1 Adverse Selection Suppose the quality of a driver is characterized by a random variable z. A higher value of = indicates a better driver and the probability of accident is lower. x is uniformly distributed between 0 and 1. Suppose the probability of having a traffic accident is 0.05 0.04z. For example, if a driver has & = 0.2, the probability of having a traffic accident is 0.05 0.04 x 0.2 = 0.042. If the traffic accident happens, the loss is 1000. All people have an intiail wealth of 1200. 1. Now we consider one single driver with = = 0.5. (15") (a) (b) (c) (d) What is the maximum amount she is willing to pay for an auto insurance policy that covers the cost of the traffic accident in full, if she is risk-neutral? (3") How will your answer to question (a) change if she is risk averse with utility function u(w) = w? (3) How will your answer to question (a) change if the policy requires a coinsurance of 30% with a deductible of 200 (i.e., the buyer should pay 200 deductible plus 30% of the total loss in excess of the deductible)? (37) If buyers are risk averse, consider two different insurance. Insurance A: coinsurance of 30% with a deductible of 200; Insurance B: coninsurance of 20% with a deductible of 400. Lay out the equations that solves for the maximum willingness to pay for the risk-averse buyers with utility function u(w) = y/w. (3') Consider the risk-averse buyer with utility function u(w) = /w. Denote maximum willingness to pay for every unit of coverage for the insurance with full coverage as Wi, the maximum willingness to pay for every unit coverage for Insurance A as Wy, the maximum willingness to pay for every unit coverage for Insurance B as Wpg. Rank W, Wa, Wp and explain. (37) 2. Now we consider an auto insurance policy that covers the total cost in full. The premium level is 30. (10") (a) (b) If all the people in the society are risk neutral. What is the fraction of people that will purchase this policy? Is the insurer's profit positive, negative, or zero? [Hint: if X follows U[0, 1], the probability of X