THE THEORY OF INTEREST

is correct we have reduced the whole problem to one ofgeometry.

Incidentally, it may be remarked here that there is evi-dently nothing inherent in the geometrical constructionas presented which necessitates a positive rather than anegative market rate of interest. A negative rate cantheoretically emerge whenever the P’s and their center ofgravity are of sufficiently low latitude or great longitude,or both, so that the common slope of the Market linestangent at the Q’s with the Willingness lines, will be lessthan 100 per cent. That this is theoretically possible isevident from inspection, provided the Willingness linesdo, as assumed, have inclinations at certain income posi-tions less than 45°. The reasons why the rate of interestis seldom or never negative have chiefly to do with theconditions introduced under the second approximationand will be more apparent in the next chapter.

§15. The Four Principles as Charted

In this geometric picture we see that the four principlesformerly stated in words (in Chapter V) are now inter-preted geometrically on the “map” as follows:

(1) Impatience principle A (that each man’s impa-tience or rate of time preference depends on his incomestream) is represented by a family of Willingness linesfor each individual.

(2) Impatience principle B (that each rate of timepreference is assimilated to the market rate of interest)is represented by the tangency at each individual’s pointQ, thus making the slope of his W line at that point equalto the slope of the M line.

(3) Market principle A (that the market will becleared) is represented by the fact that the aggregate

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