lecture3full - = I Utility Maximization u x 1 x 2 = 17 4 x...

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Recap Discussed common assumptions made on preferences complete, transitive, monotonic, convex Used utility functions to map preferences into numbers Showed that monotonic transformations of utility functions did not affect the slope of the indifference curve Measured the curvature of the indifference curve using the elasticity of substitution Constant Elasticity of Substitution utility function nested both Cobb Douglas and perfect substitutes case
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Elasticity of Substitution u ( x 1 , x 2 ) = ( α x - ρ 1 + ( 1 - α ) x - ρ 2 ) - 1
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Homothetic Tastes Tastes are homothetic when MRS only depends upon the ratio x 2 / x 1
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Budget Constraints p 1 x 1
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Unformatted text preview: = I Utility Maximization u ( x 1 , x 2 ) = 17 ( 4 x α 1 x 1-α 2 + √ π ) 32 Lagrangian Step 1: Set up the Lagrangian L ( x 1 , x 2 , λ ) = α ln ( x 1 ) + ( 1-α ) ln ( x 2 ) + λ ( I-p 1 x 1-p 2 x 2 ) Perfect Substitutes max x 1 , x 2 α x 1 + ( 1-α ) 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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