Relative profit maximization and Bertrand equilibrium with quadratic cost functions

Satoh, Atsuhiro and Tanaka, Yasuhito (2014): Relative profit maximization and Bertrand equilibrium with quadratic cost functions. Published in:

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 price in duopolistic equilibria. This range of equilibrium price is narrower and lower than the range of the equilibrium price 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 price. In this sense relative profit maximization by the firms is more aggressive than absolute profit maximization.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bertrand equilibrium, quadratic cost function, relative profit maximization
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection

References

Dastidar, K. G.(1995), ``On the existence of pure strategy Bertrand equilibrium'', Economic Theory, 5, 19-32.

Gibbons, R and K. J. Murphy (1990), ``Relative performance evaluation for chief executive officers'', Industrial and Labor Relations Review, 43, 30S-51S.

Kockesen, L., E.A. Ok and R. Sethi (2000) ``The strategic advantage of negatively interdependent preferences'' Journal of Economic Theory 92, 274-299.

Lu, Y. (2011), ``The relative-profit-maximization objective of private firms and endogenous timing in a mixed oligopoly'', The Singapore Economic Review, 56, 203-213.

Lundgren, C. (1996) ``Using relative profit incentives to prevent collusion'' Review of Industrial Organization 11, 533-50.

Matsumura, T., N. Matsushima and S. Cato (2013) ``Competitiveness and R\&D competition revisited'' Economic Modelling, 31, 541-547.

Schaffer, M.E. (1989) ``Are profit maximizers the best survivors?'' Journal of Economic Behavior and Organization12, 29-5.

Tanaka, Y. (2013) ``Irrelevance of the choice of strategic variables in duopoly under relative profit maximization'', Economics and Business Letters, 2, 75-83.

Vega-Redondo, F. (1997) ``The evolution of Walrasian behavior'' Econometrica, 65, 375-384.