Competitive insurance market. Consumers in a competitive insurance market receive utility from wealth given by:

Competitive insurance market.

Consumers in a competitive insurance market receive utility from wealth given by: U(w) = log(1 + w) (1) Wealth is random and consumers without insurance will receive either a units of wealth in the bad state of the world or z units of wealth in the good state. There are two types of insurance consumers: high-risk (type H) and low-risk (type L). For high-risk consumers, the bad state occurs with probability πH and for low-risk consumers, the probability of the bad state is πL where πL < πH. Consumers obtain insurance policies from competitive insurance companies. A policy specifies a premium f that is paid to the insurance company in the good state and a claim c that is paid to the consumer in the bad state. Therefore, a consumer with insurance will receive: x = a + c (2) in the bad state and: y = z − f (3) in the good state. Suppose that: a = 20 πL = 0.2 (4) z = 100 πH = 0.5