Monopoly Insurance with Endogenous Information

We study a monopoly insurance model with endogenous information acquisition. Through a continuous effort choice, consumers can determine the precision of a privately observed signal that is informative about their accident risk. The equilibrium effort is, depending on parameter values, either zero (implying symmetric information) or positive (implying privately informed consumers). 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. We identify a sorting effect that explains why the insurer wants to discourage information acquisition. Moreover, a public policy that decreases the information gathering costs can hurt both parties. Lower information gathering costs can harm consumers because the insurer adjusts the optimal contract menu in an unfavorable manner.