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Relative profit maximization in duopoly: difference or ratio

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  • Satoh, Atsuhiro
  • Tanaka, Yasuhito

Abstract

We compare formulations of relative profit maximization in duopoly with differentiated goods, 1) (Difference case) maximization of the difference between the profit of one firm and that of the other firm, 2) (Ratio case) maximization of the ratio of the profit of one firm to the total profit. We show that in asymmetric duopoly the equilibrium output of the more efficient (lower cost) firm in the ratio case is larger than that in the difference case and the price of the good of the more efficient firm in the ratio case is lower than that in the difference case. For the less efficient firm (higher cost firm) we obtain the converse results.

Suggested Citation

  • Satoh, Atsuhiro & Tanaka, Yasuhito, 2015. "Relative profit maximization in duopoly: difference or ratio," MPRA Paper 64096, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:64096
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    12. 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.
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    14. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in an asymmetric differentiated duopoly," MPRA Paper 55895, University Library of Munich, Germany.
    15. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative Profit Maximization in Duopoly: Difference or Ratio," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 127-141, December.
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    1. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative Profit Maximization in Duopoly: Difference or Ratio," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 127-141, December.
    2. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Free Entry Oligopoly, Cournot, Bertrand and Relative Profit Maximization," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 143-155, December.
    3. Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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    More about this item

    Keywords

    duopoly; relative profit maximization; difference; ratio;
    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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