IN TERMS OF FORMULAS

obtaining its value not in the present or first year but inthe second year, and then discounting this value soobtained by dividing it in turn by 1 + x". The next itemx IV is converted into present value, through three suchsuccessive steps, and so on. Adding together all thepresent values we obtain as resulting equations for Indi-viduals 1,2, .... n:

Xl " x l (m '> _

+ T+7 + • • • • + (i + i') (i +i") .... (i+ i(»-D) ~°-

Similar equations will hold for each of the other indi-viduals, namely:

xs " ^(m)

^ + T+T + • • ’ • + (l + i') (!+*") .... (1 +{(m-D) = °‘

, , Xn" , ,_ Xnf*> _ _ „

1 + i ’ '*■•••• "*■ ( 1+0 (1 + i ") .... (1 + u -

making in all n equations.

§12. Counting Equations and Unknowns

We therefore have as the total number of equationsthe following:

n ( m — 1) equations expressing Impatience Principle A,n (to — 1) equations expressing Impatience Principle B,m equations expressing Market Principle A, andn equations expressing Market Principle B.

The sum of these gives 2 mn — n equations in all.We next proceed to count the unknown quantities(rates of time preference, loans, and rates of interest).First as to the f s:

For Individual 1 there are /T, /T, ...., /i (m ~ 1) , thenumber of which is to — 1, and, as there is an equal

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