We consider a simple supply chain governed by a simple contract: A manufacturer sells to a retailer facing a newsvendor problem and the lone contract parameter is a per-unit wholesale price. While such contracts are undeniably common in practice, a detailed analysis of them has been missing from the literature. We develop a formulation based on the manufacturer's sale quantity that is amenable to analysis. A mild restriction on a generalization of the hazard rate assures that the manufacturer's problem is unimodal.

We show that the manufacturer sells more as market size increases but that the behavior of the wholesale price depends on how the market size changes. If the market is scaled so that the mean and standard deviation increase in lock step, the optimal wholesale price is independent of the size of the market. If the market is shifted so that the mean increases while the standard deviation is unchanged, the wholesale price is increasing in the size of the market. In either the scaled or shifted case, the coefficient of variation plays an important role in determining the optimal wholesale price. The coefficient of variation also plays a key role in determining how the decentralized channel performs relative to the integrated channel as well as how realized profits are split. We show that as the coefficient of variation falls the decentralized channel is able to capture a greater share of possible profits and that the manufacturer share of realized also rises.