Do it now or do it later. My friend Paco Vivalavida has to do an activity once between now (t = 1) and T = 4. That is, he has to choose a vector of decisions (x1, x2, x3, x4), xt {Y, N}, where xt = Y means do the activity in period t if he has not already done it at t 0 < t, and xt = N means not do the activity at t. For instance, (N, Y, N, Y ) means Paco does not do the activity at t = 1, does the activity af t = 2 if it was not done before, does not do it at t = 3 if it has not been done before and does it at t = 4 if it has not been done before. Such a strategy leads to him actually doing the activity at t = 2. Rewarding Activity. Paco loves movies and he just got a free movie ticket that he can use at the local movie theater in one of the next 4 Saturdays. Each Saturday a different movie is shown, with better movies scheduled at later dates. In particular, Pacos (undiscounted) utilities associated to each of the movies are (u1, u2, u3, u4) = (3, 5, 8, 13), while he gets 0 if he does not watch a movie at t. He has time preferences with = 1. For instance, his utility at t = 1 from (N, Y, N, Y ) is u2, while her period-2 self derives utility u2. Similarly, his period-1 self gets u4 when he chooses (N, N, N, Y ) while her period-3 self gets u4.

(b) For the remainder of the problem assume Paco is present-biased with = 0.5. If he could commit to (x1, x2, x3, x4) (e.g. by giving the coupon to a friend and instructing him to deliver it at a specific t), what would his choice be?