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Dan and Michael pay $10 each for their friend Jesse's train ticket when Jesse notices that he doesn't have any money on him. They tell Jesse that he could pay them back when they arrive at their destination and find an ATM later in the day. Jesse, being tight on money, asks whether it would be okay for him to pay them back in 2 weeks instead. They respond saying they would accept this offer if he agreed to pay back an amount higher than $10. For this problem, assume that Dan, Michael, and Jesse are all selfish (i.e., this is an intertemporal choice problem and not a social preference problem.) (use week as unit time)
a) Given that Dan is a discounted utility maximizer with 6 = 0.7 and U(y)=y13, what is the lowest arnomtt (i.e., y) that Jesse needs to offer him in two weeks for him to accept the offer?
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