2 Moral Hazard We change the setting of question 1 slightly to discuss the effect of moral hazard. =z is still the quality of a driver. The accident probability depends not only z but also on the driver's effort e. The accident probability is p = (0.05 0.04z) x exp(0.5 ). = is uniformly distributed on U[0, 1]. e can take three values: 0, 0.3, and 0.5. The private cost of effort is (e) = 18. The total loss of the traffic accident is 1000. 1. We first consider the case without insurance. (15) (a) If the driver with x = 0.5 is risk-neutral, what will be her optimal effort level? (8) (b) If the driver with = = 0.9 is risk-neutral, what will be her optimal effort level? (7) 2. Next we consider an auto insurance policy with a 30% coinsurance requirement and 200 deductible (i.e., the buyer should pay 200 deductible plus 30% of the total cost in excess of the deductible). (25') (a) Consider the person with z = 0.5 who is risk-neutral, what will be her optimal effort level? (&) (b) Consider the person with z = 0.9 who is risk-neutral, what will be her optimal effort level? (7) () Based on your analysis in question 1 and 2, is the moral hazard problem more severe for better or worse drivers? Do you think this conclusion is consistent with your real-world observation? (10) 3. Based on your answer in 2(c), does the presence of moral hazard alleviate or exacerbate the adverse selection problem? (57) 4. What can the insurer do to alleviate the adverse selection and moral hazard problem? (57) 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 is uniformly distributed between 0 and 1. Suppose the probability of having a trafhic accident is 0.05 0.04z. For example, if a driver has x = 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