General Equilibrium with Free Entry: A Synthetic Approach to the Theory of Perfect Competition

Abstract

The purpose of this essay is to explain a new theory of perfect competition that synthesizes the Arrow-Debreu-McKenzie and Marshallian theories and summarizes the recent work of a large number of researchers. The synthetic theory provides a logically precise general equilibrium framework that can be used both for positive analysis as well as to form a basis for the classical theorems of welfare economics; in these aspects it follows the ADM theory. However, as in the Marshallian theory, there is free-entry in the form of an unbounded pool of firms which have access to the existing technology. Also as in the Marshallian theory, the average cost curves available to each firm are U-shaped. In contrast to both the Marshallian and the ADM theories, we do not take price taking as a hypothesis. We use the term "perfect competition" to describe a situation in which firms are arbitrarily small relative to the markets in which they are involved. The firms in our model correctly perceive the effect of the amount that they place on the market on prices and they act to maximize profit with this in mind. "Perfectly competitive equilibria" are defined as the limit points of equilibria as firms become small relative to the market, and following Cournot, we observe that as firms become small their ability to influence price disappears. A new condition is identified which is important for the viability of competitive markets. Loosely speaking, this condition requires that prices provide the proper entry signals for firms. If one thinks of each firm as associated with the use of an unpriced and nondivisible resource, sometimes referred to as entrepreneurship, then in equilibrium the returns to that factor must fall with entry and rise with exit. Not only the stability theorems of the synthetic theory but also the existence theorem reject the application of the competitive model to a regime in which entry drives up (and exit reduces} the profit of similar firms.

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