Competitive Insurance Markets with Two Unobservables

We study a screening game in a competitive insurance market, in which insurance customers differ with respect to both accident probability and degree of risk aversion. It is shown that indifference curves of customers in different risk classes cross exactly twice: thus the single crossing property does not hold. The existence of a unique reactive equilibrium is demonstrated. This equilibrium may be markedly different from the Pareto-dominant separating equilibrium that exists when single crossing holds. In particular, types may be pooled in equilibrium, so that cross-subsidization occurs. Moreover, insurance firms can earn positive expected profit in equilibrium, despite the usual assumption of Bertrand-like price-competition among firms. We study the implications of the model for the efficiency of market equilibrium and for the effects of rate-of-return regulation of insurance firms.