When a monopolist sells an input to an oligopoly, consumer and total surplus frequently are invariant to changes in passive ownership of the monopolist by downstream firms. Within broad classes of ownership profiles, strong invariance holds: the input and output choices of downstream firms are...

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...