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**Unformatted text preview: **o it in period one, (or) do it in period two}. The utility from waiting until period two is ½*(‐9/4) = ‐9/8 and the utility from doing it in period one is ‐3/2. Period one self therefore waits until period two. Note: the choice that maximizes period zero’s utility is period one completion. Doing it in period one gives utility of ½*(‐3/2) = ‐3/4, which is higher than the utility of period zero completion (‐1) and period two completion (‐9/8). But if the choice were between doing it in period zero or doing it in period two she would choose period zero. For period zero utility is ‐1 and period two utility is ‐9/8. (c) Suppose that the student is sophisticated about her self‐control problem; that is, she is aware that her preferences today are equation (3) and her preferences tomorrow are equation (4). Explain why in that case, she will end up doing the assignment today. (Hint: What does she expect will happen if she does not do the assignment today?) A sophisticated person backward inducts (i.e., solves backward) the solution to the problem. She begins by asking herself the following question: What happens if I wait? If the woman waits and does not do the assignment in period zero she has the utility function given in equation four. Period one self seeks to maximize this function over the binary set consisting of (1) do it in period one or (2) do it in period two. The utility from waiting until period two is ½*(‐9/4) = ‐
9/8. The utility from doing it in period one is ‐3/2. Period one self therefore does it in period two. Today’s self now faces a choice between doing it now or later. If she puts the project off until the future it won’t get done until period two because period one self chooses to wait. Today’s decision is therefore between doing it today in period zero or in two days during period two. Completion in period two gives a utility of 1...

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