mid_ak - Midterm Answer Key Econ 11 Summer Session C 2008...

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Midterm Answer Key August 20, 2008 University of California, Los Angeles Each question is worth 20 points, for a total of 100 points. 1. Hisa has preferences over his consumption of beer, x , and pizza, y , ex- pressed in the function U ( x;y ) = x 1 2 y 1 2 . (a) Find Hisa±s uncompensated demand for beer and pizza. ANSWER: x ( p x ;p y ;M ) = M 2 p x y ( p x ;p y ;M ) = M 2 p y (b) State Hisa±s indirect utility function. ANSWER: V ( p x ;p y ;M ) = M 2 1 p x ± 1 2 1 p y ± 1 2 (c) Use duality and Shephard±s lemma to ²nd Hisa±s compensated de- mand functions. ANSWER: E ( p x ;p y ;U ) = 2 U ( p x ) 1 2 ( p y ) 1 2 @E ( p x ;p y ;U ) @p x = x c ( p x ;p y ;U ) = U ( p x ) 1 2 ( p y ) 1 2 @E ( p x ;p y ;U ) @p y = y c ( p x ;p y ;U ) = U ( p x ) 1 2 ( p y ) 1 2 (d) Con²rm this answer by ²nding Hisa±s compensated demand for beer and pizza using expenditure minimization. 1

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ANSWER: L ( x;y ; ) = p x x + p y y + U x 1 2 y 1 2 ± @L ( x;y ; ) @x : p x ² 1 2 x 1 2 y 1 2 ³ = 0 @L ( x;y ; ) @y : p y ² 1 2 x 1 2 y 1 2 ³ = 0 @L ( x;y ; ) : U x 1 2 y 1 2 = 0 p x p y = y ± x ± U = x 1 2 ² p x p y x ³ 1 2 x c ( p x ;p y ;U ) = U ( p x ) 1 2 ( p y ) 1 2 y c ( p x ;p y ;U ) = U ( p x ) 1 2 ( p y ) 1 2 2. Tracy spends her entire movie food budget on popcorn, x , and soda, y . Without knowing anything about her preferences, answer the following: (a) True or false: an increase in the price of x will always lead her to purchase less x . ANSWER: False: the overall change in demand for good
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This note was uploaded on 09/23/2008 for the course ECONOMICS 100 taught by Professor Brown during the Spring '08 term at Caltech.

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mid_ak - Midterm Answer Key Econ 11 Summer Session C 2008...

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