171 M2-3

# 171 M2-3 - Economics 171: Decisions Under Uncertainty...

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Economics 171: Decisions Under Uncertainty Midterm 2 Solutions: Fall 2009 1. (20 pts) Sierra is a von Neumann-Morgenstern expected utility maximizer. She prefers lottery A = (\$10, 1) to lottery B = ( x 1 , 0.4; \$10, 0.4; \$20, 0.2) where x 1 is a fixed dollar amount that’s less than \$10. a. Graph lotteries A and B in our standard triangle diagram with p 1 on the horizontal axis and p 3 on the vertical axis. (It may be helpful to make your graph to scale.) b. Lottery C = ( x 1 , 0.6; \$10, 0.2; \$20, 0.2) and lottery D = ( x 1 , 0.2; \$10, 0.8). What’s the most we can say about her preferences between C and D ? Explain. (You can use your graph from part (a).) D must be preferred to C given the parallel, linear indifference curves. c. If she is risk loving, what’s the most we can say about the dollar amount x 1 ? 1 1 10 0.2 0 1 20 10 0.4 0 2 5 iv ic AB ic mmm x m x   1 1 0 p 1 = p ( x 1 ) p 3 = p ( x 3 ) A B C D

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2. (20 pts) Wayne is a von Neumann-Morgenstern expected utility maximizer. He assigns a utility of 0 to \$0 and a utility of 1 to \$10.
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## 171 M2-3 - Economics 171: Decisions Under Uncertainty...

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