5. Consider hyperbolic discounting as introduced in Lecture. Suppose Freddy has a B = 1/2 and 5 = 1. Suppose Freddy can do the problem set at date t = 1, t = 2 or at t = 3. The disutility from doing the problem set at t = 1 is -2, at t = 2 it is -3, and t = 2 it is -5. (i.) If Freddy can commit at t = 0, when does he want to solve the problem set? (ii) If Freddy is naive about his self-control problem when does he solve the problem set? (iii) If Freddy is sophisticated about his self-control problem, When does he solve the problem set? (iv.) Bonus. If Freddy is sophisticated how much is he willing to pay for commitment