b) Each individual has an expected utility function that looks like the following: EU =p Ina\") + (1p) Ina\"), where p is the probability of an accident, P' is an individual's net income in case of an accident, and I'M is an individual's net income if no accident occurs. Assume that Wis equal to 100 and L is equal to 50. [fa person of type B is oered an actuarially fair insurance contract, derive the amount of insurance this person would choose to buy. Interpret your result. [Hint Find the optimal amount of insurance by choosing either a or b to maximize a type B person's expected utility subject to the appropriate no-prot insurance constraint] c) Would a type A person prefer full insurance at actuarial fair rates appropriate to their own risk or the insurance contract chosen by type B individuals in part b)? [Do not work this out algebraically. Derive your answer using a graph with net income in the accident state on one axis and net income in the no-accident state on the other.] Would an insurance company be willing to offer full insurance at rates appropriate to type B's risk if it could not tell type A and type B individuals apart? d) Explain how the government can help to improve problems of adverse selection like the one encountered in part c). Question 2 [Insurance: Workers' Compensation] All residents in Smallville work at the only local factory. They all earn the same annual wage W. There is some risk that a worker may suer a minor injury on the job because the factory has a lot of dangerous equipment. If a worker is hurt on the job during the year, the worker suffers a nancial loss of L (this includes doctor bills and other costs)- There are three different types of residents. Type A residents are quite accident-prone, type B residents are moderately careful, and type C residents are extremely careful. The chance that a worker of type A has an accident during the year is 2/5, the chance that a worker of type B has an accident is US, and the chance that a worker of type C has an accident is zero