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The Competitive Outcome as the Equilibrium in an Edgeworthian Price-Quantity Model

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  • Dixon, Huw David

Abstract

This paper considers a model of price-setting oligopoly with perfectly informed consumers, where firms have strictly-convex cost functions. In the standard Bertrand-Edgeworth model, there exists no pure-strategy Nash equilibrium. The author allows firms to choose both price and the quantity that they are willing to sell, output being the minimum of this quantity and demand. Firms cannot offer to sell a quantity that would bankrupt them. The paper shows that if there are enough firms, then an equilibrium exists and, in all equilibria, firms set the competitive price and each produce their competitive output. Copyright 1992 by Royal Economic Society.

Suggested Citation

  • Dixon, Huw David, 1992. "The Competitive Outcome as the Equilibrium in an Edgeworthian Price-Quantity Model," Economic Journal, Royal Economic Society, vol. 102(411), pages 301-309, March.
  • Handle: RePEc:ecj:econjl:v:102:y:1992:i:411:p:301-09
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    Cited by:

    1. Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
    2. Burguet, Roberto & Sákovics, József, 2017. "Bertrand and the long run," International Journal of Industrial Organization, Elsevier, vol. 51(C), pages 39-55.
    3. van den Berg, Anita & Bos, Iwan, 2017. "Collusion in a price-quantity oligopoly," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 159-185.
    4. Pedro Jara-Moroni, 2008. "The Cournot outcome as the result of price competition," Working Papers halshs-00587866, HAL.
    5. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    6. Robert Routledge, 2010. "On the Bertrand core and equilibrium of a market," The School of Economics Discussion Paper Series 1017, Economics, The University of Manchester.
    7. Makoto Yano, 2006. "A price competition game under free entry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 395-414, October.
    8. Jacobs, Martin & Requate, Till, 2016. "Bertrand-Edgeworth markets with increasing marginal costs and voluntary trading: Experimental evidence," Economics Working Papers 2016-01, Christian-Albrechts-University of Kiel, Department of Economics.
    9. Burguet, Roberto & Sákovics, József, 2014. "Bertrand and the long run," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-38, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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