Vertical cross-ownership, double marginalization, and social welfare

In this paper, we study the impacts of cross-ownership structure on double marginalization problem (DMP) and social welfare under downstream the Bertrand and Cournot competition. We find that in the Bertrand competition, DMP is more serious under backward cross-ownership than under forward cross-ownership. Under forward cross-ownership, because the upstream firm internalizes part of a retailer's profit, it alleviates the DMP. However, for the whole society, forward cross-ownership is beneficial with respect to backward cross-ownership. The mark-up ratio under forward cross-ownership is the largest, followed by that under vertical separation. The lowest one is under backward cross-ownership. The results hold under Cournot competition as well.