IN TERMS OF FORMULAS

principle that the maximum present market value ischosen is the same 2 as the principle that r lt the marginalrate of return over cost, shall be equal to i, the marketrate of interest.

This is true for each year-to-year relation, so that wehave, for Individual 1, the following continuous equa-tions:

n }

Jftmr- 1) _ ^ (m—1) _ ^(m—1) — ^(m—1).

Here are n(m — 1) equations expressing InvestmentOpportunity Principle B.

§8. Counting the Equations and Unknowns

Collecting our various counts of the numbers of equa-tions, we have:

For Impatience Principle A, n(m — 1) equations“ “ “ B, n(m — 1)

“ Market “ A, m “

“ “ “ B, n

For Investment Opportunity Principle A, n equations“ “ “ " B, n(m — 1) “

The sum total of these is 3n( m — 1) + 2n + m, or3 mn -f- m — n.

To compare this number with the number of unknowns,we note that all the unknowns in the first approximationare repeated;

“For the mathematical statement on this equivalence see Appendix to this chapter (Chapter XIII), §3.

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