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Capacity Constrained Price Competition when Unit Costs Differ

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Author Info

  • 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. 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.
  2. Deneckere, R., 1989. "Capacity-Constrained Price Competition When Unit Costs Differ," Purdue University Economics Working Papers 958, Purdue University, Department of Economics.
  3. 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.
  4. Julio Rotemberg & Garth Saloner, 1986. "Quotas and the Stability of Implicit Collusion," Working papers 419, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. 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.
  6. Kala Krishna, 1989. "What Do Voluntary Export Restraints Do?," NBER Working Papers 2612, National Bureau of Economic Research, Inc.
  7. Allen, Beth & Hellwig, Martin, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 175-204, April.
  8. Davidson, Carl, 1984. "Cartel stability and tariff policy," Journal of International Economics, Elsevier, vol. 17(3-4), pages 219-237, November.
  9. 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.
  10. Richard E. Levitan & Martin Shubik, 1970. "Price Duopoly and Capacity Constraints," Cowles Foundation Discussion Papers 287, Cowles Foundation for Research in Economics, Yale University.
  11. Kala Krishna, 1989. "Trade Restrictions as Facilitating Practices," NBER Working Papers 1546, National Bureau of Economic Research, Inc.
  12. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
  13. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
  14. Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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, vol. 24(3-4), pages 373-380, May.
  16. 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.
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Citations

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Cited by:
  1. Beth Allen & Raymond Deneckere & Tom Faith & Dan Kovenock, 1995. "Capacity precommitment as a barrier to entry: a Bertrand-Edgeworth approach," Staff Report 187, Federal Reserve Bank of Minneapolis.
  2. Bergman, Mats A., 1998. "Endogenous Timing of Investments Yields Modified Stackelberg Outcomes," Working Paper Series in Economics and Finance 272, Stockholm School of Economics.
  3. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer, vol. 46(1), pages 99-125, January.
  4. 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.
  5. 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.
  6. Patrick Cayseele & Dave Furth, 2001. "Two is not too many for monopoly," Journal of Economics, Springer, vol. 74(3), pages 231-258, October.
  7. 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.

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