SectionWS7 - x 2 ) = 2 u ( x 1 ,x 2 ) . 2) Show that this...

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Econ 100A - Worksheet #7 Utility Functions Simple Exercises Exercise 1 A person’s preferences among diFerent commodity bundles is as follows. : A B C ; M N O ; N P ; O f E ; F D E ; G F ; D f Q ; I C ; Q R ; C f M. Preferences are assumed to be transitive. 1) ±ind all commodity bundles that lie on the same indiFerence curve. 2) ±ind the ranking of the diFerent indiFerence curves in terms of preference. 3) Give two diFerent utility functions that may be used to represent these preferences. Exercise 2 Consider again the indiFerence map of exercise 4 in WS6: Vodka Water Show that the utility function U ( V,W ) = V represents these preferences. Exercise 3 Consider the following utility function U ( x 1 ,x 2 ) = x 1 x 2 . 1) Show that it satis²es the following property: for any bundle ( x 1 ,x 2 ) , U (2 x 1 , 2
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Unformatted text preview: x 2 ) = 2 u ( x 1 ,x 2 ) . 2) Show that this is a cardinal property.[Hint: consider the utility function V ( x 1 ,x 2 ) = x 1 x 2 . ] Exercise 4 (Some Training in Partial derivatives) Compute the partial derivatives of the following functions: 1) f ( x,y ) = 4 xy + ln y , y > . 2) f ( x,y ) = xy-x 2 x +2 y . 3) f ( x,y ) = x y . Exercise 5 or each of the following functions, nd the equation of the indiFerence curves and draw them. Compute MRS 12 ( x 1 ,x 2 ) . Do these functions all satisfy the basic axioms of consumer theory? 1) u ( x 1 ,x 2 ) = 2 x 1 + x 2 . 2) u ( x 1 ,x 2 ) = x 2-x 1 . 3) u ( x 1 ,x 2 ) = x 1 + x 2 . 4) u ( x 1 ,x 2 ) = x 2 1 x 3 2 . 1...
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This note was uploaded on 07/09/2010 for the course ECON 100A taught by Professor Woroch during the Fall '08 term at University of California, Berkeley.

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