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Unformatted text preview: x 1 = Max p 1 e ( p 1 ,p 2 ,u ) p 2 x 2 p 1 = Max p 1 kp a 1 p 2 x 2 p 1 = Max p 1 kp a 1 1 p 2 x 2 p 1 1 Max p 1 f ( p 1 ) E frqrplfv 401 2 So f ( p 1 ) = 0 implies ( a 1) kp a 2 1 + p 2 x 2 p 2 1 = 0 or kp a 1 = p 2 x 2 1 a or p 1 = # p 2 x 2 k (1 a ) $ 1 /a Thus, at the optimal value of p 1 , x 1 = kp a 1 p 2 x 2 p 1 = p 2 x 2 1 a p 2 x 2 p 2 x 2 k (1 a ) 1 /a or p 2 x 2 k (1 a ) ( x 1 ) a = # ap 2 x 2 1 a $ a or ( x 1 ) a x 2 1 a = ka a (1 a ) 1 a p 2 a 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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 Fall '08
 Burbidge,John
 Utility

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