So much for the individual. The market problem determiningthe rate of interest is here solved by finding such an orientationfor the various planes through the given points called P’s aswill bring the center of gravity of the tangential points, theQ’s, into coincidence with the fixed center of gravity of the P’s.
To proceed beyond three years would take us into the fourthdimension and beyond. Such a representation cannot be fullyvisualized, and therefore has little meaning except to mathe-maticians.
APPENDIX TO CHAPTER XII§ 1 (to Ch. XII, § 1)
Algebraic expression of rate of time preference
If W signifies wantability, or utility, or desirability and thisyear’s income is signified by X' and next year’s by X", thenA W' may be taken to signify the present wantability of, or want
XW'
for, a small increment, AX' of money this year and —will be
A JL
the want-for-one-more unit of money this year. Also AW" isthe present want for a small increment, AX”, of money avail-
able next year, and
AW"
AX"
will be the present want-for-one-more
unit of money available next year.
Exact mathematical theory requires that the marginal wantsper unit of money are the limits of those ratios when the in-
AW’
crements approach zero as their limits, or lim and lim
dW'
ordinarily written in the differential calculus: -^7 and
AW"AX"dW "dX”
which, for short, may be called w' and w”.
The rate of preference, /, for a unit of present money over a
y) f
unit of next year’s may be defined as / = --
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