Upstream pricing strategies, multiple inputs, and downstream delegation

This paper considers a delegation game between one multi-input firm and one single-input firm engaging in Cournot competition in the downstream market. Both firms purchase a standard input from a core input supplier, and the multi-input firm also needs a supplementary input provided by an independent supplier. I study two input pricing policies of the core input supplier, uniform pricing and third-degree price discrimination, and obtain the following. First, regardless of the upstream pricing strategies, both downstream firms delegate in equilibrium, but contrary to traditional analysis, delegation is mutually profitable. Second, the core input supplier prefers uniform pricing to third-degree price discrimination. Lastly, uniform pricing is more socially desirable than discriminatory pricing.