Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

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 it maximizes social welfare function, subject to incentive compatibility and individual rationality constraints. This holds for general utility functionals. In the special case of Yaari Dual Utility, we provide two partial converse statements to this result, and we give a semi-explicit characterization of optimal solutions to the social welfare maximization problem. 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 menus of contracts depends on the level of the social welfare weight, and we examine several properties thereof.