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**Unformatted text preview: **/2*(‐9/4) = ‐9/8. Finishing up today gives a happiness of ‐1. Today’s self thus completes the project in period zero (today). (d) Now suppose that the student is naive about her self‐control problem; she does not realize that her preferences are internally conflicting. That is, even though her actual preferences are given by 2 equation (3) and equation (4), when she’s making her decisions today, she believes that her preferences tomorrow will be U1 = ½ u1 + ½ u2, which is consistent with what her preferences are today. Explain why today she (incorrectly) believes that she if she postpones doing the assignment, she will do it tomorrow. What will she actually do tomorrow if she has not done the assignment by then? Explain why a student who is naïve about her self‐control problem will end up doing the assignment the day it is due, even though from today’s point of view (as well as from tomorrow’s and the next day’s point of view!) she would have preferred to do it today. If the girl is naïve then she believes period one’s preferences are U1 = ½ u1 + ½ u2. She concludes that the project will be done in period one if she postpones the assignment because period one completion maximizes her perceived set of period one preferences. She thinks she’ll get utility of ½*(‐
3/2) = ‐3/4, which is higher than ½*(9/4) = ‐9/8. If tomorrow rolls around and she hasn’t done the assignment, she will wait until period two because the preferences in period one are actually U1 = u1 + ½ u2. As shown in the previous parts, the optimal choice is to wait until period two. In the end the naïve girl does the assignment on the day it’s due. She puts it off in the first period because she incorrectly believes her period one self will have time consistent preferences given by U1 = ½ u1 + ½ u2. But when period one comes her actual preferences are U1 = u1 + ½ u2. So she waits. The end result is that the assignment is done...

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