§7. Many Families of Willingness Lines

The Willingness lines, on the other hand, are personal, or individual. The particular slope in each case is, of course, dependent on the particular income position P1. A given Individual 1 is concerned with only one Willingness line at a time, out of his whole "family" of lines—the one line which passes through his actual income position at P1. By comparing his Willingness line at that particular point with the Market line, we have a graphic picture of the motives which decide whether he will borrow or lend.

There always exists for him, potentially, other Willingness lines, passing not through his actual income position P1, but through any other income position at which he could be imagined to be. These curves represent the various rates at which Individual 1 would be willing to borrow or lend if his income position were varied. Thus Edition: current; Page: [245] the number of Willingness lines for any one Individual is infinite, and every other individual will have his own family of lines.

We conceive, then, of a map for Individual 1 alone, covered with a family of such Willingness lines infinite in number, arranged so as to vary gradually from each to the next, like the lines of elevation on a geographic contour map of a mountain.5

While Individual 1 finds all points on any one Willingness line of equal desirability or "wantability," he would rather have his income position on lines more to the "northeast," or farther from the origin. Each Willingness line might be labelled with a number representing specifically the total desirability or "wantability" pertaining to each and all of the income positions on it. It is the locus or assemblage of these points (combinations of income for the two years) equally desirable in the estimation of Individual 1. A greater aggregate income in the two years may be offset in respect to the resulting total desirability by a less convenient distribution between the two years and vice versa.6

But we are not yet interested in such differences of level or total desirability between the Willingness lines. We are here interested only in the directions of the Willingness lines at different points, representing the different Edition: current; Page: [246] degrees of impatience pertaining to different income situations. These directions, or divergences from the 45° line, picture to us how the individual would be willing to borrow or lend under all possible income circumstances.