An inspection-based price rebate and effort contract model with incomplete information

• Three strategies, named inspection, price rebate and effort, are employed.
• The second-best inspection ratio is the same as the first-best one.
• The second-best effort is less than the first-best one.
• The second-best effort is larger than first-best in the case of substitute.
• It is opposite in the case of complement.

This paper considers a supply chain contract design problem, in which a buyer purchases a batch of products from a supplier and then sells it to consumers. The product quality with a continuous type is the supplier’s private information and cannot be observed by the buyer. Furthermore, three strategies, named inspection, price rebate and effort, are simultaneously employed in the contract so as to incentivize the supplier to improve his product quality. An inspection-based price rebate and effort contract model is developed with the purpose of maximizing the buyer’s expected payoff. The optimal solution demonstrates that the second-best inspection ratio is the same as the first-best one. With respect to the supplier’s optimal effort level, if the supplier’s effort level and his product quality are substitutable, then his second-best effort level will be larger than the first-best one, while in the case of complement, it is smaller than the first-best level.