Much of the standard literature on adverse selection insurance models assumes that the only unknown parameter is the accident probability and that all consumers have the same level of risk aversion. This paper relaxes these two assumptions by allowing consumers to have different levels of risk aversion, which the insurer has no prior knowledge of these levels of risk aversion when meeting consumers for the first time. Using Bayesian learning a monopolistic insurer tries to learn a consumer's level of risk aversion. This paper shows that an insurer who learns in the two-type consumer model offers either separating contracts to the two different types of consumer or does not insure one of the types of consumer. This result is identical to the result in Stiglitz (1977) where he assumes that the monopolistic insurer has prior knowledge of a consumer's level of risk aversion. However, the insurer who learns offers different contracts when compared to the insurer who knows a consumer's level of risk aversion. By offering different contracts than the insurer who knows a consumer's level of risk aversion, the insurer who learns earns less expected profit than the insurer who knows a consumer's level of risk aversion. Monte Carlo simulation results show that the expected percentage loss in profit is significantly larger than the corresponding expected percentage changes in prices and coverage of the insurance contracts as a result of the insurer learning the levels of risk aversion of the two different types of consumer.
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