IN GEOMETRIC TERMS

Four characteristic properties may be noted:

(1) At S, taken to represent a point near the minimumof subsistence—the income situation, say, of a polar ex-plorer who is marooned and hopeless—the Willingnessline is nearly vertical. In this income position of extremeneed a person would scarcely be willing to lend at all, forto give up one iota of this year’s income in exchange forany amount promised for next year would mean too greata privation in the present. On the contrary, in order toget an added dollar today to help keep body and soul to-gether this year, he would be willing to give not only 10per cent or 25 per cent but perhaps as much as 100 percent, or 1000 per cent, or every dollar of next year’s in-come even though next year is no more promising thanthis year.

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

(3) As one passes between the two income situationsabove mentioned, from S to S', his rate of time preferencewill gradually decrease—from nearly infinity at S downnearly to zero at S', that is, the larger the income, otherthings remaining the same, the smaller the degree of im-patience.

(4) Any one Willingness line grows steeper as it pro-ceeds upward and leftward, changing from a nearly hori-zontal direction at its lower right end to a nearly verticaldirection at the opposite end.

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