CHAPTER X

FIRST APPROXIMATION IN GEOMETRIC TERMS§1. Introduction

We found in Chapter V that, if the degree of any givenindividual’s impatience depended solely on his incomestream, and if that stream could not be modified throughthe loan market or otherwise, his impatience could notbe modified either. In such a world of hermits, each per-son would have his own individual rate of time prefer-ence, the various individual rates ranging from severalthousand per cent per annum down to zero, or below. Insuch a world, since there would be no loans, there wouldbe no market rate of interest.

But we also perceived that, as soon as our hermits areallowed to swap income streams, one man exchangingsome of this year’s income for some future income ofanother, then these myriad rates of time preference orimpatience tend to come together toward a common rate,and, on the assumption that no risk attends these transac-tions, a uniform market rate of interest would actuallybe reached. In such a perfect loan market the degree ofimpatience of each person would become equal to that ofevery other person and to the rate of interest.

§2. The Map of This Year’s and Next Year’s Income

Expressing the problem with the aid of the graphicmethod, the determination of the rate of interest may

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