§2. The Six Principles

But the more fundamental theory of interest presupposes a stable purchasing power of money so that the real and nominal rates coincide. In that case the rate is theoretically determined by six sets of equations or conditions: the two Opportunity Principles; the two Impatience Principles; and the two Market Principles. The Edition: current; Page: [495] last pair may be said to cover prima facie supply and demand.

(A) The market must be cleared—and cleared with respect to every interval of time. (B) The debts must be paid.

The other two pairs represent the two sets of forces, one objective and the other subjective, behind supply and demand. The subjective pair expresses the influence of human impatience or time preference.

(A) The rate of time preference depends on the character of the various individuals concerned and on each individual's prospective income, its size, time-shape and risk.(B) Each individual's rate of time preference tends, at the margin of choice, to harmonize with the market rate of interest. Human impatience to spend and enjoy income is crystallized into the market rate.

The objective pair expresses the influence of investment opportunities.

(A) Each individual is encompassed about by opportunities to change the character of his prospective income stream. (B) At the margin of choice, any additions to an individual's future income at the cost of more immediate income constitutes a return over that cost, the rate of which return over said cost is also crystallized into the market rate of interest.

So the rate of interest is the mouthpiece at once of impatience to spend income without delay and of opportunity to increase income by delay.

Thus both from the subjective and the objective field appear prototypes, one of each for every individual, of the market rate of interest.

That rate, i, is equal to every individual's degree of impatience or rate of time preference, f, and also to his Edition: current; Page: [496] investment opportunity rate or rate of return over cost, r.

Yet these equations are not enough to make the problem determinate without those of the other four sets of determining conditions (clearing the market, repaying debts and empirical dependence of impatience and investment opportunity).

Much less is it possible to determine the rate of interest from the subjective side alone, through time preference, or from the objective side alone, through investment opportunity, or "productivity", or "technique of production".

The full explanation requires both (as well as the market principles) in order that there may be as many independent equations as unknown variables in the problem. Moreover there is not merely one rate of interest; there are many, one for each interval of time. And even so the explanation is full only under the theoretical conditions presupposed. If we pass beyond the presuppositions in order to approximate closer to the actual world, we find that, to be determinate, the problem requires more and more equations of a more and more empirical nature. This is especially true as (1) we introduce risk with its innumerable and omnipresent ramifications, involving in particular a multiplicity of rates of interest even for the same period of time; and as (2) we extend our view to admit variations in all other prices besides the rates of interest, involving thereby the whole economic equilibrium, not only of the loan market but of all markets, each interacting on every other; and as (3) we extend our view from one theoretical market to the actual markets of the whole world, involving thereby all the relations of international Edition: current; Page: [497] trade; and as (4) we take account of any other factors which may not be included in the foregoing specifications so as to take account, in particular, of all "institutional" influences, laws, politics, banking practices, government finance and so on to the end.

In the economic universe, as in astronomy, every star reacts on every other. From a practical point of view we cannot ignore the many perturbations. But from the theoretical point of view we gain clearness, simplicity and beauty, if we allow ourselves to assume certain other things equal, and confine our laws to a little part of the whole, such as the solar system.

From such a point of view, the second approximation is the most instructive, rather than the first which rules out the important element of investment opportunity, or than the third which becomes too complicated and vague for any complete theoretical treatment.