b) Each individual has an expected utility function that looks like the following: EU pin()+(1) where p is the probability of an accident, P is an individual's net income in case of an accident. and is an individual's net income if no accident occurs. Assume that W is equal to 100 and is equal to 50. If a person of type B is offered 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 i to maximize a type B person's expected utility subject to the appropriate no profit 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 by? [Do not work this our 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).