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Price competition and convex costs

Author

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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:

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    2. Gomis-Porqueras Pedro & Julien Benoît & Wang Liang, 2018. "Competitive Search with Ex-post Opportunism," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-17, January.
    3. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2014. "Robustness to strategic uncertainty," Games and Economic Behavior, Elsevier, vol. 85(C), pages 272-288.
    4. Robert R. Routledge, 2009. "On the existence of Bayesian Bertrand equilibrium," Economics Discussion Paper Series 0917, Economics, The University of Manchester.
    5. 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.
    6. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2010. "The end of the Bertrand Paradox?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00542486, HAL.
    7. Tim Friehe, 2014. "Tacit collusion and liability rules," European Journal of Law and Economics, Springer, vol. 38(3), pages 453-469, December.
    8. Heikki Peura & S. Alex Yang & Guoming Lai, 2017. "Trade Credit in Competition: A Horizontal Benefit," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 263-289, May.
    9. Julien Hardelin & Sabine Lemoyne de Forges, 2012. "Raising Capital in an Insurance Oligopoly Market," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 83-108, March.
    10. Makoto Yano & Takashi Komatsubara, 2018. "Price competition or price leadership," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 1023-1057, December.
    11. Routledge, Robert R., 2010. "Bertrand competition with cost uncertainty," Economics Letters, Elsevier, vol. 107(3), pages 356-359, June.
    12. 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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