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5. Pete has a wealth of $1, 000. Pete just bought a new car. but he is a reckless driver. 80 tomorrow when he drives to work for the first time, there is a 75% chance that he will have an accident and only a 25% chance that he will not. if he has an accident, he will have to pay $600 in damages and repairs. Suppose Pete's utility of wealth, w, is given by the function: u(w) = \\[Vi-J. a) What is the expected value of Pete's wealth tomorrow? b) What is his expected utility? c) How much would Pete be willing to pay to avoid the possible loss of income? Suppose Pete could buy car insurance. d) What is the maximum premium that the insurance company can charge to get Pete to buy this policy? e) What is the insurance company's expected profit if it charges the maximum premium that Pete is willing to pay? Pete decides to become a more a careful driver so that his chances of an accident fall to 50%. f) What happens to the premium that the insurance company can charge? g) What happens to the company's expected profit