that are complementary to one another are those the consumer in some way considers as cooperating together in the satisfaction of a particular want. Automobiles and gasoline, for example, are complementary goods. Pens, paper, and ink are complementary goods. Usually complementary goods may combine in different proportions to satisfy the particular want they are complementary to. Where they are useful only when combined in some fixed proportion, it is useful to consider them as constituting parts of one good. It is hardly more worthwhile to consider separately the items making up a pair of shoes than it would be to consider the utility of water as made up of the utility of hydrogen and oxygen. (Of course, where goods are complementary with respect to one use, but are independently useful elsewhere, it is convenient to keep them distinct.) Complementary goods are distinguished in that for each such good, its marginal utility to the consumer rises, other things being equal, as the quantities possessed of the goods complementary to it increases. The more paper that the owner of a pen acquires, the more significant a bottle of ink may appear to him.
Goods that are substitutes for one another are those the consumer considers capable, to some degree, of satisfying the same particular want. Potatoes and bread, for example, are to a degree capable of satisfying the same wants that are satisfied by the other. Airline transportation and railroad transportation are substitutes, to a degree, each for one another. It is to be noted that when two physically dissimilar commodities are perfect substitutes for one another—where, that is, there is no purpose served by a given quantity of the one that cannot be served equally well by a given quantity of the other—then, from an economic point of view, they are not “different” goods at all. If, for example, there were no purpose for which a blue pencil is used that is not perfectly served by a red pencil, and vice versa, then it would not be expedient to distinguish economically between red and blue pencils at all; they would be used interchangeably. If two nickels could perform all the uses required of a dime, and vice versa, then the two coins would make up an economically homogeneous kind of good. Within this economically homogeneous group there would be, it is true, physical differences—some members of the group being made up of two nickels, the other being each one dime. But this would be as irrelevant as, say, the different registration numbers on two identical automobiles where the difference in number is the only physical means of distinction between them.
Most substitute goods are, however, only imperfect substitutes for one another. A characteristic of goods that a consumer considers as substitutes for one another is that the marginal utility to him of any such good declines, other things being the same, as the quantity possessed of the substitute goods increases. The more rapidly the marginal utility declines in this manner, the more perfect is the substitute relationship between the goods. The special case, as we have seen, of perfect substitutes is one where the marginal utility of the one good declines, with increased possession of the other, exactly as rapidly as it would decline were the quantities possessed of this good itself to be increased in the same proportions.
MARGINAL UTILITY—SOME FURTHER REMARKS
It is worthwhile at this point to emphasize a number of points concerning the marginal utility concept as we have used it thus far. These points will serve to clarify the content of our utility analysis and, at the same time, point to the way our analysis is related to the very earliest attempts to use the tool of marginal utility.
The Paradox of Value
Modern utility theory emerged in the 1870s at the hands of Jevons, Menger, and Walras. One of the earliest uses of the theory was to sweep away a misunderstanding that had prevented the earlier classical economists from using the utility concept to explain prices.
The earlier writers found themselves unable to explain the prices of goods by reference to the use-value or utility of these goods. To be sure, the prices of many goods seem to reflect their relative degrees of usefulness to men; the classical economists would have welcomed such a theory. But they were troubled by the many goods whose prices seemed to defy any such explanation. Diamonds, for example, are clearly much less important for human life than water, yet the price of water is quite negligible compared with that of diamonds. This paradox had forced the classical economists to seek an entirely different method of explaining prices.
Marginal utility theory is able to dispose of the problem quite simply. The basis for the paradox was the premise that water is more significant for man than are diamonds. This premise is no doubt correct, but not in a way that can support the classical conclusions. Water, in the abstract, is no doubt more important than diamonds in the abstract. But for human action the greater importance of water over diamonds must be demonstrated through choice among alternatives. For an analysis of human action no other meaning can be attached to the term “more important.” From this point of view the greater importance of water must mean that we assume if a man has to choose between water and diamonds, he will choose water. But for the statement of alternatives a man must choose among, it is clearly insufficient to specify only that these are water and diamonds. One must specify the terms and conditions on which he is to choose. And here the irrelevance of the “greater importance of water over diamonds” for understanding their relative prices becomes immediately clear.
Water is more important than diamonds only where a man must choose between renouncing all water or renouncing all diamonds. Faced with such a choice it is indeed likely that a man will place diamonds distinctly in second place. But this kind of choice is one that the market does not confront the consumer with and therefore cannot have bearing on the determination of market prices. In the market a man buying or refraining from buying water is choosing not merely whether to have water or not to have water, but whether to have some additional quantity of water or not; and similarly, of course, for diamonds. Thus, the law of diminishing marginal utility provides the key.
The marginal utility of water cannot be said to be either higher or lower than that of diamonds until there are first specified (a) the size of the marginal unit and (b) the margin at which marginal quantities of water and diamonds are being compared. The marginal utility of water is indeed lower than that of diamonds—when a small quantity of water is compared with a similar weight of diamonds and when the loss of this small quantity of water would still leave the consumer with ample water. These are, in fact, the conditions under which consumers choose whether to buy water or diamonds. The quantity of water usually available is ample; thus, the margin at which an additional quantity of water is valued is such as to make its marginal utility low, according to the law of diminishing marginal utility. On the other hand, diamonds are usually possessed in sufficiently small amounts to ensure that the typically sized marginal unit still possesses high marginal utility.
If conditions were otherwise, prices would indeed reflect the altered conditions. If, for example, a thirsty owner of diamonds were to bargain in a desert with the owner of a quantity of water, we would indeed expect to find the price of water far from negligible. Clearly, in these circumstances, the marginal utility of water must be immensely higher than under normal conditions. Here, indeed, water would show itself as “more important for man than diamonds.”
The Subjective Character of Utility
The concept of utility as we have developed it thus far in this chapter, and as we shall use it to analyze the demand side of the market, is essentially a subjective concept. We must not consider utility as in anyway intrinsic to an object or service. A good is not to be thought of as bearing a tag inscribed with some degree of utility. We do not require any philosophical sophistication to distinguish sharply between the utility relevant to the analysis of human actions and such qualities as the mass, extension, and even color or beauty of an object. For the analysis of demand this distinction is of the greatest importance.
For
