§6. The Imaginary "Sheep" Example

The next example is more like that in our real world. In the real world our options are such that if present income is sacrificed for the sake of future income, the amount of future income secured thereby is greater than the present income sacrificed. That is, the income which we can extract from our environment is not, in the aggregate, a fixed quantum like a storehouse of hard-tack; still less is it like a storehouse of dwindling contents. On the contrary, Nature is, to a great extent, reproductive. Edition: current; Page: [193] Growing crops and animals often make it possible to endow the future more richly than the present. Man can obtain from the forest or the farm more by waiting than by premature cutting of trees or by exhausting the soil. In other words, Nature's productivity has a strong tendency to keep up the rate of interest. Nature offers man many opportunities for future abundance at trifling present cost. So also human technique and invention tend to produce big returns over cost.

It is difficult to imagine a precise and simple case in which the rate of return over cost is fixed as in the case of the hard-tack or the figs but, instead of being zero or negative, is positive, say 10 per cent, neither more nor less. The best example is the ingenious one worked out by Professor Harry G. Brown in which fruit trees are planted at the cost of 100 units of fruit and automatically produce 110 units of fruit a year later and then die.72 A simpler imaginary example, if we can forget certain obvious practical limitations, is that of the proverbial flock of sheep, which multiply in geometric progression affording alternately 100 units of mutton and wool today or 110 next year and ten per cent more each succeeding year. These examples symbolize a state of things in which it is always possible at the cost of 100 units out of this year's income to secure a return of 110 units next year, making a return over cost of 10 per cent. In such examples, just as in the hard-tack case with its zero per cent, or the fig case with its minus 50 per cent, the investment opportunity principles prescribe or dictate the rate of interest and the rate of time preference. These rates will in the present instance of the sheep all be 10 per cent.

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We see then that, given the appropriate environment, the investment opportunity principle may dominate interest and force it to be zero, or minus 50 per cent, or plus 10 per cent, or any other figure. Under such conditions, the rate of impatience and the rate of interest will follow suit.

In actual life, however, any shoving of real income forward or backward in time can never be done without causing a variation in the rate of return over cost. The result is that the rate of impatience influences the rate of return quite as truly as the rate of return influences impatience.