§3. The Individual's Adjustment Without Loans

What we have seen so far is that Individual 1, having discarded all income positions inside the Investment Opportunity line, has left as still eligible only the points on that curve.

As before, we assume that each individual is unconscious of having any influence on the market rate of interest. To fix our ideas suppose, as before, this rate to be 10 per cent. The only adjustments the individual can make are: (1) adjusting his position on the O line; (2) further adjusting on the M line. Problem (2) is analogous to that of Chapter X, so that Problem (1) is the only new one. The solution of Problem (1) will be found to point the way to the solution of the knottiest part of the interest problem, purposely omitted from the first approximation. This is the problem of investment opportunity, productivity, or technique of production in relation to the rate of interest.

The principle by which the individual may shift his position along the Investment Opportunity line is very similar to the principle already set forth in Chapter X by which he shifts along the Market line. It will be recalled that the individual shifted along the Market or Edition: current; Page: [267]M line according to its slope when that slope is compared, at any point, with the slope of the Willingness or W lines. We saw that, if we suppose him situated at a point on the M line at which the Willingness line drawn through that point is steeper than the Market line, he will move away from that point downward, along the M line, that is, he will borrow; while, if situated where his W line is less steep than his M line he will move upward along the M line, that is, he will lend.

Similar comparisons apply to our present problem merely by substituting Opportunity line for Market line. Suppose Individual 1 to be situated, to start with, at O1' on the Opportunity line, as shown on Chart 36. He then has the opportunity to shift to any other point on that line as formerly he could shift along the Market line. Let us, as before, proceed by small steps of $100 each. The first step is from O1' to O1''. The chart indicates that, by sacrificing $100 of this year's income, he can add $150 to next year's income, while he is willing to receive only $115 as indicated by his Willingness line drawn through O1'. The $50 net return he will receive is a 50 per cent rate of return over cost. This is his investment opportunity rate. He is willing to lend $100 for a net return of $15 or 15 per cent over cost. This measures his degree of impatience or rate of time preference. Evidently, as just hinted, he will seize the opportunity to invest for a 50 per cent return when he would be willing to take 15 per cent. This choice is represented on Chart 36 by following the Opportunity line from O1' to O1''.

If, as a second step, another $100 can bring him $140 while he would be willing to take $120, he will seize that opportunity, too, and so move on to O1'''. That is, he will Edition: current; Page: [268] choose a 40 per cent investment opportunity when his degree of impatience is only 20 per cent. Thus, he may be pictured ascending a staircase on the Opportunity line. The successive steps, in this case, grow less steep as he proceeds. At each point he decides whether to take the next step or not by comparing its steepness with that of the W line at that point. The successive W lines will be more and more steep as he goes on investing successive $100's, while the Opportunity line will become less and less steep.

When the point is reached where the Opportunity line is no longer steeper than the Willingness line, he will stop investing. The Willingness line through that point will have the same steepness as the Opportunity line, say 30 per cent. That is, the two curves will there be tangent. This point of tangency, R, is shown in Chart 37.

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The reasoning which has just been used is evidently exactly like that used in Chapter X, the only important difference being that then we had a straight line to deal with to express what the individual can do while here we have instead a curved line, or at any rate, a line which need not be straight.

And the result of this reasoning so far is also similar. The stopping point is where the can line (in Chapter X, the Market line; here, the Opportunity line) is tangent to the Willingness line.