Partial vertical ownership

A backward ownership interest held by a downstream firm yields a partial rebate of the upstream margin. Input demand increases with backward ownership, and the upstream firm optimally responds by raising price. With symmetric costs, every downstream firm's equilibrium input/output choice is invariant across a class of ownership profiles, including uniform ownership. Moreover, equity trading results in uniform holdings, so partial vertical ownership may have no real effects. With asymmetric costs ex ante, equity trading amplifies the asymmetries and shifts output toward lower-cost firms. With homogeneous goods, this improves producer and total surplus. With differentiated goods, it may harm consumers.