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Unformatted text preview: x âˆ— 1 = Max p 1 e ( p 1 ,p 2 ,u ) âˆ’ p 2 x 2 p 1 = Max p 1 kp a 1 âˆ’ p 2 x 2 p 1 = Max p 1 kp a âˆ’ 1 1 âˆ’ p 2 x 2 p âˆ’ 1 1 â‰¡ Max p 1 f ( p 1 ) E frqrplfv 401 2 So f Â± ( p 1 ) = 0 implies ( a âˆ’ 1) kp a âˆ’ 2 1 + p 2 x 2 p âˆ’ 2 1 = 0 or kp a 1 = p 2 x 2 1 âˆ’ a or p 1 = # p 2 x 2 k (1 âˆ’ a ) $ 1 /a Thus, at the optimal value of p 1 , x âˆ— 1 = kp a 1 âˆ’ p 2 x 2 p 1 = p 2 x 2 1 âˆ’ a âˆ’ p 2 x 2 Â± p 2 x 2 k (1 âˆ’ a ) Â² 1 /a or p 2 x 2 k (1 âˆ’ a ) ( x âˆ— 1 ) a = # ap 2 x 2 1 âˆ’ a $ a or ( x âˆ— 1 ) a Â± x 2 Â² 1 âˆ’ a = ka a (1 âˆ’ a ) 1 âˆ’ a Â± p 2 Â² a âˆ’ 1 = a constant. So we started with a CobbDouglas demand system and we have worked backwards to obtain the equation for a CobbDouglas indi f erence curve....
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.
 Fall '08
 Burbidge,John
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