Revenue-sharing and volume flexibility in the supply chain

We model capacity choice and utilization of a manufacturer selling products through a retailer under a revenue sharing contract. We derive the optimal revenue sharing contract which internalizes the impact on capacity, utilization choice and the final downstream price of the product and provide a valuation of the retailer and supplier under uncertainty in a multiperiod setting. In extensions of this framework, we analyze constraints on minimum delivered quantities and also build a finite-time numerical method that considers an abandonment option for the supplier and hold-up problems for the retailer, as well as the supplier's option to expand capacity. Our model predicts higher revenue sharing ratios charged by retailers when suppliers operate in more volatile upstream markets, when the product is a necessity rather than a luxury good and when retailers can impose minimum delivered quantities. On the contrary, we find that suppliers will be able to obtain a higher revenue share when operating in industries with high fixed costs and for contracts of shorter horizon since hold-up problems for retailers increase and the retailer has to provide more incentives to suppliers not to abandon op-erations. The option to expand capacity benefits more significantly the supplier compared to the retailer. Finally, we consider the decisions of a vertically integrated firm showing the gains from vertical integration and demonstrating that the optimum vertically coordinated production can be achieved in the decentralized mul-tiperiod setup through a combination of a fee per product and revenue sharing.