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Unformatted text preview: = I Utility Maximization u ( x 1 , x 2 ) = 17 ( 4 x α 1 x 1α 2 + √ π ) 32 Lagrangian Step 1: Set up the Lagrangian L ( x 1 , x 2 , λ ) = α ln ( x 1 ) + ( 1α ) ln ( x 2 ) + λ ( Ip 1 x 1p 2 x 2 ) Perfect Substitutes max x 1 , x 2 α x 1 + ( 1α ) 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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This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.
 Fall '09
 CUR
 Microeconomics, Utility

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