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 invariant to a change within the class. While passive ownership raises input demand, the upstream firm responds by raising price. Strong invariance always holds for bilateral monopoly. For a broad class of models with fixed proportions technologies, aggregate output is invariant across all passive ownership profiles. Passive ownership is privately profitable because it shifts sales from rivals.