2. (30 points) A student can go to a movie exactly once in four periods t = 0,1,2,3. The instantaneous utility, in monetary terms, from going to the movie in period t = 0 is 29, in period t : 1 it is 37, in period t = 2 it is 49, and in period t = 3 it is 67. A movie ticket costs $13, which has to be paid in the period in which the student goes to the movie (so the ticket price must be subtracted from instantaneous utility in the period in which the price is paid). The student is a hyperbolic discounter with 3 = % and (5 = 1. (a) (10 points) When does a sophisticated student go to the movie? Show your work. (b) (10 points) When does a naive student go to the movie? Show your work. (c) (10 points) Explain intuitively why the naive student ends up better off than the sophis- ticated student in this case