Christoph Schottmüller, University of Copenhagen

"Monopoly insurance with endogenous information"

Abstract

We study a monopoly insurance model in which a consumer, by making a costly effort, can choose the precision of a privately observed signal that is informative about his accident risk. The chosen equilibrium effort is, depending on parameter values, either zero (meaning symmetric information) or positive (meaning a privately informed consumer). We show that, regardless of the nature of the equilibrium, all offered contracts, also at the top, involve underinsurance; the reason is that underinsurance at the top discourages information gathering, which is in the insurer's interest due to something we call the sorting effect. We also demonstrate that a public policy that lowers the information gathering cost can be counterproductive, in the sense that it hurts both parties. The reason why it can hurt the consumer is that when information acquisition becomes easier, the insurer adjusts the optimal contract menu in an unfavorable manner. We further show, however, that if the equilibrium effort is zero, the consumer always benefits from lower information acquisition cost.