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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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    References listed on IDEAS

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    Cited by:

    1. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2014. "Robustness to strategic uncertainty," Games and Economic Behavior, Elsevier, vol. 85(C), pages 272-288.
    2. 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.
    3. Giordani, Paolo E. & Ruta, Michele, 2013. "Coordination failures in immigration policy," Journal of International Economics, Elsevier, vol. 89(1), pages 55-67.
    4. Robert R. Routledge, 2009. "On the existence of Bayesian Bertrand equilibrium," Economics Discussion Paper Series 0917, Economics, The University of Manchester.
    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.

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    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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