Optimal Contract Design under Multiple Moral Hazard - Ex Ante, Ex Post Cash Diversion, and Price Deviation

Abstract

We analyze a decentralized newsvendor production problem subject to agency issues. A principal provides funds and contracts with an agent for capacity planning. However, the agent is subject to moral hazard, such as cash diversion during production, which is unobservable to the principal. We derive the principal's optimal contract under ex ante and ex post cash diversion scenarios, which happen before and after demand is realized, respectively. Optimal contracts have simple forms and are easy to implement. Furthermore, we provide the optimal production quantity and pricing decisions. When only subjected to ex ante diversion, the optimal contract is a debt contract, which leads to underproduction and a higher price than first-best centralized production. When subjected to both ex ante and ex post diversion, the debt contract is no longer optimal. Instead, we present a modified debt repayment that resembles both debt and revenue-sharing contracts is optimal. Furthermore, we find that the optimal capacity and price depend on the level of ex post diversion efficiency with respect to which the optimal price is nonmonotonic. Finally, we consider a scenario where the actual sales price is also unobservable and find that the principal can still use a simple debt contract to deter ex ante diversion and price deviation in most regimes. However, this debt contract must have an additional clause penalizing excessive revenue.

Keywords: Optimal contract, delegation, moral hazard, newsvendor model, capacity investment, pricing