FIRST APPROXIMATION

effect will be to increase his preference rate until, at themargin, it harmonizes with the rate of interest.

To put the matter in figures, let us suppose the rateof interest is 5 per cent, whereas the rate of preferenceof a particular individual is, to start with, 10 per cent.Then, by hypothesis, the individual is willing to sacrifice$1.10 of next year’s income in exchange for $1 of thisyear’s. But, in the market, he finds he is able to obtain$1 for this year by foregoing only $1.05 of next year’s.To him this latter ratio is a cheap price. He thereforeborrows, say, $100 for a year, agreeing to return $105;that is, he contracts a loan at 5 per cent, when he iswilling to pay 10 per cent. This operation partly satisfieshis hunger for present income by drawing on his futureincome, and thus reduces his time preference from 10per cent to, say, 8 per cent. Under these circumstanceshe will borrow another $100, being willing to pay 8 percent, but required to pay only 5. This operation will stillfurther reduce his time preference, and so on throughsuccessive stages, until it is finally brought down to 5per cent. Then, for the last or marginal $100, his rate oftime preference will agree with the market rate ofinterest. 2

In like manner, if another individual, entering theloan market from the opposite side, has a rate of prefer-

3 The above-mentioned 10 per cent and 8 per cent rates of time pref-erence are not rates actually experienced by him; they merely meanthe rates of preference which he would have experienced had his in-come not been transformed to the time shape corresponding to 5 percent. As in the general theory of prices, this marginal rate, 5 per cent,being once established, applies indifferently to all his valuations ofpresent and future income. Every comparative estimate of present andfuture which he actually makes may be said to be “on the margin” ofhis income stream as actually determined.

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