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...

The dual relationship between parameters of normalized quadratic cost and profit functions is determined when firms can implement market power on the output market. An approach is developed to test the market power by comparing the profits of a firm with and without market power. Simulations...