Econ171-Spring2010-Midterm2-sols

# Econ171-Spring2010-Midterm2-sols - Economics 171: Decisions...

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Economics 171: Decisions Under Uncertainty Solutions to Midterm 2: Spring 2010 1. (28 pts) Jolene maximizes expected utility. She assigns a utility of 0 to \$0 and she assigns a utility of 1 to \$10. a. Jolene is indifferent between receiving \$6 with certainty and the lottery (\$0, 0.3; \$10, 0.7). What is her utility for \$6? u(\$6) = EU(\$0, 0.3; \$10, 0.7) = 0.3u(\$0) + 0.7u(\$10) = 0.3(0) + 0.7(1) = 0.7 b. What are her preferences between Lottery A = (\$0, 0.2; \$10, 0.8) and Lottery B = (\$6, 0.8; \$10, 0.2)? Show your work. EU(A) = 0.2(0) + 0.8(1) = 0.8 EU(B) = 0.8(0.7) + 0.2(1) = 0.76 Since EU(A) > EU(B) she prefers A over B. c. Assuming Jolene likes wealth, in what range must her utility for \$7 be? It must be between the utilities for \$6 and \$10. 0.7 < u(\$7) < 1 d. Is it possible that she prefers Lottery C = (\$0, 0.25; \$7, 0.75) over lottery B = (\$6, 0.8; \$10, 0.2)? Show your work and briefly explain. If she prefers C over B the following inequality must hold: EU(C) > EU(B) 0.25(0) + 0.75u(\$7) > 0.8(0.7) + 0.2(1) 0.75u(\$7) > 0.76 u(\$7) > 0.76/0.75 No. u(\$7) would need to be outside the range found in (c).

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2. (28 pts) Rick’s utility function is  1 2 24 ux x x  .
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## This note was uploaded on 10/21/2010 for the course ECON 809880 taught by Professor Herbnewhouse during the Spring '09 term at UCSD.

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Econ171-Spring2010-Midterm2-sols - Economics 171: Decisions...

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