Incentive compatibility and pricing under moral hazard
We study a simple insurance economy with moral hazard, in which random contracts overcome the non-convexities generated by the incentive-compatibility constraints. The novelty is that we use linear programming and duality theory to study the relation between incentive compatibility and pricing. Using linear programming has the advantage that we can impose the incentive-compatibility constraints on the agents that are uninformed (the insurance firms). In contrast, most of the general equilibrium literature imposes them on the informed agents (the consumers). We derive the two welfare theorems, establish the existence of a competitive equilibrium, and characterize the equilibrium prices and allocations. Our competitive equilibrium has two key properties: (i) the equilibrium prices reflect all the relevant information, including the welfare costs arising from the incentive-compatibility constraints; (ii) the equilibrium allocations are the same as when the incentive-compatibility constraints are imposed on the consumers.
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