§4. The Imaginary "Hard-Tack" Illustration

To fix our ideas, let us suppose these conditions to be realized on a desert island on which some sailors are shipwrecked and each left with a specified number of pounds of hard-tack and with no prospect of ever improving his lot. We shall suppose the use of this hard-tack to be the only real income open to these castaways, and that they have given up all hope of ever adding to it by accessions from outside or by cultivating the island which, for our hypothesis, must be barren. No change in their human nature need be assumed. We assume that they would react to the same income just as before the shipwreck. Merely their circumstances have changed. In consequence, the only possible variation of their income streams—consisting solely of the use of hard-tack—is that made possible by varying the time of its consumption. Suppose one of them has an initial stock of 100,000 pounds. He has the option of consuming his entire store during the first year, or of spreading its use over two or more years, but in any case he will eventually aggregate the same total income, measured in hard-tack, spread over the future, namely 100,000 pounds.

A little reflection will show that, in such a community, the rate of interest in terms of hard-tack would necessarily be zero! For, by hypothesis, the giving up of one pound of hard-tack out of present consumption can only result in an equal increase in future consumption. One pound next year can be obtained at the cost of exactly one pound this year. In other words, the rate of return over cost is zero. Since, as we have seen, this rate must equal the rates of preference, or impatience, and also the rate of interest, all these rates must be zero also.

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This case is illustrated in Chart 21. One option is to consume the hard-tack at an even rate OA through the time OB. The total income will then be represented by the area OACB. Another option is to spread it over OB', double the above-mentioned time, and consume it at the rate of OA', half the rate first mentioned, so that the same total income will be represented by the area OA'C'B'. The choice of the second use rather than the first is at the cost of that part of the earlier income represented by the rectangle AD, and gives a return exactly equal in amount represented by the rectangle DB'. If the hard-tack is not consumed at a uniform rate, the alternative income streams will not be represented by rectangles, but by the irregular and equal areas OADB and OA'DB', shown in Chart 22. The substitution of the alternative OA'DB' for OADB increases immediate income by ADA' and decreases subsequent income by the exactly equal amount BDB'.

The conclusion, that the rate of interest, under such Edition: current; Page: [188] extreme conditions supposed in the hard-tack case, must be zero, is at first startling, but it is easy to convince ourselves of its correctness. It would be impossible for any would-be lender to obtain interest above zero on his loan for the only way in which a borrower could repay a loan would be to pay it out of his original stock of hard-tack. For assuming he had the impulse to borrow 100 pounds to consume today and pay back 105 pounds at the end of a year, he would instantly perceive that he could better consume the 100 pounds of his own hard-tack, thereby sacrificing next year not 105, but only 100 pounds out of his own stock. It is equally impossible that there should be a negative rate of interest. No one would lend 100 pounds of hard-tack today for 95 receivable a year later, when he had the option of simply storing away his 100 pounds today and taking it out, undiminished, a year later. Hence, exchanges of present for future hard-tack Edition: current; Page: [189] could not exist, except at par. There could be no premium or discount in such exchange.

Nor (to turn to the subjective side) could there be any rate of preference for present over future hard-tack. The sailors would so adjust the time shape of their respective income streams that any possible rate of preference for a present over a future allowance of hard-tack would disappear, and a pound of this year's hard-tack and a pound of next year's hard-tack would be equally balanced in present estimation. For, should a man prefer one rather than the other, he would transfer some of it from the unpreferred time to the preferred time, and this process would be continued, pound by pound, until his want for a pound of immediate hard-tack and his want for a pound of future hard-tack were brought into equilibrium. Thus, if through insufficient self-control, he prefers, however foolishly, to use up much of his store in the present and so to cut down his reserve for the future to a minimum, the very scantiness of the provision for the future will enhance his appreciation of its claims, and the very abundance of his provision for the present will diminish the urgency of his desire to indulge so freely in the present.

Provided each individual is free to apportion his share of the total stock of hard-tack between present use and future use as he pleases, and provided there is some hard-tack available for both uses, the present desire for a pound of each will necessarily be the same.

(Failure of such equilibrium of want could only occur when, as in starvation, the want for the present use was so intense as to outweigh the want for even the very last pound for future use, in which case there would be none whatever reserved for the future.)

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All persons, however different in nature, would alike have a zero rate of impatience. They would differ simply in the way they distributed their income over present and future. The spendthrift and the miser would still spend and save respectively but both would value a unit of hard-tack today as the exact equivalent of one due a year hence. It is evident that some of the sailors, with a naturally keen appreciation of the future, would plan to consume their stores sparingly. Others would prefer generous rations, even with the full knowledge that starvation would thereby be brought nearer, but none of them would consume all of his stock immediately. They would, generally speaking, prefer to save out of such reckless waste at least something to satisfy the more urgent needs of the future.

In other words, a certain amount of saving (if such an operation can be called saving) would take place, without any interest at all. This conclusion coincides with conclusions expressed by Professor Carver in his Distribution of Wealth.71 It shows also that the preference for present over future goods of like kind and number is not, as some writers assume, a necessary attribute of human nature, but that it depends always on the relative provisioning of the present and future.

The foregoing imaginary hard-tack case is of great help, therefore, in emphasizing the essential rôle of the rate of return over cost. This simple example, of itself, demonstrates that no theory of interest is complete which ignores the rate of return over cost. In the example we have both elements, investment opportunity and impatience, although both are at the vanishing point, that Edition: current; Page: [191] is, the rate of return and the rate of impatience are both zero, the former, rate of return, being fixed at zero by the technical conditions of the particular environment on the desert island, and the impatience rate being forced thereby to be zero also. In this case opportunity (or the lack of it) rules impatience.

It would be possible, of course, to make this illustration somewhat more realistic by adding to our supposed supplies of hard-tack supplies of other foods, as well as of clothing and sundry other real income. But the value of the illustration is not in any realism which can be made out of it. Rather does the fact that conditions in real life do not permit such freedom of shifting real income in time (because of change in quantity or quality) reveal some of the reasons why the rate of interest is not zero.