§3. Equalization of Impatience

Under the hypothetical conditions which have been stated for the first approximation, the rates of time preference for different individuals will, by the process of borrowing and lending, become perfectly reconciled to the market rate of interest and to each other, for if, for any particular individual, the rate of preference differs from the market rate, he will, if he can, adjust the time shape of his income stream so as to bring his marginal preference rate into harmony with the interest rate. A man who, for a given income stream, has a rate of preference above the market rate will sell some of his surplus future income in return for an addition to his meager present income, i.e., he will borrow. This will have the effect of enhancing his want for one more dollar of future income and decreasing his want for one more dollar of present income. The process will continue until the rate of preference of this individual, at the margin, is equal to the rate of interest. In other words, under our hypothesis, a person whose preference rate exceeds the current rate of interest will borrow up to the point at which the two rates will become equal.

On the other hand, the man, whose temperament or whose income stream or both give him a preference rate below the market rate, will buy future income with some of his abundant present income, i.e., he will lend. The Edition: current; Page: [105] effect will be to increase his preference rate until, at the margin, it harmonizes with the rate of interest.

To put the matter in figures, let us suppose the rate of interest is 5 per cent, whereas the rate of preference of 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 this year'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 therefore borrows, say, $100 for a year, agreeing to return $105; that is, he contracts a loan at 5 per cent, when he is willing to pay 10 per cent. This operation partly satisfies his hunger for present income by drawing on his future income, and thus reduces his time preference from 10 per cent to, say, 8 per cent. Under these circumstances he will borrow another $100, being willing to pay 8 per cent, but required to pay only 5. This operation will still further reduce his time preference, and so on through successive stages, until it is finally brought down to 5 per cent. Then, for the last or marginal $100, his rate of time preference will agree with the market rate of interest.50

In like manner, if another individual, entering the loan market from the opposite side, has a rate of preference Edition: current; Page: [106] of 2 per cent, he will become a lender instead of a borrower. He will be willing to lend $100 of this year's income for $102 of next year's. As he can lend at 5 per cent when he would do so at 2, he "jumps at the chance," and invests, not $100 only, but another and another. But his present income, being drawn upon by the process, is now more highly esteemed by him than before, and his future income, being supplemented, is less highly esteemed; and under the influence of successive additions to the sums lent, his rate of preference for the present will keep rising until, at the margin, it will equal the market rate of interest.

In such an ideal loan market, therefore, where every individual could freely borrow or lend, the rates of preference or impatience for present over future income for all the different individuals would become, at the margin, exactly equal to each other and to the rate of interest.