Vertical contracting between a vertically integrated firm and a downstream rival

Compared to linear tariffs, two-part tariffs are generally perceived as being more efficient since double marginalization is avoided. We investigate the efficiency of two-part tariffs vs. linear tariffs when a vertically integrated firm sells its input also to an independent downstream firm selling a differentiated substitute product. We find that a linear tariff can generate higher consumer surplus and overall welfare than a two-part tariff when the independent downstream firm is rather powerful in negotiating the contract terms, and downstream competition is in prices (Bertrand competition). In that case, the integrated firm makes more profits under a linear tariff than under a two-part tariff. In contrast, under downstream Cournot competition two-part tariffs are always welfare-superior. Under linear demand, we find that, irrespective of the mode of downstream competition and the distribution of bargaining power, the preferred contract type of the integrated firm is always welfare-superior.