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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