Suppose you usually go to the movies on Saturdays, and the schedule at the (free) student-run movie theater consists of a mediocre movie this week, a good movie next week, a great movie in two weeks, and an excellent movie in three weeks. Denoting ut the utility of going to a movie in week t, we have u 3, u2 = 5, uz 13. 8, and u4= You must complete a problem set within the next four weeks, and, to do so, you must skip the movie some Saturday. = = 1. Suppose you are a rational agent with discount rate = 1. When do you complete the problem set? 2. Suppose you are a quasi hyperbolic agent with discount rate = = 1 and 0.5, and that you do not not take into account the fact that your future self may deviate from your initial plans. Show that, in every period, you always prefer to postpone the problem set by a week. When do you complete the problem set? 3. Now suppose that the movie theater now only allots three movie vouchers per student. Vouchers can be redeemed for specific movie tickets. Once redeemed, the tickets are non transferrable/exchangeable. When do you complete the problem set? Relate your answer to the concept of illiquid account discussed in class.