International Journal of Business and Economics Volume 13, No. 2 December, 2014

Relative Profit Maximization in Duopoly: Difference or Ratio

Atsuhiro Satoh

Faculty of Economics, Doshisha University, Japan

Yasuhito Tanaka

Faculty of Economics, Doshisha University, Japan

Abstract

We compare two 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 and (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 (higher cost) firm we obtain the converse results.

Keywords：duopoly, relative profit maximization, difference, ratio.

JEL Classifications：D42, L13, L21.

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