Vertical cross-ownership, input price discrimination, and social welfare

In this paper, we analyze the impact of vertical cross-ownership with input price discrimination on social welfare. A higher degree of product differentiation will raise industry profit, consumer surplus, and social welfare; under forward cross-ownership, a higher degree of cross-ownership has the same effect, in addition, it will reduce rival firm's profit and increase upstream firm's profit; however, under backward cross-ownership, a higher degree of cross-ownership has an opposite effect. Furthermore, under Cournot and Bertrand competition, forward cross-ownership will incentivize downstream firms to produce more via a lower input price, achieving the above effect.