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4 - On the existence of Cournot equilibrium
- Edited by Andrew F. Daughety, University of Iowa
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- Book:
- Cournot Oligopoly
- Published online:
- 07 September 2009
- Print publication:
- 27 January 1989, pp 101-121
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Summary
This paper examines the existence of n-firm Cournot equilibrium in a market for a single homogeneous commodity. It proves that if each firm's marginal revenue declines as the aggregate output of other firms increases (which is implied by concave inverse demand) then a Cournot equilibrium exists, without assuming that firms have nondecreasing marginal cost or identical technologies. Also, if the marginal revenue condition fails at a “potential optimal output”, there is a set of firms such that no Cournot equilibrium exists. The paper also contains an example of nonexistence with two nonidentical firms, each with constant returns to scale production.
Introduction
Cournot equilibrium is commonly used as a solution concept in oligopoly models, but the conditions under which a Cournot equilibrium can be expected to exist are not well understood. The nature of each firm's technology, whether all firms have identical technologies, and restrictions on the market inverse demand vary from model to model, and are all important for the existence of Cournot equilibrium. This paper examines the question of existence of (pure strategy) Cournot equilibrium in a single market for a homogeneous good. In this context there are two known types of existence theorems. The first type allows general (downward sloping) inverse demand and shows the existence of Cournot equilibrium when there are n identical firms with convex technologies (nondecreasing marginal cost and no avoidable fixed costs). See McManus [1962, 1964] and Roberts and Sonnenschein [1976].
12 - Cournot and Walras equilibrium
- Edited by Andrew F. Daughety, University of Iowa
-
- Book:
- Cournot Oligopoly
- Published online:
- 07 September 2009
- Print publication:
- 27 January 1989, pp 269-316
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Summary
Introduction
This paper unifies the two leading classical concepts of equilibrium for an economy: Walras equilibrium and Cournot equilibrium. The theory provides a fresh setting for the study of competitive markets, and leads to a description of economic equilibrium which differs in substance from the one offered by modern formal competitive theory (see, e.g., Debreu [3]).
Modern formal competitive theory does not permit free entry, hence the number of firms is fixed. Further, it is posited that firms behave in one of two ways. In one case, perfect competition is assumed: Firms act as if they have no effect on price; they maximize profit taking prices as given. In the other case, imperfect competition is assumed: Firms recognize and act on their ability to influence price. In the model we present, price and market power are determined by free entry and the size of efficient scale relative to demand. Several distinctive features of classical economic analysis occupy a central role in the development.
Specifically, we study a model in which the number of firms is determined endogenously; firms enter when it is profitable to enter, and the entry of firms is a driving force in the explanation of value. The presence of fixed costs (more precisely, the fact that the efficient scale of firms is bounded away from zero) places a limit on the number of firms which are “active” in an equilibrium.