§6 (to Ch. XIII, § 9) Walras and Pareto

WALRAS and Pareto probably deserve more attention in interest theory, as in general economic theory, than they have received.

Walras' interest theory forms an integral part of his theory of general economic equilibrium.4 His solution consists of a demonstration that the problem comprises a number of independent equations exactly equal to the number of unknowns, and that the mathematical solution of these simultaneous equations is a counterpart of the economic process by which the unknowns are determined in the market. There is thus no reasoning in a circle in the Walras system. The number of equations is exactly equal to the number of unknowns.

Walras' treatment of the problem of the determination of the rate of interest is very detailed and highly mathematical. For readers who are not familiar with his treatment I venture to attempt a brief summary. Walras assumes a market for capital goods as well as for services. He assumes that the prices of capital goods depend on the prices of their services. Since some capital goods last longer than others and all are subject to risk, he makes allowance for depreciation, amortization, and insurance.

His treatment combines the subjective and objective elements in a simple and direct manner. His cost of production equations correspond, in a general way, to my opportunity principles. His equation for the demand for savings corresponds, likewise, to my impatience principles.

Pareto's analysis of the problem of the rate of interest5 is along the lines laid down by Walras, although he was evidently not fully satisfied with Walras' treatment. Neither he nor Walras has developed a systematic theory of income but he Edition: current; Page: [519] shows, in effect, that the substitution of one income stream for another or, as he says, the "transformation in time" is only a particular case of a more general transformation which is dealt with in the theory of production. His indifference equations for consumers correspond in a general way to my impatience principles and the analogous equations for the obstacles in his treatment of production correspond likewise to my opportunity principles.

The fundamental differences between the approach of Walras and Pareto on the one hand and mine on the other seem to be four:

(1) Walras and Pareto determine the rate of interest simultaneously with all the other unknowns of the problem—the quantities of the commodities exchanged and the services used in their production and the prices of the commodities and the services, while I try to isolate the interest problem by assuming that most of such unknowns have already been determined and confine my discussion to the special factors directly affecting the rate of interest.

(2) They both treat what I call interactions or intermediate services along with the ultimate factors—our desires or tastes (les gôuts) and the obstacles which must be overcome to satisfy them—while I try at the outset to get the interactions canceled out, leaving only the income stream and (labor) sacrifice.

(3) Neither Walras nor Pareto has elaborated the concept and principles of an income stream.

(4) Neither has elaborated the concept or principles of opportunity as a choice from among a series of income streams, although it is, in part, implied in Pareto's treatment.6