_Lecture_06

_Lecture_06 - Lecture 5 1-minute review Quasi-linear Demand Functions X p x,p y,M,Y p x,p y,M • Corner solutions Income/Substitution Effects •

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Unformatted text preview: Lecture 5 1-minute review Quasi-linear Demand Functions X ( p x ,p y ,M ) ,Y ( p x ,p y ,M ) • Corner solutions Income/Substitution Effects • Slutsky • Hicks Compensated Demand Functions (Hicks) 1 Sometimes pictures/graphs are useful. • own price demand function : graph X as a function of p x – keeping p y ,M constant • other price demand function : graph X as a function of p y – keeping p x ,M constant • Engel curve : graph X as a function of M – keeping p x ,p y constant • income expansion path trace optimal choice as M ↑ – keeping p x ,p y constant 2 Example: Cobb-Douglas utility function U ( x,y ) = x a y b X ( p x ,p y ,M ) = a a + b M p x Y ( p x ,p y ,M ) = b a + b M p y 3 4 5 6 7 Do these calculations for CES utility U ( x,y ) = 5 x 1 / 5 + 5 y 1 / 5 Demand functions X ( p x ,p y ,M ) ,Y ( p x ,p y ,M ) Lagrangian L ( x,y,λ ) = 5 x 1 / 5 + 5 y 1 / 5- λ ( p x x + p y y- M ) = 0 Equations x- 4 / 5- λp x = 0 y- 4 / 5- λp y = 0 p x x + p y y- M = 0 8 x- 4 / 5 p x = y- 4 / 5 p y y- 4 / 5 = p y p x !...
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This note was uploaded on 04/01/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Fall '07 term at UCLA.

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_Lecture_06 - Lecture 5 1-minute review Quasi-linear Demand Functions X p x,p y,M,Y p x,p y,M • Corner solutions Income/Substitution Effects •

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