TIME PREFERENCE (IMPATIENCE)

sions only and hence can represent the dependence of amagnitude on only one independent variable. Even asurface can only represent dependence on two. But forour requirement, i.e., in order to represent the depen-dence of a man’s impatience on the infinite number ofsuccessive elements constituting his income stream, weshould need not two or three dimensions simply but aspace of n dimensions.

We may represent, however, the relation between timepreference and income by a schedule like the ordinarydemand schedule and supply schedule, if we make a listof income streams of all possible sizes, shapes, and prob-abilities, specifying for each individual income all itscharacteristics—its size, time shape (that is, its relativemagnitude in successive time intervals), and the cer-tainty or uncertainty of its various parts, to say nothingof its heterogeneous and varying composition. Havingthus compiled a list of all possible income streams, itwould only be necessary for us to assign to each of themthe rate of impatience pertaining to it.

Such a schedule would be too complicated and cumber-some to be carried out in detail; but the following willroughly indicate some of the main groups of which itwould consist. In this schedule I have represented, bythe three horizontal lines, three different classes of income—two extreme types and one mean type—so that thecorresponding rates of time preference range themselvesin a descending series of numbers. The three vertical col-umns show three different classes of individuals, two be-ing of extreme types, and the third of a mixed or mediumtype. Thus, the numbers in the table grow smaller as weproceed toward the right and as we proceed downward,the smallest numbers of all being the lower right-hand

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