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Capacity-Constrained Price Competition When Unit Costs Differ

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  • Raymond J. Deneckere
  • Dan Kovenock

Abstract

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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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 861.

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Date of creation: Dec 1988
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Handle: RePEc:nwu:cmsems:861

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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Julio J. Rotemberg & Garth Saloner, 1986. "Quotas and the Stability of Implicit Collusion," NBER Working Papers 1948, National Bureau of Economic Research, Inc.
  7. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
  8. Deneckere, Raymond J & Kovenock, Dan, 1992. "Price Leadership," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 143-62, January.
    • Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. 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.
  10. Kala Krishna, 1989. "What Do Voluntary Export Restraints Do?," NBER Working Papers 2612, National Bureau of Economic Research, Inc.
  11. Krishna, Kala, 1989. "Trade restrictions as facilitating practices," Journal of International Economics, Elsevier, vol. 26(3-4), pages 251-270, May.
  12. Davidson, Carl, 1984. "Cartel stability and tariff policy," Journal of International Economics, Elsevier, vol. 17(3-4), pages 219-237, November.
  13. 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.
  14. 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.
  15. 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.
  16. Deneckere, R., 1989. "Capacity-Constrained Price Competition When Unit Costs Differ," Purdue University Economics Working Papers 958, Purdue University, Department of Economics.
  17. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
  18. 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.
  19. Allen, Beth & Hellwig, Martin, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 175-204, April.
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Cited by:
  1. Allen, B. & Deneckere, R. & Faith, T. & Kovenock, D., 1994. "Capacity Precommitment as a Barrier to Entry: A Bertrand-Edgeworth Approach," Purdue University Economics Working Papers 1062, Purdue University, Department of Economics.
  2. Raymond Deneckere & Dan Kovenock, 1994. "Capacity-Constrained Price Competition when Unit Costs Differ," Industrial Organization 9411001, EconWPA, revised 15 Nov 1994.
  3. Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Patrick Cayseele & Dave Furth, 2001. "Two is not too many for monopoly," Journal of Economics, Springer, vol. 74(3), pages 231-258, October.
  5. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer, vol. 46(1), pages 99-125, January.
  6. Bergman, Mats A., 1998. "Endogenous Timing of Investments Yields Modified Stackelberg Outcomes," Working Paper Series in Economics and Finance 272, Stockholm School of Economics.
  7. Robinson, W.T. & Min, S., 1998. "Is the First to Market the First to fail?: Empirical Evidence for Manufacturing Business," Purdue University Economics Working Papers 1115, Purdue University, Department of Economics.

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