Mixed Duopoly under Vertical Differentiation: a Stackelberg-Nash-Cournot equilibrium model

In this paper we study a vertically differentiated duopoly market with a profit maximizing firm (private firm) and a total surplus maximizing firm (public firm). The technological conditions are assumed identical for both firms and are described by unit costs which are constant with respect to quantity, though increasing in quality. No specific form is given to the relation between unit costs and quality. We prove that the socially optimal solution can be sustained as a market outcome by using a public firm as a market agent. We also provide conditions on the constant unit cost function under which every market outcome is a social optimum.