§4. The Willingness Line

So far we have used the new type of chart only to show how the individual can move—change his income situation. The next question is: in which one of the two directions on the Market line will he actually move? The answer depends on his degree of impatience compared with the market rate of interest. We have seen how the market rate of interest is represented graphically by the slope, relatively to 45°, of the Market line in Chart 26. We are now ready to make a similar graphic representation of the individual's rate of time preference or impatience. This is expressed by a series of curved lines showing on what terms, at any income position (such as P1), the individual would be willing to lend or borrow, say $100. What one is willing to do and what he can do are two quite different things. The Market line of Chart 26 shows what he can do, while the Willingness lines, now to be described, will show what he would be willing to do.

Individual 1's impatience is such that he would be Edition: current; Page: [239] willing, if necessary, as shown in Chart 27, to borrow his first $100 at 30 per cent, considerably above the market rate, 10 per cent. That is, he would be willing to sacrifice $130 out of next year's income in order to add $100 to this year's income. To get a second $100 this year, he would not be willing to pay quite so much, but only, say, $120. A third $100 would be worth to him only $110; a fourth still less, and so on. These willingness points make a curved staircase, the steps being from P1 to W1', from W1' to W1'', and so on, in which each tread is taken to be $100, but the risers are decreasing as the borrower steps down southeasterly, being successively 130, 120, 110. The Edition: current; Page: [240] Willingness line, P1W1IV, is not a straight line like P1M1 in Chart 26, but a curved line. The steepness of each step, or ratio of risers to tread, or slope of the curves shows the degree of impatience at that particular step.

The Willingness line through P1 extends, of course, in both directions. It shows not only on what terms Individual 1 would be willing to borrow, but also on what terms he would be willing to lend. At point P1, he is willing to lend the first $100 at 40 per cent, a second, at 50 per cent, and so on. Everyone theoretically is ready either to borrow or to lend according to the terms. Individual 1 is here represented as barely willing at P1 either to borrow $100 at 30 per cent, or to lend $100 at 40 per cent. In short, he would be willing to substitute the combination represented by any given point on his Willingness line for the combination represented by any other point on the same line. All points on that line are, by hypothesis, equally desirable to Individual 1. Each segment of the Willingness line, by the divergence of its slope from 100 per cent, shows the degree of impatience at the particular income position there represented.

Consequently, P1W1 might be called an Impatience line quite as well as a Willingness line3 for Individual 1. There would be another Willingness line, or W line, for any other individual. The W lines thus differ from the Market, or M, lines which are common to everybody in the market.