2010_lecture_5_ho

2010_lecture_5_ho - Economics 101—Lecture 5 The Basic...

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Unformatted text preview: Economics 101—Lecture 5 The Basic Model of Consumer Choice III George J. Mailath January 27, 2011 In our last episode 1 Utility maximization subject to a budget constraint typically requires MRS ij = U i U j = p i p j . 2 illustrated this using Cobb-Douglas. 3 Perfect substitutes and perfect complements illustrate that this is not always true. 4 Demand functions: x ( p , I ) solve max U ( x ) subject to ∑ i p i x i ≤ I . 5 Indirect utility function V ( p , I ) = U ( x ( p , I )) . 6 And now some examples! Example: Cobb-Douglas U ( x 1 , x 2 ) = x α 1 x β 2 , for some α , β > 0. Example: perfect complements U ( x 1 , x 2 ) = min { α x 1 , β x 2 } , for some α , β > 0. Example: Perfect substitutes U ( x 1 , x 2 ) = α x 1 + β x 2 , for some α , β > 0. Interpretation of the multiplier Recall that V ( p , I ) = U ( x ( p , I )) = U ( x ( p , I )) + λ ( p , I )( I − ∑ i p i x i ( p , I )) so that ∂ V ( p , I ) ∂ I = ∑ i U i ( x ( p , I )) ∂ x i ( p , I ) ∂ I +...
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This note was uploaded on 03/02/2011 for the course ECON 101 taught by Professor Dannicatambay during the Spring '08 term at UPenn.

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2010_lecture_5_ho - Economics 101—Lecture 5 The Basic...

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