§6. Market Equilibrium

Just as in the first approximation, so in this second approximation there are two successive problems:

• (1) How the individual reacts to a given rate of interest.
• (2) How market equilibrium determines that rate.

The first of these two problems having now been solved, we are ready for the second, the market problem—to show how market equilibrium is established. This is precisely as in Chapter X, except that the M line, instead of rotating about a fixed point P, now rolls around the O line.

The problem, then, is simply to draw a set of straight M lines, one for each individual, each person's M line being tangent to his Opportunity line at a point P, all such M lines being parallel to each other, to find on each of them the point Q at which it is tangent to a W line of the person concerned, then to roll these straight lines around said Opportunity lines, while still keeping them Edition: current; Page: [276] all parallel, until they so slant that the center of gravity of the Q's shall coincide with the center of gravity of the P's. This slope, thus determined, signifies the rate of interest which will clear the market.

Let us recapitulate. We have given:

• (1) The Market lines, just as in the first approximation.
• (2) The families of Willingness lines, one family for each individual, just as in the first approximation.
• (3) The Opportunity lines, one only for each individual, that is, a series of points takes the place of the single point P1 in the first approximation.

We also have, correspondingly, three rates:

• (1) The market rate of interest represented by the slope (over and above that of 100 per cent) of each and every straight Market line.
• (2) The degree of impatience, or rate of time preference, one of each person, represented by the slope of the Willingness lines and depending on his income situation, as finally determined after all adjustments have been made.
• (3) The rate of return over cost, or the investment opportunity rate, one for each person, represented by the slope of the Opportunity line and depending on the position chosen on it.

The charts of this chapter interpret the second approximation exactly as the charts of Chapter X interpreted the first approximation, but with two new investment opportunity principles added to the four principles common to both Chapters X and XI and already geometrically interpreted in Chapter X. That is:

The Investment Opportunity Principle A is represented by the Opportunity line.

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The Investment Opportunity Principle B is represented by the tangency of the Opportunity line with the Market line, so that the marginal rate of return over cost is equal to the rate of interest.

This last principle, combined with Impatience Principle B, means that each individual so adjusts his position (first along the Opportunity line to P and then along the Market line to Q) that the Market line PQ shall be tangent to the first at P and to the second at Q. This Q will be his income situation finally chosen. To clear the market the Q's must be so chosen that their center of gravity coincides with that of the P's.