Capacity-Constrained Price Competition When Unit Costs Differ
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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- Kala Krishna, 1988. "What Do Voluntary Export Restraints Do?," NBER Working Papers 2612, National Bureau of Economic Research, Inc.
- Allen, Beth & Hellwig, Martin, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 175-204, April.
- Deneckere, R.J. & Kovenock, D. & Sohn, Y.Y., 1991. "Quotas and Tariffs with Endogenous Conduct," Purdue University Economics Working Papers 1006, Purdue University, Department of Economics.
- Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
- Julio J. Rotemberg & Garth Saloner, 1989. "Tariffs vs Quotas with Implicit Collusion," Canadian Journal of Economics, Canadian Economics Association, vol. 22(2), pages 237-44, May.
- Deneckere, Raymond J & Kovenock, Dan, 1992.
Review of Economic Studies,
Wiley Blackwell, vol. 59(1), pages 143-62, January.
- Richard E. Levitan & Martin Shubik, 1970.
"Price Duopoly and Capacity Constraints,"
Cowles Foundation Discussion Papers
287, Cowles Foundation for Research in Economics, Yale University.
- Osborne, Martin J. & Pitchik, Carolyn, 1986.
"Price competition in a capacity-constrained duopoly,"
Journal of Economic Theory,
Elsevier, vol. 38(2), pages 238-260, April.
- Osborne, Martin J. & Pitchik, Carolyn, 1983. "Price Competition in a Capacity-Constrained Duopoly," Working Papers 83-08, C.V. Starr Center for Applied Economics, New York University.
- Deneckere, R.J. & Kovenock, D., 1994.
"Capacity Constrained Price Competition when Unit Costs Differ,"
Purdue University Economics Working Papers
1056, Purdue University, Department of Economics.
- Raymond J. Deneckere & Dan Kovenock, 1988. "Capacity-Constrained Price Competition When Unit Costs Differ," Discussion Papers 861, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Raymond Deneckere & Dan Kovenock, 1994. "Capacity-Constrained Price Competition when Unit Costs Differ," Industrial Organization 9411001, EconWPA, revised 15 Nov 1994.
- Julio J. Rotemberg & Garth Saloner, 1986.
"Quotas and the Stability of Implicit Collusion,"
NBER Working Papers
1948, National Bureau of Economic Research, Inc.
- Kala Krishna, 1985.
"Trade Restrictions as Facilitating Practices,"
NBER Working Papers
1546, National Bureau of Economic Research, Inc.
- Judith R. Gelman & Steven C. Salop, 1983. "Judo Economics: Capacity Limitation and Coupon Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 315-325, Autumn.
- Hwang, Hong & Mai, Chao-cheng, 1988. "On the equivalence of tariffs and quotas under duopoly : A conjectural variation approach," Journal of International Economics, Elsevier, vol. 24(3-4), pages 373-380, May.
- Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
- David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
- Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
- Deneckere, R., 1989. "Capacity-Constrained Price Competition When Unit Costs Differ," Purdue University Economics Working Papers 958, Purdue University, Department of Economics.
- Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
- Davidson, Carl, 1984. "Cartel stability and tariff policy," Journal of International Economics, Elsevier, vol. 17(3-4), pages 219-237, November.
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