Question 3. Consider the following competitive market for insurance. There are two states of the world: good and bad B. Consumers have wealth 10,000, but if the bad state occurs their wealth is reduced by 3,600. Consumers are expected utility maximisers, with common utility function u(x) = x There are two types of consumers: high risk types H and low risk types L. The probabili ties that H and L types find themselves in the bad state are p = 0.6 and p = 0.2. There is probability B = 0.6 that a consumer picked at random is type L. Firms are risk-neutral expected profit maximisers. The firm offers consumers a state- contingent contracts e = (06.09) in exchange for their endowment e = (@n). (a) Explain what is meant by a competitive equilibrium of this market. (2 marks) (b) Explain and derive the equilibrium insurance contracts under the assumption that there is perfect information regarding consumer types. (3 marks) (e) Explain and derive the equilibrium insurance contracts under the assumption that there is void information regarding consumer types. (2 marks) (d) Explain the Hirshleifer effect and use the results in (b) and (e) to give a numerical example of the Hirshleifer effect. (2 marks) Question 3. Consider the following competitive market for insurance. There are two states of the world: good and bad B. Consumers have wealth 10,000, but if the bad state occurs their wealth is reduced by 3,600. Consumers are expected utility maximisers, with common utility function u(x) = x There are two types of consumers: high risk types H and low risk types L. The probabili ties that H and L types find themselves in the bad state are p = 0.6 and p = 0.2. There is probability B = 0.6 that a consumer picked at random is type L. Firms are risk-neutral expected profit maximisers. The firm offers consumers a state- contingent contracts e = (06.09) in exchange for their endowment e = (@n). (a) Explain what is meant by a competitive equilibrium of this market. (2 marks) (b) Explain and derive the equilibrium insurance contracts under the assumption that there is perfect information regarding consumer types. (3 marks) (e) Explain and derive the equilibrium insurance contracts under the assumption that there is void information regarding consumer types. (2 marks) (d) Explain the Hirshleifer effect and use the results in (b) and (e) to give a numerical example of the Hirshleifer effect. (2 marks)