3070_PSet-4_Solutions[1]

3070_PSet-4_Solutions[1] - Economics 3070-001 Spring 2008...

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Economics 3070-001 Spring 2008 Problem Set 4 Solutions 1. Aunt Joyce purchases two goods, perfume and lipstick.  Her preferences are  represented by the utility function ( 29 PL L P U = , , where  P  denotes the ounces of perfume used and  L  denotes the quantity of  lipsticks used.  Let  P P  denote the price of perfume,  P L  denote the price of lipstick,  and  I  denote Aunt Joyce’s income. a. Derive her demand for perfume.  Your answer should be an equation that  gives  P  as a function of  P P   P L   , and  I . We will simply follow the “cookbook” procedure.  Setting  MRS P , L  equal to the  price ratio  P / P L  gives us P P P L P P P L P P MU MU P P MRS L P L P L P L P L P L P = = = = , Plugging the tangency condition into the budget constraint gives us P P L P L P L P P I P I P P I P P P P P P I L P P P 2 2 = = = + = + Therefore, Aunt Joyce’s demand for perfume is given by
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Economics 3070-001 Spring 2008 P P I P 2 = .
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Economics 3070-001 Spring 2008 b. Derive her demand for lipstick.  Your answer should be an equation that  gives  L  as a function of  P P   P L   , and  I . To get her demand for lipstick, we need only plug the demand for perfume into  the tangency condition: L P L P L P P I L P I P P L P P P L 2 2 = = = Therefore, Aunt Joyce’s demand for lipstick is given by L P I L 2 = . c. Is lipstick a normal good?  Draw her demand curve for lipstick when  I  = 200 Label the demand curve  D 1 .  Draw her demand curve for lipstick when  I  =  300  and label this demand curve  D 2 . A normal good is a good that a consumer purchases more of as income rises.  Since Aunt Joyce’s demand for lipstick increases as  I  increases, lipstick is a  normal good. The two demand curves are depicted in the figure below:
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Economics 3070-001 Spring 2008 P L L D 1 D 2 10 10 12.25 12.25
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Economics 3070-001 Spring 2008 d. What can be said about her cross-price elasticity of demand of perfume with  respect to the price of lipstick? In part a, we found that Aunt Joyce’s demand for perfume is given by P P I P 2 = . Since her demand for perfume does not depend on  P L , Aunt Joyce’s cross-price  elasticity of demand of perfume with respect to the price of lipstick is zero.  That  is, a 1% change in the price of lipstick generates a 0% change in the demand for  perfume. 2.
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This note was uploaded on 02/06/2009 for the course ECON 3070 taught by Professor Loh,joyce during the Fall '07 term at Colorado.

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3070_PSet-4_Solutions[1] - Economics 3070-001 Spring 2008...

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