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Question 3 Suppose Smith is considering buying theft insurance for a car. Before he buys insurance, his wealth is 0 if there is a theft, and the value of the car, i.e., 12, otherwise. If Smith is careful where he parks, a theft occurs with probability 0.5. However, if he is careless, the probability rises to 0.75. Smith is risk averse and, other things equal, he has a mild preference to be careless, a preference worth only some small amount (close to zero) 6 > 0 to him. The insurance company is risk neutral. and the market is competitive. The insurance company offers a contract 0 = (m, y). in which Smith pays premium :1: and receives compensation y if there is a theft. (a) [15 marks] Derive the equilibrium contract 0 = (w,y) when the insurance com- pany can observe whether Smith has been careful or careless. Illustrate using a state-space diagram. (b) [20 marks] Suppose that the company cannot observe Smith's action (i.e., care is observable only to Smith). Determine graphically the equilibrium contract 0 = (m,y) under asymmetric information. Explain in a diagram the tradeoff between efficient risksharing and incentives