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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. Burguet, Roberto & Sákovics, József, 2017. "Bertrand and the long run," International Journal of Industrial Organization, Elsevier, vol. 51(C), pages 39-55.
    2. Pedro Jara-Moroni, 2008. "The Cournot outcome as the result of price competition," PSE Working Papers halshs-00587866, HAL.
    3. Anton Miglo, 2020. "Crowdfunding in a Competitive Environment," JRFM, MDPI, vol. 13(3), pages 1-38, February.
    4. Robert Routledge, 2010. "On the Bertrand core and equilibrium of a market," Economics Discussion Paper Series 1017, Economics, The University of Manchester.
    5. R. A. Edwards & R. R. Routledge, 2023. "Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 569-586, June.
    6. Jozsef Sakovics & Lluis Bru & Daniel Cardona, 2018. "Block sourcing," Edinburgh School of Economics Discussion Paper Series 287, Edinburgh School of Economics, University of Edinburgh.
    7. Edwards, Robert A. & Routledge, Robert R., 2022. "Information, Bertrand–Edgeworth competition and the law of one price," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    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. 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.
    10. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium with a large number of firms," Discussion Papers 04-12, Indian Statistical Institute, Delhi.
    11. Canoy, Marcel & Weddepohl, Claus, 1995. "Alternative conjectures in a Bertrand-Edgeworth model," European Journal of Political Economy, Elsevier, vol. 11(3), pages 577-598, September.
    12. Bos, Iwan & Vermeulen, Dries, 2021. "On pure-strategy Nash equilibria in price–quantity games," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    13. 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.
    14. 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.
    15. Bos, Iwan & Marini, Marco A. & Saulle, Riccardo D., 2024. "Myopic oligopoly pricing," Games and Economic Behavior, Elsevier, vol. 145(C), pages 377-412.
    16. Heywood, John S. & Li, Dongyang & Ye, Guangliang, 2023. "Private provision of price excludable public goods by rivals," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 291-307.
    17. Clark, Ken & Kaas, Leo & Madden, Paul, 2006. "Minimum wage increases can lead to wage reductions by imperfectly competitive firms," Economics Letters, Elsevier, vol. 91(2), pages 287-292, May.
    18. Peck, James, 2018. "Competing mechanisms with multi-unit consumer demand," Journal of Economic Theory, Elsevier, vol. 177(C), pages 126-161.
    19. 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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