Abstract

We consider a competitive model of insurance provision where consumers are privately informed about their risk level and preferences. The presence of two-dimensional heterogeneity introduces novel distribution effects absent from the one-dimensional model typically studied in the literature. Focusing on the case of small preference heterogeneity, we obtain explicit formulas for equilibrium prices and payoffs. We use these results to study the use of demographic characteristics in pricing (risk classification) and the effect of changes to the risk distribution.

We study risk classification by considering the public release of a signal that is informative about individual risk and show that it leads interim and ex-ante welfare improvements if, and only if, the signal structure satisfies a certain monotonicity condition, while non-monotonic signals may harm some consumers and be overall welfare reducing. We also show that an increase in the risk distribution, according to the monotonic likelihood ratio property (MLRP), leads to higher prices and lower welfare, while risk-distribution increases in the sense of first order stochastic dominance (FOSD) can be beneficial for some consumers.