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Unformatted text preview: = I Utility Maximization u ( x 1 , x 2 ) = 17 ( 4 x Î± 1 x 1Î± 2 + âˆš Ï€ ) 32 Lagrangian Step 1: Set up the Lagrangian L ( x 1 , x 2 , Î» ) = Î± ln ( x 1 ) + ( 1Î± ) ln ( x 2 ) + Î» ( Ip 1 x 1p 2 x 2 ) Perfect Substitutes max x 1 , x 2 Î± x 1 + ( 1Î± ) x 2 subject to p 1 x 1 + p 2 x 2 = I Perfect Substitutes 2 Negative Values Perfect Complements max x 1 , x 2 ( min { x 1 , 2 x 2 } ) subject to p 1 x 1 + p 2 x 2 = I Max Preferences max x 1 , x 2 ( max { x 1 , 2 x 2 } ) subject to p 1 x 1 + p 2 x 2 = I More than Two Goods Kinked Budget Constraints...
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 Fall '09
 CUR
 Microeconomics, Utility, X1, p1 x1

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