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Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium

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Kolstad, Charles D
Mathiesen, Lars

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Abstract

In this paper, a theorem is developed giving necessary and sufficient conditions for the uniqueness of homogeneous product Cournot equilibria. The result appears to be the strongest to date and the first to involve both necessity and suffi ciency. The theorem states that an equilibrium is unique if and only if the determinant of the Jacobian of marginal profits for firms prod ucing positive output is positive at all equilibria. The proof uses f ixed point index theory from differential topology. Copyright 1987 by The Review of Economic Studies Limited.

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Publisher Info
Article provided by Blackwell Publishing in its journal Review of Economic Studies.

Volume (Year): 54 (1987)
Issue (Month): 4 (October)
Pages: 681-90
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Handle: RePEc:bla:restud:v:54:y:1987:i:4:p:681-90

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