THE THEORY OF INTEREST

able to Individual 1 aside from any further shifts throughborrowing or lending. Instead of having no choice but afixed position as in Chapter X, he now has the opportun-ity to choose any one of many income positions, but willactually confine his choice to those positions representedupon the boundary line 0/ Oi Iv . This may be called theInvestment Opportunity line or briefly the O line for In-dividual 1. Every individual, of course, has his own 0line.

§2. The Investment Opportunity Line

The reason why we may exclude all points inside ofthis boundary line is evident. The inside points wouldnever be chosen under any circumstances, since each in-side point is excelled by some points on the boundary inrespect to both years’ incomes. Thus the point A inChart 35 will certainly not be chosen if the individual hasthe opportunity to substitute any other point to thenorth or east of it, or between north and east.

But in no case can income be increased indefinitely.There are limits in whatever direction we try—whetherthis year, next year, or both. These limits make up theboundary line 0/ Ox Iv . Chart 35 represents Individual 1as having the opportunity to shift his income position onthis map in an eastward direction only up to the posi-tion Oi. In other words, he can increase his income in thepresent year without changing his income in the next yearonly up to that limit O x ’. Technical limitations, includingpersonal limitations, are assumed to forbid his pushing tothe right beyond 0/.

In the same way, starting again at A, he has theopportunity to move northward on this map—that isto increase next year’s income without changing this

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