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171 M2-2

# 171 M2-2 - Economics 171 Decisions Under Uncertainty...

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Economics 171: Decisions Under Uncertainty Solutions to Midterm 2: Winter 2010 1. (24 pts) Lottery A = (\$30, 1), lottery B = (\$0, 0.4; \$30, 0.4; \$50, 0.2) and lottery C = (\$0, 0.6; \$50, 0.4). a. Graph lotteries A , B and C 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. Nicola’s preferences are consistent with expected utility maximization. She prefers A to B and she prefers B to C . Illustrate these preferences by drawing appropriate indifference curves in your graph to (a). A good answer will illustrate these preferences with two or three parallel, linear indifference curves. c. If Nicola’s u (\$0) = 0 and u (\$50) = 1, what’s the most we can say about her u (\$30)? This problem can be worked in two different ways: 1. Using the geometry from the graph. ( ) ( ) ( ) ( ) ( ) \$30 0 0.2 0 1 \$30 0.2 0 \$30 1 \$30 \$30 0.5 IC BC m m u u u u u > > > > 1 1 0 p 1 = p ( x 1 ) p 3 = p ( x 3 ) C B A

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2. Purely algebraically. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0.4 0 0.4 \$30 0.2 1 0.6 0 0.4 1 0.4 \$30 0.2 \$30 0.5 EU B EU C u u u > + + > + > > 2. (26 pts) Gerald maximizes expected utility. He assigns a utility of 0 to \$0 and he
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171 M2-2 - Economics 171 Decisions Under Uncertainty...

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