(Solved by Humans)-Ashley can do the problem set in any of three periods; t = 0, 1,

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Ashley can do the problem set in any of three periods; t = 0, 1, 2. The instantaneous utility cost of doing the problem set in period t = 0 is 4, in period t = 1 it is 6, and in period t = 2 it is 9. Ashley is a naive hyperbolic discounter with ? =0.5 and ? = 1

a)?Show that Ashley does the problem set in period 2.

b)?Suppose that Ashley's friends have a policy of taking her out in the period she finishes the problem set. Her utility from being taken out is 3 (and this does not depend on which period she is taken out). Show that in this case she does the problem set in period 0. Explain intuitively how tying the unpleasant task to a pleasant one overcomes procrastination in this example.

c)?Suppose instead that Ashley's friends, thinking that she has to do the problem set anyway, have a policy of taking her out on a single night of her choosing (not necessarily when she does the problem set). Would this policy work? (You do not need to do the math to just explain carefully.)