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Capacity Constrained Price Competition when Unit Costs Differ

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  • Deneckere, R.J.
  • Kovenock, D.

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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Bibliographic Info

Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1056.

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Length: 45 pages
Date of creation: 1994
Date of revision:
Handle: RePEc:pur:prukra:1056

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Keywords: prices ; costs ; competition;

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References

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  1. Raymond J. Deneckere & Dan Kovenock, 1988. "Capacity-Constrained Price Competition When Unit Costs Differ," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 861, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Julio J. Rotemberg & Garth Saloner, 1986. "Quotas and the Stability of Implicit Collusion," NBER Working Papers 1948, National Bureau of Economic Research, Inc.
  3. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(4), pages 569-97, October.
  4. Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Kala Krishna, 1985. "Trade Restrictions as Facilitating Practices," NBER Working Papers 1546, National Bureau of Economic Research, Inc.
  6. Osborne, Martin J. & Pitchik, Carolyn, 1983. "Price Competition in a Capacity-Constrained Duopoly," Working Papers, C.V. Starr Center for Applied Economics, New York University 83-08, C.V. Starr Center for Applied Economics, New York University.
  7. Deneckere, R., 1989. "Capacity-Constrained Price Competition When Unit Costs Differ," Purdue University Economics Working Papers, Purdue University, Department of Economics 958, Purdue University, Department of Economics.
  8. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, American Economic Association, vol. 70(4), pages 651-59, September.
  9. Davidson, Carl, 1984. "Cartel stability and tariff policy," Journal of International Economics, Elsevier, Elsevier, vol. 17(3-4), pages 219-237, November.
  10. 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, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
  11. Kala Krishna, 1989. "What Do Voluntary Export Restraints Do?," NBER Working Papers 2612, National Bureau of Economic Research, Inc.
  12. Julio J. Rotemberg & Garth Saloner, 1989. "Tariffs vs Quotas with Implicit Collusion," Canadian Journal of Economics, Canadian Economics Association, Canadian Economics Association, vol. 22(2), pages 237-44, May.
  13. Deneckere, R.J. & Kovenock, D. & Sohn, Y.Y., 1991. "Quotas and Tariffs with Endogenous Conduct," Purdue University Economics Working Papers, Purdue University, Department of Economics 1006, Purdue University, Department of Economics.
  14. Judith R. Gelman & Steven C. Salop, 1983. "Judo Economics: Capacity Limitation and Coupon Competition," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 14(2), pages 315-325, Autumn.
  15. Hwang, Hong & Mai, Chao-cheng, 1988. "On the equivalence of tariffs and quotas under duopoly : A conjectural variation approach," Journal of International Economics, Elsevier, Elsevier, vol. 24(3-4), pages 373-380, May.
  16. Richard E. Levitan & Martin Shubik, 1970. "Price Duopoly and Capacity Constraints," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 287, Cowles Foundation for Research in Economics, Yale University.
  17. Allen, Beth & Hellwig, Martin, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(2), pages 175-204, April.
  18. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
  19. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(1), pages 1-26, January.
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Citations

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Cited by:
  1. Miklos-Thal, Jeanine, 2008. "Optimal Collusion under Cost Asymmetry," MPRA Paper 11044, University Library of Munich, Germany.
  2. 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, Purdue University, Department of Economics 1115, Purdue University, Department of Economics.
  3. Beth Allen & Raymond Deneckere & Tom Faith & Dan Kovenock, 1995. "Capacity precommitment as a barrier to entry: a Bertrand-Edgeworth approach," Staff Report, Federal Reserve Bank of Minneapolis 187, Federal Reserve Bank of Minneapolis.
  4. Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Raymond J. Deneckere & Dan Kovenock, 1988. "Capacity-Constrained Price Competition When Unit Costs Differ," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 861, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Bergman, Mats A., 1998. "Endogenous Timing of Investments Yields Modified Stackelberg Outcomes," Working Paper Series in Economics and Finance, Stockholm School of Economics 272, Stockholm School of Economics.
  7. Patrick Cayseele & Dave Furth, 2001. "Two is not too many for monopoly," Journal of Economics, Springer, Springer, vol. 74(3), pages 231-258, October.

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