§1. Hypotheses of First Approximation

IN the last chapter we reached three conclusions:

• (1) that the rate of time preference, or impatience for present over future goods, is, in the last analysis, a preference for present over future enjoyment income, or, let us say, real income;
• (2) that the degree of impatience depends, for any given individual, upon the character of his real income-stream—in particular, on its size, time shape, and probability;
• (3) that the nature of this dependence differs with different individuals.

The question at once arises: will not the actual degrees of impatience of different individuals necessarily be very different, and if so, what relation do these different rates have to the market rate of interest? Is the market rate of interest a sort of average of these individual degrees of impatience, or does it equalize them?

It is doubtless true that the different rates of impatience of different individuals who are not connected through a common loan market do vary widely. In a nation of Edition: current; Page: [100] hermits, in which there existed no mutual lending and borrowing, individuals would be independent of each other. But, among ourselves who have access to a common loan market, borrowing and lending do, at least, tend to bring into equality the marginal rates of impatience in different minds. Absolute equality is not reached even among those making use of such a market; but this is because of the limitations of the market and, in particular, because of the risk element. This element will be considered in the third approximation, but for simplicity of exposition is omitted in the first two approximations.

Here we shall assume a perfectly competitive market, one in which each individual is so small a factor as to have, singly, no perceptible influence on the rate of interest, and in which there is no limitation on the amount of lending and borrowing other than that caused by the rate of interest itself. The would-be borrower is thus supposed to be able to obtain as large or small a loan as he wishes at the market price—the rate of interest. He is not cut down to $5,000 when he is willing to borrow $100,000, merely because he cannot furnish enough collateral security or a satisfactory endorser. He can buy a loan as he can buy sugar, as much or as little as he pleases, if he will pay the price.

In the actual world, of course, no such perfect market exists. While many people in New York City can obtain as large loans as they wish, there are thousands who are unable to obtain any at all. The price of a loan is paid not in the present, as the price of sugar is paid, but in the future. What the lender gets when he makes the loan is not payment but a promise of payment, and the future being always uncertain he needs some sort of assurance that this promise will be kept. We are assuming in the Edition: current; Page: [101] first and second approximations that there will never be a lack of such assurance. This amounts almost to assuming that there is no risk in the world. The element of risk is assumed to be entirely lacking, both with respect to the certainty of the expected income streams belonging to the different individuals, and with respect to the certainty of repayment for loans. In other words, we assume that each individual in the market is free to give up any part of his income during one period of time to some other person in consideration of receiving back an addition to his own income during another period of time.

We assume further that thus to buy and sell rights to various parts of his income stream is the only method open to any individual to alter his income stream. Such trading between present and future dollars may be in the form of loans, since a loan is the sale of future money for present money, or it may be in the guise of buying and selling bonds or other securities conveying title to fixed sums of money. In any case the trading reduces itself to buying and selling titles to future income. Prior to such exchange, the income stream of each individual is assumed to be fixed in size and shape. Each capital instrument which he possesses, including himself, is assumed to be capable of only a single definite series of services contributing to his income stream. Each individual is a stipendiary with a definite income which he receives and spends according to a foreknown schedule—so much next year, so much the year after, and so forth.

Thus the assumptions of our first approximation are: (1) that each man's income stream is initially certain and fixed; (2) that he is a negligible element in a vast and perfect competitive loan market; (3) that he has Edition: current; Page: [102] free access to this market, whether as borrower or lender, to any desired extent, at the market rate; (4) that his sole method of modifying his future income stream is through such borrowing or lending (or, more exactly and generally, through trading income).