Optimal Contracts under General Mixed Constraints: Continuity, Structure, and Applications

This paper characterizes optimal contract structures under adverse selection when the principal faces a general class of mixed (involving allocation and transfer) constraints. We establish conditions for the existence and the continuity of the optimal allocation. We show that under regularity conditions, the optimal continuous contract features at most three distinct regions: segments where the constraint is slack and the allocation follows a modified Baron-Myerson path, alternating with segments where the constraint binds. Assuming non-generic cases are excluded, the binding constraint forces a constant allocation (bunching) over a range of agent types. This framework encompasses a wide range of applications, including enforcement limits, budget constraints, and quality regulations. Our analysis demonstrates how bunching can arise endogenously from optimal design under smooth constraints, distinct from exogenously induced behavioural responses documented empirically.