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Endogenous Capacities and Price Competition: The Role of Demand Uncertainty

  • de Frutos, Maria-Angeles
  • Fabra, Natalia

This paper analyzes a model of capacity choice followed by price competition under demand uncertainty. Under various assumptions regarding the nature and timing of demand realizations, we obtain general predictions concerning the role of demand uncertainty on equilibrium outcomes. We show that it reduces the multiplicity of equilibria, it may rule out the existence of symmetric equilibria, and it leads to endogenous capacity asymmetries even though firms are ex-ante symmetric. Furthermore, as compared to the certainty equivalent game, demand uncertainty reduces prices and increases consumer surplus, but it also decreases total welfare because of the emergence of idle capacity. By relying on the analysis of firms' reaction functions as well as on the theory of submodular games, we are able to show that a subgame perfect equilibrium always exists and to fully characterize it.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6096.

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Date of creation: Feb 2007
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Handle: RePEc:cpr:ceprdp:6096
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  1. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
  2. Gal-Or, Esther, 1984. "Price Dispersion with Uncertain Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 441-57, June.
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  8. 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.
  9. Benoit, Jean-Pierre & Krishna, Vijay, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 23-35, January.
  10. Veronika Grimm & Gregor Zoettl, 2006. "Capacity Choice under Uncertainty: The Impact of Market Structure," Working Paper Series in Economics 23, University of Cologne, 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. Dan Kovenock & Raymond Deneckere & Tom Faith & Beth Allen, 2000. "Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach," Economic Theory, Springer, vol. 15(3), pages 501-530.
  13. de Frutos, María-Ángeles & Fabra, Natalia, 2011. "Endogenous capacities and price competition: The role of demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 399-411, July.
  14. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  15. Amir, Rabah & Wooders, John, 2000. "One-Way Spillovers, Endogenous Innovator/Imitator Roles, and Research Joint Ventures," Games and Economic Behavior, Elsevier, vol. 31(1), pages 1-25, April.
  16. Morten Hviid, 1989. "Sequential Capacity and Price Choices in a Duopoly Model with Demand Uncertainty," Discussion Papers 89-09, University of Copenhagen. Department of Economics.
  17. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
  18. Reynolds, Stanley S. & Wilson, Bart J., 2000. "Bertrand-Edgeworth Competition, Demand Uncertainty, and Asymmetric Outcomes," Journal of Economic Theory, Elsevier, vol. 92(1), pages 122-141, May.
  19. Natalia Fabra & Nils‐Henrik M von der Fehr & María‐Ángeles de Frutos, 2011. "Market Design and Investment Incentives," Economic Journal, Royal Economic Society, vol. 121(557), pages 1340-1360, December.
  20. Dechenaux, Emmanuel & Kovenock, Dan, 2003. "Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames," Purdue University Economics Working Papers 1164, Purdue University, Department of Economics.
  21. Grant, Simon & Quiggin, John, 1996. "Capital Precommitment and Competition in Supply Schedules," Journal of Industrial Economics, Wiley Blackwell, vol. 44(4), pages 427-41, December.
  22. Gabszewicz, J.J. & Poddar, S., . "Demand fluctuations and capacity utilization under duopoly," CORE Discussion Papers RP -1269, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. 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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  25. Moreno, Diego & Ubeda, Luis, 2006. "Capacity precommitment and price competition yield the Cournot outcome," Games and Economic Behavior, Elsevier, vol. 56(2), pages 323-332, August.
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