Price versus quantity in a mixed duopoly: The case of relative profit maximization

- We reconsider the endogenous selection of each firm's price or quantity in a mixed duopoly.
- We assume that a private firm maximizes its relative profit.
- When each firm's relative performance is high, quantity competition is observed in the equilibrium.
- When each firm's relative performance is low, price competition is observed in the equilibrium.
- The two equilibrium competitions can be supported by the dominant strategies of both firms.

This paper examines the endogenous choice problem of each firm's price or quantity contract in a mixed duopoly composed of one social welfare maximizing public firm and one relative profit-maximizing private firm. In this paper, we show that unless the degree of product differentiation and the degree of importance of the private firm's relative performance are low, the quantity competition can analytically become the unique equilibrium market structure on the basis of the dominant strategies of the public firm and the private firm when the degree of importance of firm 1's relative performance is sufficiently high. This result contrasts strikingly with that obtained in a standard mixed duopoly composed of one social welfare-maximizing public firm and one absolute profit maximizing private firm. In addition, even in the area wherein both the degree of product differentiation and the degree of the private firm's relative performance are sufficiently low, through numerical simulations, the quantity competition tends to become the unique equilibrium market structure when the degree of importance of the private firm's relative performance is sufficiently high, whereas the price competition tends to become the unique equilibrium market structure when the degree of importance of the private firm's relative performance is sufficiently low.