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Econ171-Winter2009-Final-sols

# Econ171-Winter2009-Final-sols - Economics 171 Decisions...

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Economics 171: Decisions Under Uncertainty Solutions to Final Exam: Winter 2009 1. (10 pts) Lottery A = (\$50, 0.2; \$80, 0.8). Lottery B = (\$60, 0.2; \$80, 0.8) a. Which lottery is chosen by the maximin criterion? B b. Which lottery is chosen by the maximax criterion? Indifferent. c. What does first order stochastic dominance say about the two lotteries? Show your work/explain. B FOSD A. Going from A to B, the 0.2 mass on \$50 shifts right to \$60. d. What does second order stochastic dominance say about the two lotteries? Show your work/explain. B must SOSD A because it FOSD A.

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2. (15 pts) Fran is a vNM expected utility maximizer. She needs to choose between lottery A and lottery B . Lottery A is (\$0, 0. 2; \$100, 0.8) and lottery B is (\$20, 0.4; \$100, 0.6). Assume her utility for \$0 is 0 and that her utility for \$100 is 1. a. She’s indifferent between a lottery that’s (\$0, 0.7; \$100, 0.3) and a certain payment of \$20. What’s her utility for \$20? EU(\$0, 0.7; \$100, 0.3) = u(\$20) 0.7(0) + 0.3(1) = u(\$20) u(\$20) = 0.3 b. Will she choose lottery A or B ? Show your work. EU(A) = 0.2(0) + 0.8(1) = 0.8 EU(B) = 0.4(0.3) + 0.6(1) = 0.72 She prefers A to B. c. She is indifferent between lottery B and lottery C which is (\$0, 0.2; \$20, 0.3; \$150, 0.5). What’s her utility for \$150? EU(C) = 0.2(0) + 0.3(0.3) + 0.5u(\$150) = 0.72 0.5u(\$150) = 0.63 u(\$150) = 1.26
3. (15 pts) Hayley’s utility function is 2 5 5 u x = .

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Econ171-Winter2009-Final-sols - Economics 171 Decisions...

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