Jill possesses $160,000 worth of valuables. She faces a 0.2 probability of a burglary, where she would lose jewelry worth $70,000. She can buy an insurance policy for $15,000 that would fully reimburse the $70,000. Her utility function is U(X) = 4X0.5.
a. What is the actuarially fair price for the insurance policy?
b. Should she buy this insurance policy?
c. What is the most that she is willing to pay for an insurance policy that fully covers it against loss?