198s2009.hw4.key

198s2009.hw4.key - 1 Department of Economics, HKUST ECON...

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Unformatted text preview: 1 Department of Economics, HKUST ECON 198 Microeconomic Theory I Semester: Spring 2008/09 Tutor: Peter K. Tsui Office number: Room 2393 (ext.7597) Email: ecpeter@ust.hk Office hours: Wed 3:00p.m. – 5:00p.m. Homework #4 (Answer Key) Note: This answer key serves only as guidelines for grading. Giving the same answers as suggested below is no guarantee of full credits. 1. 2 2. No. I do not agree. It depends on the person’s degree of risk aversion and the payoffs of each option. A risk-neutral person will take the favorable gamble. Or more generally, a person will quit certainty for uncertainty as long as ) ( ) ( gamble not U gamble EU > . 3. (a) 60 2 . 2 . 20 1 . 60 5 . 100 ) ( = × + × + × + × = A R E 2 . ) 60 20 ( 1 . ) 60 60 ( 5 . ) 60 100 ( )] ( [ 2 2 2 2 × − + × − + × − = − A A R E R E 2 . ) 60 ( 2 × − + 1840 = 44 5 . 20 4 . 60 1 . 100 ) ( = × + × + × = B R E 5 . ) 44 20 ( 4 . ) 44 60 ( 1 . ) 44 100 ( )] ( [ 2 2 2 2 × − + × − + × − = − B B R E R E = 704 669 . 6 2 . 20 2 . 60 1 . 100 5 . = + + + = A EU A B EU EU < = + + = 334 . 6 20 5 . 60 4 . 100 1 . Hence, Jack should choose project A. (b) 105 . 17 ) ( ) ( = − = A A A R Var R E U A B B B U R Var R E U > = − = 467 . 17 ) ( ) ( Hence, John should choose project B. 4. (a) Jenny would be willing to pay p to insure her house against being destroyed by fire as long as: ) 00 , 600 ($ 2 . ) 000 , 000 , 2 ($ 8 . ) ( U U p W U + ≥ − => 000 , 600 $ 2 . 000 , 000 , 2 $ 8 . 000 , 000 , 2 $ + ≥ − p => 6 . 457 , 345 $ ≤ p (b) John would be willing to accept the insurance contract as long as: ) 000 , 400 , 1 $ ( 2 . ) ( 8 . ) ( − + + + ≤ p W V p W V W V => ) 000 , 400 , 1 $ ( 2 . ) ( 8 . − + + + ≤ p W p W W...
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This note was uploaded on 04/03/2010 for the course ECON ECON198 taught by Professor Leungsiufai during the Fall '09 term at HKUST.

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198s2009.hw4.key - 1 Department of Economics, HKUST ECON...

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