Partial privatization in mixed duopoly with price and quality competition

We analyze price and quality competition in a mixed duopoly in which a profit-maximizing private firm competes against a state-owned public firm. We first show that the welfare-maximizing public firm provides a lower quality product than the private firm when they are equally efficient. In order to maximize social welfare, government manipulates the objective of the public firm that is given by a convex combination of profits and social welfare. It is demonstrated that an optimal incentive of the public firm is welfare maximization under the absence of quality competition, but it is neither welfare maximization nor profit maximization under the presence of quality competition. The result supports a completely mixed objective between welfare and profit maximizations or partial privatization of the public firm.