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Unformatted text preview: Midterm 2 Econ 330 – Economic Behavior and Psychology Professor Sydnor Spring 2010 Problem 1: [3 pts] In this class we have talked about time inconsistency and things like smoking. Usually it has been in the context of thinking about how often to smoke, or how difficult it is to stop smoking. We have not talked that much about the decision to start smoking in the first place. It could be argued that many people who start smoking do so with the intention of smoking socially then and in the future. That is, they feel that the benefits of enjoying a cigarette among friends are worth the health costs, perhaps because it is “cool”. But they do not feel that smoking consistently, including in one’s own car and one’s own home would be worth the costs. Yet, of course, many smokers do end up smoking in great quantities that are not confined to social situations. Now think about what it’s like to have a first cigarette (though I’m sure none of you have tried them…). Most people cough and do not actually enjoy cigarettes when they first try them. In light of that insight, discuss how projection bias (intrapersonal empathy gaps) may help explain why people start smoking in the first place. Problem 2: [17pts] Raul likes pizza and was happy to find out that his office had partnered with some local pizza shops to do taste tests over lunch. Three different pizza shops are going to bring in lunch over the next three weeks (call these Weeks 1, 2, and 3). Because the pizza shops cannot accommodate the entire office for lunch, each employee is allowed to go to precisely one of the tasting lunches. Now each person has slightly different preferences and some people haven’t tried the pizza before, so there will be a lot of randomness in when people go. Raul, however, knows his preferences. His favorite pizza will be available on Week 3, his second favorite on Week 2, and his least favorite on Week 1. To be more specific, the following table gives Raul’s instantaneous utility from attending the lunch in each week (the little u for that week): Week (t) ut 1
1 3 2
1 6 3
2 0 In any Period where Raul does not go for pizza, we just normalize his instantaneous utility to be 0. Raul has time preferences that are quasi‐hyperbolic, with β = ¾ and δ = 1. So Raul’s overall utility functions by period are: , , U3=u3 Each week when the lunch day comes along, Raul gets to decide that day whether or not to go for the pizza. He realizes, of course, that going in Period 1 or 2 will mean that he does not go in future periods. [4 pts] a. If Raul is naïve, explain what period he will go for pizza. Briefly explain his thought process. [4 pts] b. If Raul is sophisticated, explain what period he will go for pizza. Briefly explain his thought process. [1 pts] c. Would you say in this case that Raul is better off being naïve or sophisticated? It may be useful in answering this to imagine a Period 0 Raul and how such a Raul would feel about the outcome. Explain briefly. Now suppose that Raul’s co‐worker, Betty, who is organizing the lunches offers him a commitment device. She tells Raul that she knows he loves the Period 3 pizza and that she imagines he might be having difficulty waiting until Period 3. She offers to put his name on a sign‐in sheet for Period 3 that will commit him to getting pizza that period – basically she will ban him from getting the pizza in another period other than Period 3. However, Raul will have to do her a favor that he finds unpleasant (let your imagination run wild…). Raul has to make the choice of whether or not to commit in Period 1. If he commits, then he can only eat the pizza in Period 3, but will experience a decrease in his instantaneous utility (little u) during Period 1 of ‐1. If he does not commit, then he is left to his own devices and acts as in (a) or (b). [4 pts] d. If Raul is naïve, will he take the commitment offer? Explain briefly. [4 pts] e. If Raul is sophisticated, will he take the commitment offer? Explain briefly. Problem 3: [20 pts] A consumer lives for three periods, t = 0, 1, 2 (don’t ask me why I’m counting from 0 now, I’m just annoying like that…). In each of the periods t = 0 and t = 1, she decides whether to hit or not hit. Hitting in period 0 or 1 gives the consumer some instantaneous pleasure in that period (to be explained below), but leads her to experience instantaneous displeasure of 7 utils in the next period. That is, if she hits in period 0, this decreases her instantaneous utility in Period 1 by 7, and if she hits in period 1, this decreases her instantaneous utility in period 2 by 7. Note: It may make it easier if you think of the person as starting out with instantaneous utility each period of 0, and to this you may add the pleasure of hitting in that period (if they hit) and subtract the disutility of 7 that comes if they hit in the previous period. The consumer is a hyperbolic discounter: self 0 maximizes , while self 1 maximizes . Let β = 0.5 and δ = 1. [5 pts] a. Suppose that the instantaneous pleasure from hitting in either period 0 or 1 is 3. (Note: they could potentially hit in both of those period, neither period, or just one of them, but in the period they hit, they will experience a positive instantaneous utility of 3) i.
What does a naïve consumer do? ii.
What does a sophisticated consumer do? iii.
Explain your answers to (i. and ii.) very briefly and in intuitive terms. [4 pts] b. Now suppose that the instantaneous pleasure from hitting in period 0 or 1 is 4. What does each type of consumer do? Explain very briefly where your answers come from, either using math or simple intuitive arguments. [4 pts] c. Show that for both naifs and sophisticates all selves (i.e., each of the periods) are worse off (in terms of overall utility) when the pleasure from hitting is 4 rather than 3. d. Explain intuitively, but briefly, how it is possible that an increase in the pleasure from hitting [2 pts] can make the person worse off (even though it is not accompanied by an increase in the future cost of hitting). [5 pts] e. Now suppose that the instantaneous pleasure from hitting in period 0 is 4, but the instantaneous pleasure from hitting in period 1 depends on whether the consumer resisted the drug in period 0. Specifically, if she hit in period 0, the instantaneous utility from hitting in period 1 is 4, and if she did not hit in period 0, the instantaneous utility from hitting in period 1 is 3. What does each type of consumer do? Explain the intuition. ...
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- Spring '11