§2. The Investment Opportunity Line

The reason why we may exclude all points inside of this boundary line is evident. The inside points would never be chosen under any circumstances, since each inside point is excelled by some points on the boundary in respect to both years' incomes. Thus the point A in Chart 35 will certainly not be chosen if the individual has the opportunity to substitute any other point to the north 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—whether this year, next year, or both. These limits make up the boundary line O1' O1IV. Chart 35 represents Individual 1 as having the opportunity to shift his income position on this map in an eastward direction only up to the position O1'. In other words, he can increase his income in the present year without changing his income in the next year only up to that limit O1'. Technical limitations, including personal limitations, are assumed to forbid his pushing to the right beyond O1'.

In the same way, starting again at A, he has the opportunity to move northward on this map—that is to increase next year's income without changing this Edition: current; Page: [265] year's—but only up to a certain limit O1IV. Or he can move in a somewhat northeasterly direction and better himself for both years at once, but again he can do this only up to a certain limit, O1'' or O1'''.

The boundary line O1' O1IV, made up of these limiting points may, of course, take various forms, but, for the present it will be assumed to be a curve concave toward the origin. It is simply a geometric picture of the technical limitations of an individual's income in the two years considered, assuming, as always, all other years' income to remain the same. It is the locus, or line, of options Edition: current; Page: [266] and may be called the Option line or the Opportunity line,9 and is designated as O1 for Individual 1.