Salesforce Contracting Under Uncertain Demand and Supply: Double Moral Hazard and Optimality of Smooth Contracts

We consider the compensation design problem of a firm that hires a salesperson to exert effort to increase demand. We assume both demand and supply to be uncertain with sales being the smaller of demand and supply and assume that, if demand exceeds supply, then unmet demand is unobservable (demand censoring). Under single moral hazard (i.e., when the salesperson's effort is unobservable to the firm), we show that the optimal contract has an extreme convex form in which a bonus is provided only for achieving the highest sales outcome even if low realized sales are due to low realized supply (on which the salesperson has no influence). Under double moral hazard (i.e., when the firm can also take supply-related actions that are unobservable to the salesperson), we show that the optimal contract is smoother as it involves positive compensation for intermediate sales outcomes to assure the salesperson that the firm does not have an incentive to deviate to an action that hurts the agent; in fact, under certain conditions, the contract is concave in sales. We also determine conditions under which, if possible, the firm should postpone contracting until after supply is realized.