§16. The Geometric Method

These charts do, for the ideas they illustrate, what supply and demand curves do for the ideas illustrated by them.

Like all graphic methods, the one here applied is intended to segregate basic tendencies from the rough-and-tumble of real life, and set these tendencies going as they cannot go in real life. It condenses a year's income into an infinitesimal time; it confines our variations to two years only; it disregards the element of risk; it pictures next year's income as a certainty; it disregards the lack of security that limits the ease with which an individual can slide his series of transactions along the M line; it assumes that the market is perfect.

Again, the Willingness lines should not be drawn as continuous curves. They are actually rough and jagged, so that, for this reason alone, the nicety of adjustment which would obtain under the assumption of continuity is lost. We know also that most individuals require a considerable stimulus even to start sliding along a Market line. Besides the height of the rate of interest, there is the trouble of negotiating a loan, establishing a line of credit, Edition: current; Page: [260] and practical considerations without end. One result is that in order to reverse one's direction on the Market line, a bigger rise or fall of the interest rate would be needed than the charts as here used would suggest. It takes a push to dislodge the individual from P in either direction. The same sort of considerations cause his position Q to be determined without the nicety of precision suggested by the continuous curves.

But all these and other practical considerations do not destroy the fact that each of our four determining conditions represents a reality—a real tendency even when in actual practice balked or neutralized.

The relationship of the rate of time preference to income is analogous to that of marginal utility or cost to consumption or production. In order to show how the marginal desirability of sugar in the case of Individual 1 is related to his consumption of sugar, we employ a curve, which, under certain assumptions, becomes the familiar demand curve for sugar. Such a curve has come into universal use.

Why has no similar curve been used to indicate the corresponding relationship between time preference (a marginal desirability derivative) and income? There are many reasons, but perhaps chief is the difficulty of finding a suitable graphic method for variables so diverse and related to each other in so complicated a manner. The map of the Willingness, or Impatience, lines partly solves this problem. So far as two periods of time are concerned, it "puts on the map" the whole problem of interest.