Winter 2008 - Newhouse's Class - Exam 2 (Version A)

Winter 2008 - Newhouse's Class - Exam 2 (Version A) -...

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Economics 171: Decisions Under Uncertainty Midterm 2 – Solutions – Winter 2008 1. (25 pts) Joe’s utility function is 1 3 3 ux = . a. Calculate Joe’s coefficient of absolute risk aversion. 25 33 5 3 1 2 3 2 ', ' ' 3 2 '' 2 3 '3 u x x u x u x λ −− == =− = b. Find Joe’s certainty equivalent for lottery p = (\$1, 0.6; \$64, 0.4). ( ) ( ) () 1 11 3 1 3 1 3 30 . 6 3 1 0 . 4 3 6 4 36 . 6 2.2 \$10.6 ux EU p x x x x = ⎡⎤⎡ =+ ⎢⎥⎢ ⎣⎦⎣ = = c. Find Joe’s risk premium for lottery p = (\$1, 0.6; \$64, 0.4). () ( ) ( ) () () () 0.6 1 0.4 64 26.2 26.2 10.6 \$15.6 Ep Rp Ep C = = d. Bill is at least as risk averse as Joe. What’s the most that can be said about Bill’s risk premium for lottery p = (\$1, 0.6; \$64, 0.4). \$15.6 B R

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2. (30 pts) Lottery a = (\$40, 0.25; \$80, 0.75). Lottery b = (\$16, 0.25; \$88, 0.75). a. Show or explain why b is mean-preserving spread of a . () ( ) ( ) 0.25 40 0.75 80 70 0.25 16 0.75 88 70 Ea Eb =+= The two lotteries have the same mean. To move from lottery a to lottery b the mass on \$40 is pushed to the left and the mass on \$80 is pushed to the right.
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Winter 2008 - Newhouse's Class - Exam 2 (Version A) -...

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