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Relative profit maximization and Bertrand equilibrium with quadratic cost functions

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  • Atsuhiro Satoh
  • Yasuhito Tanaka

Abstract

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

Suggested Citation

  • 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.
  • Handle: RePEc:ove:journl:aid:9999
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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.
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    5. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    6. Kockesen, Levent & Ok, Efe A. & Sethi, Rajiv, 2000. "The Strategic Advantage of Negatively Interdependent Preferences," Journal of Economic Theory, Elsevier, vol. 92(2), pages 274-299, June.
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    Cited by:

    1. Satoh, Atsuhiro & Tanaka, Yasuhito, 2015. "Relative profit maximization and the choice of strategic variables in duopoly," MPRA Paper 63000, University Library of Munich, Germany.
    2. Jacek Prokop & Michał Ramsza & Bartłomiej Wiśnicki, 2015. "A Note on Bertrand Competition under Quadratic Cost Functions," Gospodarka Narodowa, Warsaw School of Economics, issue 2, pages 5-14.
    3. Masahiko Hattori & Yasuhito Tanaka, 2014. "Incentive for adoption of new technology in duopoly under absolute and relative profit maximization," Economics Bulletin, AccessEcon, vol. 34(3), pages 2051-2059.
    4. Tanaka, Yasuhito & Satoh, Atsuhiro, 2016. "Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand," MPRA Paper 73925, University Library of Munich, Germany.
    5. Hattori, Masahiko & Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Minimax theorem and Nash equilibrium of symmetric three-players zero-sum game with two strategic variables," MPRA Paper 85503, University Library of Munich, Germany.
    6. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and Bertrand equilibrium with convex cost functions," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 8, pages 1-15.
    7. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative Profit Maximization in Duopoly: Difference or Ratio," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 127-141, December.
    8. Atsuhiro SATOH & Yasuhito TANAKA, 2016. "Equivalence of Cournot and Bertrand equilibria in duopoly under relative profit maximization: A general analysis," Journal of Economics and Political Economy, KSP Journals, vol. 3(3), pages 513-523, September.
    9. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game," MPRA Paper 85452, University Library of Munich, Germany.
    10. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Two person zero-sum game with two sets of strategic variables," MPRA Paper 73272, University Library of Munich, Germany.
    11. Satoh, Atsuhiro & Tanaka, Yasuhito, 2017. "Sion's minimax theorem and Nash equilibrium of symmetric multi-person zero-sum game," MPRA Paper 82148, University Library of Munich, Germany.
    12. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Symmetric multi-person zero-sum game with two sets of strategic variables," MPRA Paper 75838, University Library of Munich, Germany.
    13. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand," MPRA Paper 75837, University Library of Munich, Germany.
    14. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Free Entry Oligopoly, Cournot, Bertrand and Relative Profit Maximization," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 143-155, December.

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    JEL classification:

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

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