DISCUSSION OF SECOND APPROXIMATION

from any capital is fixed in aggregate amount, but thatthe times of receiving that income are controllable atwill. This species of choice occurs approximately in thecase of durable goods for consumption, which neither im-prove nor deteriorate with time. A stock of grain, forinstance, may be used at almost any time, with little dif-ference in the efficiency of the use and little cost exceptfor storage. The same is true of coal, cloth, iron, and otherdurable raw materials, as well as, to some extent, of fin-ished products such as tools and machinery, though usu-ally deterioration from rust, or other injury by the ele-ments, will set in if the use is too long deferred. Anothersimple example is a definite sum of money in a strongbox which may be spent at any time, or times, desired.Thus a strong box containing $100,000 may be so usedas to yield a real income of $100,000 for one year, or $10,-000 a year for ten years, or $4,000 a year for twenty-fiveyears.

Such options afforded by durable goods (as when touse them) are perhaps the simplest of all options. Sinceextreme cases are especially instructive, let us imagine acommunity in which the income from all capital is ofthe character just described. That is, we suppose thetotal quantity of income obtainable is absolutely fixed,but the times at which it can be obtained are absolutelyoptional. This community would then be endowed witha definite quantum of income as fixed as the quantity ofmoney in a strong box. That is, every dollar of incomesacrificed from one year’s income would eke out anyother income by that same amount, a dollar, no more andno less; conversely, every dollar of income enjoyed in oneyear would reduce indulgence elsewhere by exactly a dol-lar. The rate of interest would be reduced to zero.

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