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Capacity-Constrained Price Competition when Unit Costs Differ

Author

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  • Raymond Deneckere

    (University of Wisconsin)

  • Dan Kovenock

    (Purdue University)

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.

Suggested Citation

  • Raymond Deneckere & Dan Kovenock, 1994. "Capacity-Constrained Price Competition when Unit Costs Differ," Industrial Organization 9411001, University Library of Munich, Germany, revised 15 Nov 1994.
  • Handle: RePEc:wpa:wuwpio:9411001
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    References listed on IDEAS

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    1. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    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. Julio J. Rotemberg & Garth Saloner, 1989. "Tariffs vs Quotas with Implicit Collusion," Canadian Journal of Economics, Canadian Economics Association, vol. 22(2), pages 237-244, May.
    4. 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.
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    6. 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.
    7. 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 111-122, February.
    8. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Oxford University Press, vol. 53(2), pages 175-204.
    9. Davidson, Carl, 1984. "Cartel stability and tariff policy," Journal of International Economics, Elsevier, vol. 17(3-4), pages 219-237, November.
    10. 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.
    11. 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.
    12. Julio J. Rotemberg & Garth Saloner, 1986. "Quotas and the Stability of Implicit Collusion," NBER Working Papers 1948, National Bureau of Economic Research, Inc.
    13. Kala Krishna, 1988. "What Do Voluntary Export Restraints Do?," NBER Working Papers 2612, National Bureau of Economic Research, Inc.
    14. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    15. Krishna, Kala, 1989. "Trade restrictions as facilitating practices," Journal of International Economics, Elsevier, vol. 26(3-4), pages 251-270, May.
    16. Raymond J. Deneckere & Dan Kovenock, 1992. "Price Leadership," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 143-162.
      • Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. 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.
    18. Deneckere, R., 1989. "Capacity-Constrained Price Competition When Unit Costs Differ," Purdue University Economics Working Papers 958, Purdue University, Department of Economics.
    19. 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.
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    Cited by:

    1. Patrick Cayseele & Dave Furth, 2001. "Two is not too many for monopoly," Journal of Economics, Springer, vol. 74(3), pages 231-258, October.
    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. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    4. 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.
    5. Bergman, Mats A., 1998. "Endogenous Timing of Investments Yields Modified Stackelberg Outcomes," SSE/EFI Working Paper Series in Economics and Finance 272, Stockholm School of Economics.
    6. Dan Kovenock & Raymond Deneckere & Tom Faith & Beth Allen, 2000. "Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 501-530.
    7. Raymond J. Deneckere & Dan Kovenock, 1992. "Price Leadership," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 143-162.
      • Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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