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Relative profit maximization and Bertrand equilibrium with convex cost functions

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  • Satoh, Atsuhiro
  • Tanaka, Yasuhito

Abstract

This study derives pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions and seek to maximize the weighted sum of their absolute and relative profits. The study shows that there exists a range of equilibrium prices in duopolistic equilibria. This range of equilibrium prices is narrower and lower than the range of equilibrium prices in duopolistic equilibria under pure absolute profit maximization. Moreover, the larger the weight on the relative profit, the narrower and lower the range of equilibrium prices. In this sense, relative profit maximization is more aggressive than absolute profit maximization.

Suggested Citation

  • Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and Bertrand equilibrium with convex cost functions," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 8, pages 1-15.
    • Handle: RePEc:zbw:ifweej:201434
    DOI: 10.5018/economics-ejournal.ja.2014-34
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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.
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    5. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
    6. Yuanzhu Lu, 2011. "The Relative-Profit-Maximization Objective Of Private Firms And Endogenous Timing In A Mixed Oligopoly," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 56(02), pages 203-213.
    7. Atsuhiro Satoh & Yasuhito Tanaka, 2013. "Relative profit maximization and Bertrand equilibrium with quadratic cost functions," Economics and Business Letters, Oviedo University Press, vol. 2(3), pages 134-139.
    8. Miller, Nolan H & Pazgal, Amit I, 2001. "The Equivalence of Price and Quantity Competition with Delegation," RAND Journal of Economics, The RAND Corporation, vol. 32(2), pages 284-301, Summer.
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    Cited by:

    1. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Sion's mini-max theorem and Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group," Papers 1809.02466, arXiv.org.

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    More about this item

    Keywords

    Bertrand equilibrium; convex cost function; relative profit maximization;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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