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Price competition and convex costs

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  • Weibull, Jörgen

    () (Dept. of Economics, Stockholm School of Economics)

Abstract

In the original model of pure price competition, due to Joseph Bertrand (1883), firms have linear cost functions. For any number of identical such price-setting firms, this results in the perfectly competitive outcome; the equilibrium price equal the firms’ (constant) marginal cost. This paper provides a generalization of Bertrand’s model from linear to convex cost functions. I analyze pure price competition both in a static setting - where the firms interact once and for all - and in dynamic setting - where they interact repeatedly over an indefinite future. Sufficient conditions are given for the existence of Nash equilibrium in the static setting and for subgame perfect equilibrium in the dynamic setting. These equilibrium sets are characterized, and it is shown that there typically exists a whole interval of Nash equilibrium prices in the static setting and subgame perfect equilibria in the dynamic setting. It is shown that firms may earn sizable profits and that their equilibrium profits may increase if their production costs go up.

Suggested Citation

  • Weibull, Jörgen, 2006. "Price competition and convex costs," SSE/EFI Working Paper Series in Economics and Finance 622, Stockholm School of Economics, revised 23 Feb 2006.
  • Handle: RePEc:hhs:hastef:0622
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    File URL: http://swopec.hhs.se/hastef/papers/hastef0622.pdf
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    References listed on IDEAS

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    1. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    2. Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-1172, September.
    3. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    4. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
    5. Allen, Beth & Hellwig, Martin, 1986. "Price-Setting Firms and the Oligopolistic Foundations of Perfect Competition," American Economic Review, American Economic Association, vol. 76(2), pages 387-392, May.
    6. Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-386, May.
    7. Noel, Michael, 2004. "Edgeworth Price Cycles: Evidence from the Toronto Retail Gasoline Market," University of California at San Diego, Economics Working Paper Series qt64j579g9, Department of Economics, UC San Diego.
    8. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    9. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, January.
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    Cited by:

    1. Giordani, Paolo E. & Ruta, Michele, 2013. "Coordination failures in immigration policy," Journal of International Economics, Elsevier, vol. 89(1), pages 55-67.
    2. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2014. "Robustness to strategic uncertainty," Games and Economic Behavior, Elsevier, vol. 85(C), pages 272-288.
    3. Robert R. Routledge, 2009. "On the existence of Bayesian Bertrand equilibrium," The School of Economics Discussion Paper Series 0917, Economics, The University of Manchester.
    4. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen, 2010. "Robustness to strategic uncertainty in price competition," SSE/EFI Working Paper Series in Economics and Finance 0726, Stockholm School of Economics, revised 08 Apr 2010.
    5. Argenton, Cédric & Müller, Wieland, 2012. "Collusion in experimental Bertrand duopolies with convex costs: The role of cost asymmetry," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 508-517.

    More about this item

    Keywords

    Bertrand competition;

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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