Fall 2007 - Newhouse's Class - Exam 2

# Fall 2007 - Newhouse's Class - Exam 2 - Economics 171:...

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Economics 171: Decisions Under Uncertainty Midterm 2 (November 15, 2007) – Solutions 1. (25 pts) Beth’s utility function is 1 ln 2 ux = . Matthew’s utility function is ln vx x =+ . a. Calculate Beth’s coefficient of absolute risk aversion. 2 2 11 ', ' ' 22 1 '' 1 2 1 ' 2 uu xx u x x λ == =− = b. Show whether Beth is nonincreasingly, nondecreasingly or constantly risk averse. 2 1 0 < Beth is nonincreasingly risk averse. c. Find Beth’s certainty equivalent for lottery p = {\$e, 0.5; \$e 3 , 0.5}. () 33 2 1 3 ln ; ln 2 2 \$,0 .5 ;\$ ,0 11 13 1 22 22 1 ln 1 2 ln 2 ue e e e u e u e x x xe = = =+= = = d. Calculate Matthew’s coefficient of absolute risk aversion.

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() 2 22 11 '1 ;' ' '' 1 '1 1 vv xx v x vx x η =+ =− −− = + + + e. Without calculating it explicitly, what’s the most that can be said about Matthew’s certainty equivalent for lottery p = {\$e, 0.5; \$e 3 , 0.5}? Briefly explain. First note that Beth is at least as risk averse as Matthew. 1 1 1 This must hold since 0. x λη => = + +> > Therefore Matthew’s certainty equivalent must be at least as big as Beth’s. 2 Matt CE e 2. (24 pts) Bill is a risk averse, von Meumann-Morgenstern utility maximizer. Determine his preferences between each of the following pairs of lotteries. Explain why. a. a = {\$10, 0.2; \$20, 0.3; \$40, 0.5}, b = {\$10, 0.4; \$40, 0.6} [ ] ( ) ( ) [] () () 0.2 10 0.3 20 0.5 40 \$28 0.4 10 0.6 40 \$28 is a mean preserving spread of . Ea Eb ba ab =++= =+= ; b. c = {\$50, 0.4; \$90, 0.6}, d = {\$40, 0.2; \$60, 0.2; \$70, 0.2; \$100, 0.4} [ ] ( ) [] () () () ( ) 0.4 50 0.6 90 \$74 0.2 40 0.2 60 0.2 70 0.4 100 \$74 is equivalent to zero conditional-mean noise.
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## This note was uploaded on 04/23/2008 for the course ECON 171 taught by Professor Newhouse during the Fall '07 term at UCSD.

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Fall 2007 - Newhouse's Class - Exam 2 - Economics 171:...

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