On the Anti-Competitive and Welfare Effects of Cross-Holdings with Product Differentiation

The anti-competitive effects of cross-holdings have been extensively analyzed in the literature. While the literature has generally focused on cases with homogenous products, this paper is the first attempt to analyze welfare as well as the anti-competitive effects of cross-holdings allowing for product differentiation. We show that the known results established with homogenous products continue to hold with product differentiation. However, both the strength of the anticompetitive effects and the conditions resulting in these effects critically depend on the degree of product differentiation. Furthermore, cross-holdings generally increase social welfare with complementary products in quantity competition but decrease it with substitutable products in price competition. Our analysis has useful empirical and policy applications.