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

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

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Economics 171: Decisions Under Uncertainty Midterm 2 – Solutions – Winter 2008 1. (25 pts) Joe’s utility function is 1 4 4 ux = . a. Calculate Joe’s coefficient of absolute risk aversion. 37 44 7 4 1 3 4 3 ', ' ' 4 3 '' 3 4 '4 u x x u x u x λ −− == =− = b. Find Joe’s certainty equivalent for lottery p = ($1, 0.6; $81, 0.4). () () () 1 11 4 1 4 1 4 4 0.6 4 1 0.4 4 81 47 . 2 1.8 $10.5 ux EU p x x x x = ⎡⎤⎡ =+ ⎢⎥⎢ ⎣⎦⎣ = = c. Find Joe’s risk premium for lottery p = ($1, 0.6; $81, 0.4). () ( ) ( ) () () () 0.6 1 0.4 81 33 33 10.5 $22.5 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; $81, 0.4). $22.5 B R
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2. (30 pts) Lottery a = ($8, 0.25; $80, 0.75). Lottery b = ($32, 0.25; $72, 0.75). a. Show or explain why a is mean-preserving spread of b . () () ( ) () ( ) ( ) 0.25 8 0.75 80 62 0.25 32 0.75 72 62 Ea Eb =+ = =+= The two lotteries have the same mean. To move from lottery a to lottery b the mass on $32 is pushed to the left and the mass on $72 is pushed to the right. b. Show that a is equal to b plus 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 Winter '07 term at UCSD.

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

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