THIRD APPROXIMATION

Rates of time preference in any one market tendtoward equality by the practice of borrowing and lend-ing, and more generally, that of buying and selling, butthis equality is no longer, in all cases, attainable, becauseof limitations on the freedom to modify the incomestream at will, li m itations growing out of the existence ofthe element of risk and consequent limitations on theborrowing power.

THE TWO MARKET PRINCIPLESA. Principle of Clearing the Market

In the first two approximations, where the element ofrisk was considered absent, it was shown that the aggre-gate modification of the income streams of all individ-uals for every period of time was zero. What was bor-rowed equaled what was lent, or what was added by salewas equal to what was subtracted by purchase. The sameprinciple still applies, for what one person pays, anotherperson must receive. The only difference is that, in aworld of chance, the actual payments may be quite differ-ent from those originally anticipated and agreed upon,that is, will often be defaulted, in whole or in part.

B. Principle of Repayment

In the former approximations, the total present valueof the prospective modifications of one’s income streamwas zero, that is, the present value of the loans equaledthe present value of the borrowings, or the present valueof the additions and subtractions caused by buying andselling balanced each other. In our present discussion, inwhich future income is recognized as uncertain, this prin-ciple still holds true, but only in the sense that the present

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