Winter 2008 - Newhouse's Class - Problem Set 2

# Winter 2008 - Newhouse's Class - Problem Set 2 - Econ 171...

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Econ 171 Winter 2008 Problem Set 2 - Solutions 1. Lottery A pays –\$10 with probability 0.2 and pays \$10 with probability 0.8. Lottery B pays 0 with probability 0.4 and pays \$10 with probability 0.6. Lottery C pays \$10 with probability 0.8 and \$20 with probability 0.2. Lottery D pays –\$10 with probability 0.1, \$10 with probability 0.8 and \$20 with probability 0.1. Lottery E pays 0 with probability 0.2, \$10 with probability 0.7 and \$20 with probability 0.1. a. Consider a mixture of Lotteries A and C, x A + (1 – x )C. For what value of x is the mixture equivalent to Lottery D? () ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) \$10 in the mixture 0.2 1 0 0.1 \$10 in 0.5 We should check that we get the correct values for the other states. \$10 in the mixture 0.5 0.8 1 0.5 0.8 0.8 \$10 in \$20 in the mixture 0.5 0 1 0.5 0.2 Px x P D x PP D P −= + = = = =+ = = 0.1 \$10 in PD == b. Consider a mixture of Lotteries B and C, y B + (1 – y )C. For what value of y is the mixture equivalent to Lottery E? ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) \$0 in the mixture 0.4 1 0 0.2 \$0 in 0.5 We should check that we get the correct values for the other states. \$10 in the mixture 0.5 0.6 1 0.5 0.8 0.7 \$10 in \$20 in the mixture 0.5 0 1 0.5 0.2 0.1 Py y P E y E P = = = = = = \$10 in PE = c. Suppose an individual has preferences CEDAB ;;;; . Which of our four axioms is violated by these preferences? Explain why. These preferences violate the independence axiom. The individual prefers A to B but also prefers 0.5 B + 0.5 C to 0.5 A + 0.5 C . Notice that 0.5 A + 0.5 C is equivalent to D and that 0.5 B + 0.5 C is equivalent to E .

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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 - Problem Set 2 - Econ 171...

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