§7. The Influence of Time Shape

The concept of time shape of the income stream34 is best treated not apart from size but as combined with size and thus will constitute a complete specification of the size at each successive period of time. Types of income of different time shapes are shown on the charts in Chapter I. Uniform income is represented in Chart 1; increasing income in Chart 2; decreasing income in Chart 3. Fluctuating income is represented in both Charts 2 and 3.

The fact that a person's income is increasing tends to make his preference for present over future income high, as compared with what it would be if his income were flowing uniformly or at a slackening rate; for an increasing income means that the present income is relatively Edition: current; Page: [74] scarce and future income relatively abundant. A man who is now enjoying an income of only $5000 a year, but who expects in ten years to be enjoying one of $10,000 a year, will today prize a dollar in hand far more than the prospect of a dollar due ten years hence. His great expectations make him impatient to realize on them in advance. He may, in fact, borrow money to eke out this year's income and promise repayments out of his supposedly more abundant income ten years later. On the other hand, a progressively dwindling income, one such that present income is relatively abundant and future income relatively scarce, tends to appease impatience—i.e., to reduce the want for present as compared with that for future income. A man who has a salary of $10,000 at present but expects to retire in a few years on half pay will not have a very high rate of preference for present over future income. He may even want to save from his present abundance in order to provide for coming needs.

These are, of course, only some of the various effects which various time shapes have on time preference. The important point is that it does make a difference to a man's time preference whether his income has one time shape or another, just as it makes a difference whether his income is, as a whole, larger or smaller.

The extent of these effects will, of course, vary greatly with different individuals. If two persons both have exactly the same sort of ascending income, one may have a rate of time preference, or degree of impatience, indicated by 10 per cent, while the other may have one of only 4 per cent. What we need to emphasize here is merely that, if for either man a descending income were substituted for an ascending income, he would experience a reduction of impatience; the first individual's might fall Edition: current; Page: [75] from 10 to 7 per cent, and the second's from, say, 4 to 3 per cent.

If, now, we consider the combined effect on time preference of both the size and the time shape of income, we shall observe that those with small incomes are much more sensitive to time shape in their feeling of impatience than are those with larger incomes. For a poor man, a very slight stinting of the present suffices to enhance enormously his impatience for present income; and oppositely, a very slight increase in his present income will suffice enormously to diminish that impatience. A rich man, on the other hand, presumably requires a relatively large variation in the comparative amounts of this year's and next year's income in order to suffer any material change in his time preference.

It will be clear to readers of Böhm-Bawerk that the dependence of time preference on the time shape of a person's income stream is practically identical with what he called the "first circumstance" making for the superiority of present over future goods:

"The first great cause of difference in value between present and future goods consists in the different circumstances of want and provision in present and future.... If a person is badly in want of certain goods, or of goods in general, while he has reason to hope that at a future period he will be better off, he will always value a given quantity of immediately available goods at a higher figure than the same quantity of future goods."35

The only important difference between this statement and that here formulated is that in this book the "provision" has the definite meaning contained in the income concept.

It is only for completeness that I have included in the Edition: current; Page: [76] list of characteristics of income affecting interest the composition of the income. It recognizes the fact that, strictly speaking, a man's real income is not one simple homogeneous flow of money, but a mosaic or skein of threads of many heterogeneous elements of psychic experience. An income of $5000 may comprise for one individual one set of enjoyable services, and for another, an entirely different set. The inhabitants of one country may have relatively more house shelter and less food in their real incomes than those of another. Those differences will have, theoretically, an influence in one direction or the other upon the time preference. Food being a prime necessity, a decrease of the proportion of food, or nourishment, even though total income remain the same, will have an effect upon the impatience similar to the effect of the diminution of total income.

For practical purposes, however, we may ordinarily neglect the characteristic of income called composition; for ordinarily any variation in the mere composition of family budgets will very seldom be sufficient to have any appreciable effect on the rate of interest.

Hereafter, therefore, all the elements of income will be considered as lumped together in a single sum of money value. Our picture of income henceforth may be considered as a flag or pennant without regard to stripes but seen as a whole, stretching out into the future. Each man's pennant has a definite width varying with the distance from the flagstaff.