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Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard

Edward C. Prescott
Robert M. Townsend

Abstract

This paper explores the extent to which standard, general equilibrium analysis of Pareto optima and of competitive equilibria can be applied to environments with moral hazard and adverse selection problems. Allowing for lotteries, contracts with random components, we first establish that an adverse-selection insurance economy, a moral-hazard insurance economy, a signaling economy, and a private-information labor market economy are all special cases of a simple, general structure. We then show that techniques for characterizing Pareto optimal contracts as solutions to concave programming problems are useful and nice and appear to be broadly applicable; allowing for lotteries, we show how to characterize the optimal allocations for the adverse-selection insurance and labor market economies. We then show that standard existence and optimality theorems for competitive equilibria apply in the linear space containing lotteries if agents with characteristics which are distinct and privately observed at the time of initial trading enter the economy-wide resource constraints in a homogeneous way (other kinds of diversity are not critical). For economies with moral hazard which satisfy the homogeneity condition, competitive contract markets single out a subset of the optima and thus can be consistent with apparent unemployment and with a random allocation of labor supplied though all households are averse to risk. The adverse-selection insurance and signaling economies, however, do not satisfy the homogeneity condition and are difficult to decentralize efficiently with a price system.