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3 Vacation Time Olivia has a coupon deal for skiing that she can use anytime in the next four weeks. The weather, however, is currently mediocre, and gets incrementally better each wwk. As a result, her valuation for skiing in each week is as follows: 0 If she goes in week 1, she gets a utility value of 3. o If she goes in week 2, she gets a utility value of 5. o If she goes in week 3, when the weather is even better, she receives a benet of 8. o If she goes in week 4, when the weather is nearly perfect, she receives a utility benet of 13. She bears no cost for going on the trip except for the opportunity cost of using the coupon. (a) Draw the decision tree of Olivia's decision-making process. (b) If Olivia's behavior is time-consistent, and her discount factor 6 is equal to 1 (so she has no impatience), when will she choose to go skiing? You must show the reasoning behind your answer to get credit. Suppose instead Olivia acts as if she has a quasi-hyperbolic utility function, with ,6 = % and 6 = 1. That is, when making her decisions, she discounts all future benets by %. (c) When will Olivia choose to go skiing if she is naive about her time inconsistency? That is, she assumes that in the future she will act as if she is time-consistent. You must show the reasoning behind your answer to get credit. (d) When will Olivia choose to go skiing if she is sophisticated about her time inconsistency? That is, she knows that if she leaves the decision for next weekend, she will act in a time-inconsistent manner. You must show the reasoning behind your answer to get credit