Abstract
Abstract This study derives pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions and seek to maximize the weighted sum of their absolute and relative profits. The study shows that there exists a range of equilibrium prices in duopolistic equilibria. This range of equilibrium prices is narrower and lower than the range of equilibrium prices in duopolistic equilibria under pure absolute profit maximization. Moreover, the larger the weight on the relative profit, the narrower and lower the range of equilibrium prices. In this sense, relative profit maximization is more aggressive than absolute profit maximization.
Highlights
Using a model developed by Dastidar (1995) we study pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions, and they seek to maximize the weighted sum of their absolute and relative profits instead of their absolute profits themselves
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 maximization2, 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 is more aggressive than absolute profit maximization
Summary
Using a model developed by Dastidar (1995) we study pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions, and they seek to maximize the weighted sum of their absolute and relative profits instead of their absolute profits themselves. 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 is more aggressive than absolute profit maximization. In this paper we extend this result to a case of general demand functions and convex cost functions
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