Salesforce Contracting Under Demand Censorship

We study salesforce contracting in an environment where excess demand results in lost sales and the demand information is censored by the inventory level. In our model, a firm contracts with a risk-neutral sales agent with limited liability whose effort increases the demand stochastically. The firm designs the incentive contract and invests in inventory; the agent decides the sales effort. We find that the sales-quota-based bonus contract is optimal in such an environment, and the quota should be set equal to the inventory level when the first-best solution is not attainable. We further reveal that demand censorship can introduce peculiar effects on the optimal sales effort and service level that the firm implements. From our analysis of the additive and multiplicative effort cases, we find that in the additive effort case, it can be optimal, under demand censorship, for the firm to induce an effort and maintain a service level both greater than those under the first-best solution. Scenarios also exist where the firm should induce zero effort. For the multiplicative effort case, the optimal sales effort under demand censorship is lower than the first-best effort, whereas the optimal service level is higher than the first-best service level. The agent earns zero rent in the additive effort case but may earn a positive rent in the multiplicative effort case. Finally, our numerical analysis shows that demand censorship can have a significant negative impact on the value of contracting with the sales agent, especially when the sales margin is low and the market uncertainty is high.