Arrow and Debreu: Existence of an Equilibrium for a Competitive Economy

Arrow, KJ, and G Debreu. 1954. “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22:265-290.

This piece builds upon Walras’ work exploring market clearing behavior. “Walras did not…give any conclusive arguments to show that the equations, as given, have a solution” (265). Two general “theorems” emerge from this paper: “…if every individual has initially some positive quantity of every commodity available for sale, then a competitive equilibrium will exist,” and, “…the existence of competitive equilibrium if there are some types of labor with the following two properties: (1) each individual can supply some positive amount of at least one such type of labor; and (2) each such type of labor has a positive usefulness in the production of desired commodities” (266).

The authors then go through a rather long list of assumptions that underly their economic approach. These assumptions are rather standard, classical economic assumptions. There is also a discussion of “consumption vectors”. These are seen, in a way, as being accounting tools for measuring the various consumption patterns of consumers.

The historical overview of equilibrium seeking models is quite useful. Here, the authors make detailed distinctions between different models of the economy that are market clearing.

UPDATE:

Stemming from Walras: “It was assumed that each consumer acts so as to maximize his utility, each producer acts so as to maximize his profit, and perfect competition prevails, in the sense that each producer and consumer regards the prices paid and received as in- dependent of his own choices” (265).

On the need for these types of models: “Descriptively, the view that the competitive model is a reasonably accurate description of reality, at least for certain purposes” (265).

Results of this paper: “The main results of this paper are two theorems stating very general conditions under which a competitive equilibrium will exist” (266).