Incentive compatibility and pricing under moral hazard

We show how to recover equilibrium prices supporting incentive-efficient allocations in a classic insurance economy with moral hazard. Our key modeling choice is to impose the incentive-compatibility constraints on insurance firms, and not on consumers as in Prescott and Townsend [Pareto optima and competitive equilibria with adverse selection and moral hazard, Econometrica 52 (1984) 21-45]. We show that equilibrium prices of insurance contracts are equal to the sum of the shadow costs arising from the resource and incentive-compatibility constraints in the planner's problem. The equilibrium allocations are the same as when the incentive-compatibility constraints are imposed on consumers. As in Prescott and Townsend, the two welfare theorems hold.