§1 (to Ch. XII, § 1) Algebraic expression of rate of time preference

IF W signifies wantability, or utility, or desirability and this year's income is signified by X' and next year's by X'', then DW' may be taken to signify the present wantability of, or want for, a small increment, DX' of money this year and will be the want-for-one-more unit of money this year. Also DW'' is the present want for a small increment, DX'', of money available next year, and will be the present want-for-one-more unit of money available next year.

Exact mathematical theory requires that the marginal wants per unit of money are the limits of those ratios when the increments approach zero as their limits or lim and lim ordinarily written in the differential calculus: and which, for short, may be called w' and w''.

The rate of preference, f, for a unit of present money over a unit of next year's may be defined as

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