Relative profit maximization and Bertrand equilibrium with quadratic cost functions

Authors

  • Atsuhiro Satoh Osaka University of Commerce
  • Yasuhito Tanaka Doshisha University

DOI:

https://doi.org/10.17811/ebl.2.3.2013.134-139

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.

Author Biographies

Atsuhiro Satoh, Osaka University of Commerce

Lecturer, Faculty of Economics

Yasuhito Tanaka, Doshisha University

Professor, Faculty of Economics

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Published

2013-09-23

How to Cite

Satoh, A., & Tanaka, Y. (2013). Relative profit maximization and Bertrand equilibrium with quadratic cost functions. Economics and Business Letters, 2(3), 134-139. https://doi.org/10.17811/ebl.2.3.2013.134-139