives A and B about 50 percent of the time, upon repeated opportunities. This shifting is alleged to be a demonstration that Jones is really indifferent as between the two alternatives. Yet what is the reasonable inference? Clearly, that in some cases, A was preferred to B on Jones’ value scale, and that in the others, the positions were shifted so that B was preferred to A. In no case was there indifference between the two alternatives. The shift of choice indicates a shift in the preference scale, and not indifference on a constant value scale. Of course, if we were dealing with psychology, we could enter into a discussion of intensities of preferences and opine that the man, with respect to his underlying personality, was relatively indifferent rather than intensely biased, as between the two alternatives. But in praxeology we are not interested in the concrete content of his value scales nor in his underlying personality. We are interested in value scales as revealed through choice.
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. 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. 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 “package”—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.
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.
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.
Economics has made such extensive use of the term “value” that it would be inexpedient to abandon it now. However, there is undoubtedly confusion because the term is used in a variety of different ways. It is more important to keep distinct the subjective use of the term in the sense of valuation and preference, as against the “objective” use in the sense of purchasing power or price on the market. Up to this chapter, “value” in this book has meant the subjective individual “valuing” process of ranking goods on individual “value scales.”
In this chapter, the term “value of capital” signifies the purchasing power of a durable good in terms of money on the market. If a house can be sold on the market for 250 ounces of gold, then its “capital value” is 250 ounces. The difference between this and the subjective type of value is apparent. When a good is being subjectively valued, it is ranked by someone in relation to other goods on his value scale. When a good is being “evaluated” in the sense of finding out its capital value, the evaluator estimates how much the good could be sold for in terms of money. This sort of activity is known as appraisement and is to be distinguished from subjective evaluation. If Jones says: “I shall be able to sell this house next week for 250 ounces,” he is “appraising” its purchasing power, or “objective exchange-value,” at 250 ounces of gold. He is not thereby ranking the house and gold on his own value scale, but is estimating the money price of the house at some point in the future. We shall see below that appraisement is fundamental to the entire economic system in an economy of indirect exchange. Not only do the renting and selling of consumers’ goods rest on appraisement and on hope of monetary profits, but so does the activity of all the investing producers, the keystone of the entire productive system. We shall see that the term “capital value” applies, not only to durable consumers’ goods, but to all nonhuman factors of production as well—i.e., land and capital goods, singly and in various aggregates. The use and purchase of these factors rest on appraisement by entrepreneurs of their eventual yield in terms of monetary income on the market, and it will be seen that their capital value on the market will also tend to be equal to the discounted sum of their future yields of money income.
We are omitting possible shifts in rank resulting from the increasing utility of money, which would only complicate matters unduly.
W. Stanley Jevons, The Theory of Political Economy (3rd ed.; London: Macmillan & Co., 1888), pp. 59–60.
See Appendix A below, “The Diminishing Marginal Utility of Money,” and Rothbard, “Toward a Reconstruction of Utility and Welfare Economics.”
Mises, Human Action, p. 102. Dr. Bernardelli justly says:
If someone asks me in abstracto whether my love for my country is greater than my desire for freedom, I am somewhat at a loss how to answer, but actually having to make a choice between a trip in my country and the danger of losing my freedom, the order of intensities of my desire becomes only too determinate. (Harro F. Bernardelli, “What has Philosophy to Contribute to the Social Sciences, and to Economics in Particular?” Economica, November, 1936, p. 451)
Also see our discussion of “consumer surplus” in section 4 above.
Schumpeter, History of Economic Analysis, pp. 94 n. and 1064.
See chapter 1, pp. 73–74.
Cf. the excellent discussion of the sizes of units in Wicksteed, Common Sense of Political Economy, I, 96–101 and 84.
Mises, 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.
It 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.
For 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.”
On appraisement and valuation, cf. Mises, Human Action, pp. 328–30.