THE THEORY OF INTEREST

If this list of options be assumed for convenience ofanalysis to consist of an infinite number of options vary-ing from one to another, not by sudden jumps, but con-tinuously, the complete list can be expressed by thosepossible values of y/, y", • • • yi m) which will satisfy anempirical equation. There will be one such equation foreach individual, thus:

= 0 ,

•Paiys, y”,- ■ -y2 m) ) = o,

<Pn(y n '> y”, ■. ■ y n {m) ) = 0 .

Here are n equations, expressing the Investment Oppor-tunity Principle A. The form of each of these equationsdepends on the particular technical conditions to whichthe capital of the Individual concerned is subjected. Itcorresponds to the 0 line of Chapter XI except that onlytwo years were there represented whereas here all myears are represented. Any one equation sets the limita-tions to which the variation of the income stream of aparticular individual must conform. Each set of valuesof y-L, y”, ... 2/i (m> which will satisfy this equation rep-resents an optional income stream.

§7. Opportunity Principle B. ( n(m — 1) Equations)

Out of this infinite number of options the individualhas opportunity to choose any one rather than any other.That particular one will be chosen for which the presentvalue is greater than for any other, in other words, is themaximum.

If the options differ by continuous gradations this

[306]