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171 M2-6 - Economics 171 Decisions Under Uncertainty...

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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 u x = . a. Calculate Joe’s coefficient of absolute risk aversion. 2 5 3 3 5 3 1 2 3 2 ' , '' 3 2 '' 2 3 ' 3 u x u x x u x u x λ = = − = − = − = b. Find Joe’s certainty equivalent for lottery p = ($1, 0.6; $64, 0.4). ( ) ( ) ( ) ( ) 1 1 1 3 3 3 1 3 1 3 3 0.6 3 1 0.4 3 64 3 6.6 2.2 $10.6 u x 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 E p R p E p CE p = + = = = = 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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