A consumer lives for four periods, t= 0, 1, 2, 3. In each of the periods, she can decide whether to "hit" or "not hit". Hitting in a period t other than period 3 gives the consumer pleasure of 1 in period t and displeasure of 2 in period t + 1. Hitting in period 3 still gives the same pleasure in period 3—but since this is the last period—there is no unpleasantness associated with it. The consumer is a hyperbolic discounter; that is, self 0 maximizes the following discounted utility function: uo + βδι, + βδ?u, + βδBug self 1 maximizes U1 + B8u2 + B82u3 and so on. Let B = 0.5 and 8 = 0.9. Show that with no commitment technology available, the consumer decides to hit in every period. b. Show that all selves would be better off if hitting was banned (that is, if the consumer was prevented from hitting in every period). c. Suppose that the consumer is sophisticated, and self 0 has two choices: she can either ban the product starting immediately, or not ban it at all. Would she choose to ban it? Explain the intuition. d. Would a naive self 0 decide to have the product banned? Explain the intuition. Now suppose self 0 can decide not only whether to have the product banned, but also when the ban should start. Without any extra calculation, what do you think a sophisticated self 0 will choose? e.