ak2 - Homework #2 due August 18 in class Econ 11 Summer...

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Homework #2 due August 18 in class University of California, Los Angeles Each question is worth 5.25 points, for a total of 25 points. 1. Jessica spends all her income on books for school and cigarettes. The utility she derives from these goods is described by the function U ( b;c ) = 3 ln b + ln c . (a) Use the Lagrangian method to derive Jessica±s monthly demand func- tions for books and cigarettes. If cigarettes cost $5 per pack and books cost $50 each, while Jessica±s mother gives her $200 a month for expenses, how many books and cigarettes will Jessica choose to purchase? Jessica±s Lagrangian is L = 3 ln b + ln c + ( M p b b p c c ) which gives us ²rst order conditions @L @b : 3 b b = 0 (1) @L @c : 1 c c = 0 (2) @L : M p b b p c c = 0 (3) We use (1) and (2) to ²nd the relationship 3 c b = p b p c c = p b 3 p c b and plug this into (3) M = p b b + p c p b 3 p c b ± = p b b + p b 3 b = 4 3 p b b to ²nd the demand functions b ( p b ;p c ;M ) = 3 M 4 p b c ( p b ;p c ;M ) = M 4 p c 1
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This means that if cigarettes cost $5 per pack and books cost $50 each, while Jessica has $200 in income, Jessica will choose to purchase b (50 ; 5 ; 200) = 3 (200) 4 (50) = 3 c (50 ; 5 ; 200) = 200 4 (5) = 10 cigarettes by half? How much should the government tax cigarettes? 5 packs of cigarettes c (50 ; 5 + t; 200) = 200 4 (5 + t ) = 5 200 = 20 (5 + t ) t = 5 The government needs to tax cigarettes by $5 per pack. of cigarettes by half? By how much should her mother reduce her income?
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This note was uploaded on 09/23/2008 for the course ECON 11 taught by Professor Cunningham during the Summer '08 term at UCLA.

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ak2 - Homework #2 due August 18 in class Econ 11 Summer...

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