Vertical integration and market foreclosure with convex downstream costs

In a framework with an upstream monopoly and a downstream duopoly, we analyze the impact of convex costs on the downstream level. In contrast to the case of constant marginal costs, vertical integration does not imply complete market foreclosure. While the non-integrated downstream firm receives a strictly positive amount of the intermediate good, the downstream allocation is inefficient. However, a parametrized example indicates that competition at the downstream level may increase aggregate welfare.