§8. A Typical Family of Willingness Lines

While we cannot, of course, tell exactly how any human being would act if far from the income situation in which he is actually placed, yet we know what in a way would be characteristic of him. Chart 31 is believed to represent roughly a family of Willingness lines typical of most human beings. It is best analyzed by following the dotted straight line SS' running northeast, midway between the axes and therefore comprising points which represent, in each case, equal incomes in both years.

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Four characteristic properties may be noted:

(1) At S, taken to represent a point near the minimum of subsistence—the income situation, say, of a polar explorer who is marooned and hopeless—the Willingness line is nearly vertical. In this income position of extreme need a person would scarcely be willing to lend at all, for to give up one iota of this year's income in exchange for any amount promised for next year would mean too great a privation in the present. On the contrary, in order to get an added dollar today to help keep body and soul together this year, he would be willing to give not only 10 per cent or 25 per cent but perhaps as much as 100 per cent, or 1000 per cent, or every dollar of next year's income even though next year is no more promising than this year.

(2) At S', taken to represent an exceedingly large income—say $1,000,000 for each of the two years—the Willingness line is nearly at right angles to the SS' line; that is, nearly at 45° to the two axes, for with such a large income the two years would seem almost on even terms. Presumably one with this income would not be willing, in order to get $1000 more income this year, to give up much over $1000 out of next year's income.

(3) As one passes between the two income situations above mentioned, from S to S', his rate of time preference will gradually decrease—from nearly infinity at S down nearly to zero at S', that is, the larger the income, other things remaining the same, the smaller the degree of impatience.

(4) Any one Willingness line grows steeper as it proceeds upward and leftward, changing from a nearly horizontal direction at its lower right end to a nearly vertical direction at the opposite end.

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