Winter 2008 - Newhouse's Class - Problem Set 3

Winter 2008 - Newhouse's Class - Problem Set 3 - Econ 171...

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Econ 171 Winter 2008 Problem Set 3 – Solutions 1. Maggie’s utility function is 1 2 2 ux = . Lisa’s utility function is ln vx = and Bart’s utility function is 3 wx = . a. Calculate each person’s coefficient of absolute risk aversion. Rank these three people from most to least risk averse. Note: For all of these we’re assuming x > 0. 3 2 13 1 22 1 2 2 12 1 1 21 2 1 1' '1 2 Maggie: ' , '' , 2'2 ' Lisa: ' , '' , ' '' 6 Bart: ' 3 , '' 6 , 2 '3 M L B LM B x u u x x u x v x x xv x w x x λ λλ −− == = = = = = =− = = = >> Lisa is the most risk averse; Maggie is in the middle and Bart is the least risk averse. b. Show whether Lisa is nonincreasingly, nondecreasingly or constantly risk averse. Lisa is nonincreasingly risk averse. 2 0 L x x = −≤ . c. Find Maggie’s certainty equivalent for lottery { } $1,0.4; $36,0.6 p = . What is her risk premium for lottery p ? () () () ± ± ± ± 11 1 2 0.4 2 1 0.6 2 36 8 Let be her certainty equivalent to . 28 $16 EU p x p ux EU p x x ⎡⎤⎡ =+ = ⎢⎥⎢ ⎣⎦⎣ = = =
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() ± () ( ) Let be her risk premium for . 0.4 1 0.6 36 16 $6 M M R p RE p x =− =+ ⎡⎤ ⎣⎦ = d. Explain how Lisa’s and Bart’s risk premium’s will compare to Maggie’s for this lottery. You don’t need to calculate the exact values. R L > $6 and R B < $6. Lisa’s risk premium will be greater than Maggie’s since Lisa is more risk averse than Maggie.
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Winter 2008 - Newhouse's Class - Problem Set 3 - Econ 171...

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