On Monday morning, Polly Putitov faces the same assignment as Darryl Dawdle. It will also take her 12 hours to finish the term paper. However on day t, her preferences about time spent writing over the next 3 days are represented by
U(xt, xt+1, xt+2) = −x2t – 1/2 x2t+1 – 1/4 x2t+2.
(a) Does Polly’s three-period utility function have exponential or hyperbolic discounting? _________ If exponential, what is the discount rate δ; if hyperbolic, what is the parameter k? ___________
(b) On Monday morning Polly makes a plan for finishing the term paper that maximizes her Monday utility function
U(xM, xT, xW) = −x2M – 1/2 x2T – 1/4 x2W
subject to xM + xT + xW = 12. How many hours does Polly plan to work on Monday? ___________ On Tuesday? __________ On Wednesday? __________
(c) Polly spent 12/7 hours working on the project on Monday and completed the amount of work she planned to do on Monday. On Tuesday morning, her utility function is
U(xT, xW, xTh) = −x2T – 1/2 x2W – 1/4 x2Th.
Since work on Thursday won’t help to get the paper done before the deadline, she will set xTh = 0, and she will choose xT and xW to maximize
−x2T – 1/2 x2W
subject to the constraint that xT + xW is equal to 12−(12/7). How much will she work on Tuesday? ______________ On Wednesday? ___________ Do these quantities agree with the plans she made on Monday? ___________ Does Polly have time-consistent preferences? ______________