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must be made clear that the fifth and sixth shirts, as well as each of the four already possessed, being different units of the same good, are perfect substitutes for one another. The shirt numbered 6 has lower utility than that numbered 5 only because it is to be acquired later. Once the man has bought the sixth shirt, it may well be that the shirt numbered 6 may actually be worn for the most important occasion. When we say that a sixth shirt has lower utility value than a fifth, what we actually mean then is that the utility of any one shirt, when six shirts are owned, is lower than that of any shirt in a five-shirt wardrobe. This is so because the utility of any shirt in a man’s wardrobe means simply the difference its loss would make to him. A man owning shirts numbered 1 to 6, contemplating the loss of shirt number 3, is in exactly the same position as if he would be contemplating the loss of shirt number 6. Any use shirt number 3 would be put to, were shirt number 6 to be sacrificed, can be perfectly served by one of the other shirts, when it is shirt number 3 that is to be given up. The marginal utility of any one particular unit in a stock of shirts, or any other good, even the marginal utility of the unit devoted to a more important use than any of the other units, is exactly the same as the marginal utility of the unit devoted to the least important use—since it is this least important use that is at stake.

      This rather obvious fact can be fruitfully borne in mind throughout economics whenever the adjective “marginal” appears.

       THE MARGINAL UTILITIES OF RELATED GOODS

      It is useful for many purposes to distinguish between goods that, for a given consumer, are unrelated and goods that are related. Unrelated goods are those whose marginal utility depends only on the quantity of it possessed, not on the quantity possessed of the others. Related goods, on the other hand, are any group of goods whose marginal utility depends, in some way, not only on the quantities of the good itself possessed, but also on the quantities possessed of the other goods in the group.

      The relationship between related goods can be one of two kinds. Related goods can be either complementary to one another or substitutes for one another.

      Goods 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

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