(c) If the insurer decides to raise insurance premium, does it always increase insurer's profit? (5) 4. Suppose there are two types of losses. Insurance for Type-I loss coverage is compulsory and insurance for Type-II loss coverage is optional. If Type-I loss is 400 and Type-1II loss is 600. The premium for Type-I loss insurance is 12 and the premium for Type-II loss insurance is 18. Assume all drivers in the society are risk neutral. Suppose the insurance covers Type-II loss coverage in full. (107) (a) What's the fraction of drivers that will purchase the Type-II loss coverage? (5) (b) Will the profit of insurer be positive, negative or zero? Is the profit of insurer higher or lower than your answer in question 2(a)? (57) 1 Adverse Selection Suppose the quality of a driver is characterized by a random variable z. A higher value of z indicates a better driver and the probability of accident is lower. x 1s 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 (a) (b) 3. Now we consider one single driver with z = 0.5. (15") 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)? (3) 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) = /w. (3') Consider the risk-averse buyer with utility function u(w) = y/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 Wg. Rank W un, Wa, Wg and explain. (3') we consider an auto insurance policy that covers the total cost in full. The premium is 30. (10) 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 U0, 1], the probability of X