Cross-ownership on R&D and welfare in a mixed oligopoly: revisiting with convex cost

This paper revisits how private cross-ownership affects cost-reducing R & D, production quantities, consumer surplus, firms' profits and social welfare in a mixed oligopoly with a convex cost function. We show that increasing cross-ownership reduces private firms' R & D but increases the semi-public firm's R & D. Further, both consumer surplus and social welfare could be enhanced through cross-ownership when the convexity of cost function is small. However, increasing cross-ownership could hurt consumers and social welfare when the convexity of cost function is large. Our finding highlights that the convexity of cost function is very important to the welfare implications of cross-ownership. Hence, antitrust authorities should be more careful when assessing the welfare effects of partial ownership in different industries.