Fall 2007 - Newhouse's Class - Final Exam (Version B)

# Fall 2007 - Newhouse's Class - Final Exam (Version B) -...

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Economics 171: Decisions Under Uncertainty Final – Solutions (Fall 2007) – Version B 1. (6 pts) Imagine that you’re running a race next week. The race will be attended by either recreational runners or by Olympic hopefuls. If you spend the next week playing poker you’ll finish in the middle of the pack if the race is attended by recreational runners and you’ll finish towards the back if the race if attended by Olympic hopefuls. If you train for the next week you’ll win regardless of the type of other people who attend. a. What actions are available to you? {Play poker, Train} b. What states of nature could occur? {Recreational runners, Olympic hopefuls} c. What are the possible outcomes? {Finish towards the back, Finish in the middle, Win} 2. (12 pts) Stu enjoys meeting people. The below table gives the number of people he will meet depending on the place he visits and the weather. It also gives the probability of each type of weather. Weather Sunny ( p = 0.8) Rainy ( p = 0.2) Disco 20 people 30 people Choice of hangout Beach 35 people 5 people a. If he wants to maximize the expected number of people he meets where should he hang out? E[Disco] = 0.8(20) + 0.2(30) = 22 E[Beach] = 0.8(35) + 0.2(5) = 29 He should hang out at the beach. Stu assigns a utility of 0 to meeting 5 people and he assigns a utility of 0.7 to meeting 30 people. He’s indifferent between meeting 20 people with certainty and a lottery that has probability 0.7 of meeting 30 people and probability of 0.3 of meeting 5 people. He’s also indifferent between meeting 30 people

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with certainty and a lottery that has probability 0.9 of meeting 35 people and probability of 0.1 of meeting 5 people. b. Give Stu’s utility for meeting 20 people and for meeting 35 people. U(20) = 0.7(0.7) + 0.3(0) = 0.49 0.8 = 0.9U(35) + 0.1(0) U(35) = 0.7/0.9 = 0.78 c. If he wants to maximize expected utility where should he hang out? EU[Disco] = 0.8(0.49) + 0.2(0.7) = 0.53 EU[Beach] = 0.8(0.78) + 0.2(0) = 0.62 He should hang out at the beach. 3. (9 pts) Below is a CDF for A , a uniform [4, 24] distribution. Graph the CDF of a distribution B such that A second order stochastically dominates B but A doesn’t first order stochastically dominate B . Briefly explain.
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