Deke's utility function is given by U = , where y represents annual income in thousands of dollars. Deke is currently earning an income of $25,000 (therefore y = 25) and can earn that income next year with certainty. He is offered the chance to take a new job that offers a .6 probability of earning $36,000 and a .4 probability of earning $9,000. a. Should he take the new job? Show clearly how you arrive at your answer. b. Suppose Deke takes the new job. Use the information provided above to determine whether he would be willing to buy insurance to protect him fully against the variable income associated with this new job. If he is willing to purchase insurance, how large a premium is he willing to pay for it? Show clearly how you arrive at your answer. (Be sure to indicate exactly how much insurance coverage Deke would purchase.)