Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

TL;DR

This paper characterizes incentive-efficient contract menus in a monopolistic insurance market with private information, showing their equivalence to social welfare maximization and analyzing their structure under different risk attitudes and type orderings.

Contribution

It provides a theoretical framework for incentive-efficient insurance contracts with private types, including a semi-explicit solution for Yaari dual utility and analysis under different risk type orderings.

Findings

Incentive-efficient menus maximize social welfare under IC and IR constraints.

Optimal contracts allocate higher coverage to higher types with higher premiums.

At the optimum, the lowest type is indifferent, and the highest type receives full coverage.

Abstract

We study a monopolistic insurance market with hidden information, where the agent's type $\theta$ is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this framework, we show that a menu of contracts is incentive efficient if and only if it maximizes social welfare, subject to incentive compatibility and individual rationality constraints. This equivalence holds for general concave utility functionals. In the special case of Yaari Dual Utility, we provide a semi-explicit characterization of optimal incentive-efficient menus of contracts. We do this under two different settings: (i) the first assumes that types are ordered in a way such that larger values of $\theta$ correspond to more risk-averse types who face stochastically larger losses; whereas (ii) the second assumes that larger values of $\theta$ correspond to less risk-averse types who face stochastically larger losses. In both settings, the structure of optimal incentive-efficient menus of contracts depends on the level of the social welfare weight. Moreover, at the optimum, higher types receive greater coverage in exchange for higher premia. Additionally, optimal menus leave the lowest type indifferent, with the insurer absorbing all surplus from the lowest type; and they exhibit efficiency at the top, that is, the highest type receives full coverage.