THE THEORY OF INTEREST

By the use of this notation we avoid negative signs andso the necessity of distinguishing between the expressionsfor loans and repayments or for lenders and borrowers.

§2. Impatience Principle A (Three Equations)

The first condition determining interest, namely, Im-patience Principle A, that the rate of preference for eachindividual depends upon his income stream, is repre-sented for Individual 1 by the following equation:

h — Fi (c/ + a;/, ci" + a*")which expresses / x as dependent on, or, in mathematicallanguage, as a function of the two income items of thetwo respective years, F x being not a symbol of a quantitybut an abbreviation for “function." In case the indi-vidual lends instead of borrows, the equation representsthe resulting relation between his marginal rate of prefer-ence and his income stream as modified by lending; theonly difference is that, in this case, the particular nu-merical value of x' is negative and that of x" positive.The equation is the algebraic expression for the depen-dence of the slope of a Willingness line on the incomeposition of Individual 1.

In like manner, for Individual 2, we have the equationiz — Ei (ci + X2', Cz" ,

and, for the third individual,

iz = F s (c a ' -f- Xs', C3" -(- £3").

These three equations therefore express ImpatiencePrinciple A.

§3. Impatience Principle B (Three Equations)

Impatience Principle B requires that the marginalrates of time preference of the three different individuals

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