198s2009.hw1.key

198s2009.hw1.key - 1 Department of Economics HKUST ECON 198...

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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: [email protected] Office hours: Wed 3:00p.m. – 5:00p.m. Homework #1 (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. (a) If we assume α , β and δ are positive, t h e n δ β α α z y x f x 1 − = δ β α β z y x f y 1 − = δ β α αβ z y x f xy 1 1 − − = δ β α α α z y x f xx 2 ) 1 ( − − = δ β α β β z y x f yy 2 ) 1 ( − − = ) ( 2 3 2 3 2 3 2 12 2 < + − = + − − − δ β α β α αβ z y x f f f f f f f yy x y x xx y Hence, this utility function is strictly quasi-concave. It follows that the indifferent curves are convex to the origin. 2 (b) y x f x + = 2 x y f y + = 2 1 = xy f 2 = xx f 2 = yy f 6 6 6 2 2 2 2 12 2 > + + = + − xy y x f f f f f f f yy x y x xx y Hence, this utility function is NOT quasi-concave. It follows that the Hence, this utility function is NOT quasi-concave....
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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.hw1.key - 1 Department of Economics HKUST ECON 198...

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