This paper characterizes the set of NASH equilibria in a price setting duopoly in which firms have limited capacity, and in which unit costs of production up to capacity may differ. Assuming concave revenue and efficient rationing, we show that the case of different unit costs involves a tractable generalization of the methods used to analyze the case of identical costs. However, the supports of the two firms' equilibrium price distributions need no longer be connected and need not coincide. In addition, the supports of the equilibrium price distributions need no longer be continuous in the underlying parameters of the model. Two applications of our characterization are pursued. In the Kreps-Scheinkman model of capacity choice followed by Bertrand-Edgeworth price competition we show that, unlike in the case of identical costs, Cournot equilibrium capacity levels need not arise as subgame-perfect equilibria. The low-cost firm has greater incentive to price its rival out of the market than exists under Cournot behavior. Our second application is to the analysis of the effects of tariffs and quotas in a model in which a domestic market is supplied by a price setting duopoly consisting of a domestic and a foreign firm. We obtain a strong nonequivalence result.
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Deneckere, Raymond J & Kovenock, Dan, 1992.
"Price Leadership,"
Review of Economic Studies,
Blackwell Publishing, vol. 59(1), pages 143-62, January.
[Downloadable!] (restricted)
Other versions:
Raymond Deneckere & Dan Kovenock, 1988.
"Price Leadership,"
Discussion Papers
773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
[Downloadable!]
Varian, Hal R, 1980.
"A Model of Sales,"
American Economic Review,
American Economic Association, vol. 70(4), pages 651-59, September.
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Levitan, Richard & Shubik, Martin, 1972.
"Price Duopoly and Capacity Constraints,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-22, February.
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Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
Raymond Deneckere & Dan Kovenock, 1988.
"Price Leadership,"
Discussion Papers
773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
[Downloadable!]
Other versions:
Deneckere, Raymond J & Kovenock, Dan, 1992.
"Price Leadership,"
Review of Economic Studies,
Blackwell Publishing, vol. 59(1), pages 143-62, January.
[Downloadable!] (restricted)