**Unformatted text preview: **t today (in period zero) then her period‐one self has utility given by U1 = u1 + u2. The choice set she maximizes her function over is binary: do the assignment in period one or do it in period two. If she does it in period one she receives ‐3/2 utils. And if she does it in period two she receives ‐9/4 utils. Period one self therefore chooses to do the assignment in period one. Today’s self (period zero) now faces the decision to do it now or put it off. She knows that if she puts it off until the future it will be done in period one. The choice in period zero is therefore between completing the assignment in period zero or in period one. She gets a utility of ‐1 by doing it today in period zero. If she waits she gets ‐3/2. The assignment is completed today. 1 (b) Now suppose that instead of being perfectly patient, the student has a preference for indulging immediate gratification; she overweights the present relative to all future dates by a factor of one‐
half. That is, her overall utility today (period 0) is UO = uO + ½ u1 + ½ u2, (3) and her overall utility tomorrow (period 1) is U1 = u1 + ½ u2. (4) (Economists say that an individual with this kind of discounting structure has a self‐control problem – or has time‐inconsistent preferences – because, as you will see, suchan individual has preferences that are internally conflicting, depending on when you ask her.) Using equation (4), explain why if she has not done the assignment by tomorrow, she will choose to do it in two days rather than doing it tomorrow. Using equation (3), explain why from today’s point of view, she would prefer to do the assignment tomorrow instead of today, but if she had to choose between doing it today or doing it in two days, she would prefer to do it today. If the person doesn’t 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 {d...

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