Capacity allocation under downstream competition and bargaining

Abstract

In this study, we consider a monopolistic supplier’s capacity-allocation problem under bargaining. The supplier can allocate one type of key element to either an external channel with a manufacturer, an internal channel, or both. The firms use the element to produce substitutable final products and compete in the product market. By building a stylized model, we characterize the equilibrium decisions under different channel choices. The conditions of the equilibrium channel choices are derived. We find that the supplier’s shared capacity increases with his bargaining power, but the manufacturer’s shared capacity decreases with her bargaining power. Meanwhile, the higher bargaining power may backfire on the manufacturer, because her loss from a decreased shared capacity may dominate her benefit from an increase in her bargaining power.Under the dual channel, as market competition intensifies, the high-cost firm’s shared capacity always decreases; however, the low-cost firm’s shared capacity decreases and increases sequentially if the manufacturer’s bargaining power is sufficiently small, and increases if her bargaining power is sufficiently large. The reason is that the low-cost firm’s competitive advantage relative to the high-cost firm is amplified by the manufacturer’s increased bargaining power. Either firm’s production cost improvement can benefit the other. If the firms’ demand functions are asymmetric, an increased customer valuation on the manufacturer’s products benefits the supplier; an increased price sensitivity to demand on the supplier’s products may harm the manufacturer. Moreover, when the supplier sells to two manufacturers, one manufacturer can gain from an increase in the competing manufacturer’s bargaining power.