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Winter 2008 - Newhouse's Class - Final Exam (Version A)

# Winter 2008 - Newhouse's Class - Final Exam (Version A) -...

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Economics 171: Final Exam Solutions – Winter 2008 1. (6 pts) Lottery A pays either \$25 or \$50. Lottery B pays either \$10 or \$75. a. Which lottery is chosen according to the Maximax criterion? B is chosen because its highest payout is higher than A ’s highest payout. b. Which lottery is chosen according to the Maximin criterion? A is chosen because its lowest payout is higher than B ’s lowest payout. c. What additional information is needed to determine the expected payout of each lottery? The probabilities of the outcomes. 2. (12 pts) Shelly has a choice between lottery A = (\$10, 0.2; \$50, 0.8) and lottery B = (\$10, 0.4; \$50, 0.4; \$70, 0.2). Assume her utility for \$10 is 0 and that her utility for \$70 is 1. Shelly is indifferent between receiving \$50 with certainty and a lottery equal to (\$10, 0.2; \$70, 0.8). a. Which lottery has a higher expected value (in terms of the dollar payout)? E[ A ] = 0.2(10) + 0.8(50) = \$42 E[ B ] = 0.4(10) + 0.4(50) + 0.2(70) = \$38 A has a higher expected value. b. Give her utility for \$50. u (\$50) = EU(\$10, 0.2; \$70, 0.8) = 0.2 u (\$10) + 0.8 u (\$70) = 0.2(0) + 0.8(1) = 0.8 c. Which lottery will she choose if she maximizes expected utility? EU[ A ] = 0.2(0) + 0.8(0.8) = 0.64 EU[ B ] = 0.4(0) + 0.4(0.8) + 0.2(1) = 0.52 A has a higher expected utility.

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3. (12 pts) Lottery A is a uniform [\$4, \$24] distribution. Lottery B is (\$8, 0.5; \$24, 0.5). What does first order stochastic dominance say about lotteries A and B ? What does second order stochastic dominance say about lotteries A and B ? FOSD doesn’t say anything about them. One is not always equal or below the other. SOSD doesn’t say anything either. ( ) ( ) 8 4 14 4 0 cannot SOSD . 0 cannot SOSD . B A A B F F ds A B F F ds B A < < 1 0.8 0.6 0.4 0.2 A 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 B
4. (15 pts) Apu is a risk averse, von Neumann-Morgenstern expected utility maximizer. His utility function satisfies our usual assumptions.

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• Winter '07
• Newhouse