a scale of values. Without other goods or services, there is no scale of values and hence no utility concept at all.
The relative character of utility means that men’s preferences can be the subject of interpersonal comparisons. There is, as we have seen, no value scale upon which the relative positions of a loaf-of-bread-for-A and a loaf-of-bread-for-B can be observed. But it may be possible for an observer to discover whether a loaf of bread bears the same relationship to twenty cents on A’s scale of values as it does on B’ s; and it may be possible to assert that a loaf of bread has greater utility to A than twenty cents, but that for B the situation is reversed. In fact, this kind of assertion is, as we shall discover, the foundation of market theory.
The Ordinal Character of Utility
Two conflicting approaches to utility theory are met in the literature. The older (but by no means extinct) approach was to treat the utility of a good for an individual as a magnitude to which, in principle, a cardinal number could be assigned. An apple has, let us say, 10 units of utility; a shirt, 50 units; and so on. Such an approach involves the postulation of a numerical scale of utility against which the utilities of goods might—again only in principle—be measured with precision.2 The theoretical concept of numerical quantities of utility involves, again, the notion that a larger “quantity of utility” (one, that is, comprising a larger number of “units” of utility) is built up through the addition of smaller quantities of utility or of units of utility. A good with utility of 10 possesses 10 times the utility of a good with unit utility; and so on. The cardinal utility approach would consider a man enlarging his stock of a good as, at the same time, increasing his store of utility afforded by possession of the good. The total store of utility afforded by the entire stock would be the sum of the successive increments of utility obtained as the stock successively expanded from the acquisition of the first unit up to the addition of the last acquired unit. The rate at which the addition of successive physical units of the good increases the total utility of a stock of the good is termed (in the cardinal terminology) the “marginal utility” of the good.3
The ideas, however, underlying the cardinal approach present considerable conceptual difficulty. Without attempting to enlarge on this difficulty, we can contrast this approach with the currently more accepted ordinal approach. This view denies the very notion of cardinal quantities of utility. The only numbers that can be assigned to utilities are ordinal numbers. Utilities can be arranged in order; for example, first, second, and so on. They cannot however be assigned numerical magnitude. A shirt may be said to have greater utility than an apple; one may not say how many times the utility of the shirt is greater. A “unit” of utility has no meaning for the ordinal approach. When men value goods, they arrange them in order of value; they do not attach cardinal numbers to them.
The discussion we have presented in this chapter follows the ordinal approach to utility. For us, the utility of a good corresponds to a ranking on the scale of values; to speak of the utility of a good is to involve only the comparison of its significance with that of some other good. An important consequence of our adopting this ordinal viewpoint is that the term “marginal utility” is used in this book in a somewhat different sense from its use in a “cardinal” approach. This matter of terminology needs a brief explanation.
Total Utility and Marginal Utility
For a cardinal utility theorist, we have seen, the term “marginal utility” is used in contradistinction to “total utility.” Total utility refers to the quantity of (cardinal) utility afforded by a stock of a commodity. Marginal utility refers to the rate at which total utility changes as the size of the stock of the commodity changes. An approximation to this rate of change of total utility is given by the amount of change in that utility resulting from a one-unit increase in the stock of the commodity. (Sometimes cardinal utility theorists loosely refer to this approximation as “marginal utility.”)4
For ordinal utility theory, such a distinction between total and marginal utility is not called for. Since there is no cardinal quantity of utility that increases, there can be no such concept as a rate of change of such a quantity. For an ordinal theory, marginal utility means the significance attached to the addition to (or decrease of) the quantity possessed of a good by the marginal unit. It does not, it must be noticed, refer to a change in the significance of the stock of the good, but to the significance of a change in the size of the stock. But total utility, too, for the ordinal theorist means the significance attached to the acquisition or loss of a given stock of the commodity. Both the utility of a stock of a good and the marginal utility of a marginal unit being added (or subtracted) from the stock “are total utilities” (in that they do not refer to “rates of change”); but, and more important, at the same time they are both “marginal utilities” in the sense that the utility of any quantity of a good, large or small, implies that this quantity is being considered “marginally”—that is, that somebody is contemplating the acquisition or loss of this quantity.
The “marginal unit,” in fact, is never anything else than the unit that happens to be under consideration. It is the unit relevant to the act of choice confronting a man. The size of this unit depends only on the circumstances of the situation where a choice has become necessary. A man may be contemplating the purchase of several shirts. For certain sums of money, he can buy one, two, or several shirts. In choosing among the alternatives open to him, the man will be comparing the marginal utilities of the appropriate number of shirts—that is, the smallest number of shirts separating one possible decision from another. If any number of shirts can be bought, then a single shirt is the marginal unit; if shirts can be bought only in packages of three, then three shirts make up the marginal unit—and the decision whether or not to buy additional shirts will involve the difference that three more shirts will make to the purchaser’s sense of well-being. Suppose a situation where a man is forced to choose between purchasing all of a supply of shirts or of obtaining none at all; then the entire supply would be the relevant “unit.” The man must assess the difference that the entire supply would mean to him in considering the attractiveness of the price it can be had at. In such a situation the marginal unit is the entire supply, and the man is in a position where the “marginal utility of shirts” means nothing else than the significance to him of this entire shirt supply.
MARGINAL UTILITY AND THE CONDITIONS FOR EXCHANGE
The utility analysis discussed in this chapter provides a framework within which to understand the emergence of exchange between individuals. Interpersonal exchange is the essence of the market process, and market theory is devoted to the explanation of the way objects will be produced for exchange, the quantities that will be offered for exchange, and the rates at which different exchanges will take place. Here we analyze the basic conditions that exist when two individuals exchange goods. This analysis will be fundamental to much of the subsequent material in this book.
The conditions for exchange exist between two individuals A, B, whenever a specific quantity of a good possessed by A is ranked lower on his value scale than a specific quantity of a good possessed by B, while the ordering is the reverse on B’s value scale. That is, wherever the marginal utility of a quantity of one good possessed by A is lower for A than that of a quantity of another good possessed by B, while for B the marginal utility of the latter quantity is the lower, then each of the two gain by giving up what is less important to him in exchange for what is more important.
If these conditions are absent, no exchange can take place. It is not sufficient that A ranks B’s brand new automobile higher than his own ancient jalopy; if B concurs in A’s relative valuation, both vehicles will remain where they are. No exchange will take place freely unless each party believes that he will be better off having made the exchange. This fundamental and self-evident truth is the central theme of the market process and of its theory.