A consumer lives for four periods, t = 0, 1, 2, 3. In each of the...
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A consumer lives for four periods, t = 0, 1, 2, 3. In each of the periods, she can decide whether to "smoke" or "not smoke". Smoking in period t gives the consumer pleasure equivalent to 10 utils that period, followed by displeasure equivalent to -18 utils in the following period, t+1. In the last period, the consumer still receives pleasure, but has no future unpleasantness that follows. The consumer is a hyperbolic discounter; that is, self 0 maximizes the following discounted utility function: uo+B[du₁ +8²u2+8³u3]; self 2 maximizes the following utility function: u₁ + [6u2 +62u3], and so on. Assume that and that 8 = 1. (a) Show that with no commitment technology available, the consumer decides to smoke in every period. (b) Calculate the utility of the individual for every period (period 0, period 1, period 2, period 3) assuming (i) that the individual smoked in every period, and (ii) that the individual did not smoke in any period. Show that all selves (including the period 0 self!) are made better off if smoking was banned. (c) What does a naive person believe that her future selves will do: smoke or not? (d) If the consumer is naive, 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. (e) Suppose that the consumer is sophisticated, and self 0 has the same two choices. Would she choose to ban it? (f) Now suppose that the pleasure from smoking a cigarette drops to 8 utils per period, but the disutility remains unchanged. Show that the consumer will not smoke. (g) Explain the intuition as to how a person can be made better off when they are offered worse cigarettes. (h) Now suppose that the instantaneous pleasure from smoking in period 0 is 10, but the instantaneous pleasure from smoking in period 1 depends on whether the consumer resisted smoking in period 0. Specifically, if she smokes in period 0, the instantaneous utility from smoking in period 1 is 10, and if she did not smoke in period 0, the instantaneous utility from smoking in period 1 is 8. What does each type of consumer (naive vs. sophisticate) do? Explain the intuition. A consumer lives for four periods, t = 0, 1, 2, 3. In each of the periods, she can decide whether to "smoke" or "not smoke". Smoking in period t gives the consumer pleasure equivalent to 10 utils that period, followed by displeasure equivalent to -18 utils in the following period, t+1. In the last period, the consumer still receives pleasure, but has no future unpleasantness that follows. The consumer is a hyperbolic discounter; that is, self 0 maximizes the following discounted utility function: uo+B[du₁ +8²u2+8³u3]; self 2 maximizes the following utility function: u₁ + [6u2 +62u3], and so on. Assume that and that 8 = 1. (a) Show that with no commitment technology available, the consumer decides to smoke in every period. (b) Calculate the utility of the individual for every period (period 0, period 1, period 2, period 3) assuming (i) that the individual smoked in every period, and (ii) that the individual did not smoke in any period. Show that all selves (including the period 0 self!) are made better off if smoking was banned. (c) What does a naive person believe that her future selves will do: smoke or not? (d) If the consumer is naive, 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. (e) Suppose that the consumer is sophisticated, and self 0 has the same two choices. Would she choose to ban it? (f) Now suppose that the pleasure from smoking a cigarette drops to 8 utils per period, but the disutility remains unchanged. Show that the consumer will not smoke. (g) Explain the intuition as to how a person can be made better off when they are offered worse cigarettes. (h) Now suppose that the instantaneous pleasure from smoking in period 0 is 10, but the instantaneous pleasure from smoking in period 1 depends on whether the consumer resisted smoking in period 0. Specifically, if she smokes in period 0, the instantaneous utility from smoking in period 1 is 10, and if she did not smoke in period 0, the instantaneous utility from smoking in period 1 is 8. What does each type of consumer (naive vs. sophisticate) do? Explain the intuition.
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a Without a commitment technology the consumer decides to smoke in every period because the immediate pleasure of 10 utils outweighs the future disple... View the full answer
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