Strategic Inventories in Vertical Contracts

Classical reasons for carrying inventory include fixed (nonlinear) production or procurement costs, lead times, nonstationary or uncertain supply/demand, and capacity constraints. The last decade has seen active research in supply chain coordination focusing on the role of incentive contracts to achieve first-best levels of inventory. An extensive literature in industrial organization that studies incentives for vertical controls largely ignores the effect of inventories. Does the ability to carry inventory influence the problem of vertical control? Conversely, can inventories arise purely due to incentive effects? This paper explicitly considers both incentives and inventories, and their interplay, in a dynamic model of an upstream firm (supplier) and a downstream firm (buyer) who can carry inventories. In our model, none of the classical reasons for carrying inventory exists. However, as we prove, the buyer's optimal strategy in equilibrium is to carry inventories, and the supplier is unable to prevent this. These inventories arise out of purely strategic considerations not yet identified in the literature, and have a significant impact on the equilibrium solution as well as supplier, buyer, and channel profits. We prove that strategic inventories play a pivotal role under arbitrary contractual structures, general (arbitrary) demand functions and general (finite or infinite) horizon lengths. As one example, two-part tariff contracts do not lead to optimal channel performance, nor can the supplier extract away all of the channel profits, in our dynamic model. Our results imply that firms can and must carry inventories strategically, and that optimal vertical contracts must take the possibility of inventories into account.