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

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

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Economics 171: Final Exam Solutions – Winter 2008 1. (6 pts) Lottery A pays either $5 or $50. Lottery B pays either $10 or $85. 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? B 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, 0.3; $50, 0.7) 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, 0.1; $70, 0.9). a. Which lottery has a higher expected value (in terms of the dollar payout)? E[ A ] = 0.3(10) + 0.7(50) = $38 E[ B ] = 0.4(10) + 0.4(50) + 0.2(70) = $38 The expected values are equal. b. Give her utility for $50. u ($50) = EU($10, 0.1; $70, 0.9) = 0.1 u ($10) + 0.9 u ($70) = 0.1(0) + 0.9(1) = 0.9 c. Which lottery will she choose if she maximizes expected utility? EU[ A ] = 0.3(0) + 0.7(0.9) = 0.63 EU[ B ] = 0.4(0) + 0.4(0.9) + 0.2(1) = 0.56 A has a higher expected utility.
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3. (12 pts) Lottery A is a uniform [$4, $24] distribution. Lottery B is ($4, 0.2; $14, 0.8). 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 . AB BA FF d s B A d s A B −< 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
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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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This note was uploaded on 04/23/2008 for the course ECON 171 taught by Professor Newhouse during the Winter '07 term at UCSD.

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

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