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4. Mr. Gary is going on a major vacation, on which he is planning to spend $10,000. The utility he will get from the trip is a function of how much he actually spends, Y, according to the function UH) = ln Y. (a) If there is a 25% chance that Mr. Gary will lose $1,000 of his spending money, what is the expected utility of the trip? (5 points) (b) Suppose an insurance company offers Gary full insurance against this loss at an actuarially fair premium. What is the amount of this premium? Would Gary buy this insurance? Explain fully. (6 points) (c) What is the maximum amount Gary would be willing to pay for this insurance? (6 points) ((1) Suppose that, once Gary has the insurance, he would become more careless with his money, as a result of which the probability of the $1,000 loss goes up to 30%. What is the actuarially fair premium now? Would Gary buy the insurance at this price? Explain. (8 points)