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Unformatted text preview: Economics 101A (Lecture 9) Stefano DellaVigna September 24, 2009 Outline 1. Slutsky Equation II 2. Complements and substitutes 3. Do utility functions exist? 1 Slutsky Equation II • Slutsky Equation ∂x ∗ i ( p , M ) ∂p i = ∂h i ( p , v ( p , M )) ∂p i − x ∗ 1 ( p 1 , p 2 , M ) ∂x ∗ i ( p , M ) ∂M • Important result! Allows decomposition into substi tution and income e f ect • Example 1 (ctd.): CobbDouglas. Apply Slutsky equation • x ∗ i = αM/p i • h ∗ i = • Derivative of Hicksian demand with respect to price: ∂h i ( p , u ) ∂p i = • Rewrite h ∗ i as function of m : h i ( p , v ( p , M )) • Compute v ( p , M ) = • Substitution e f ect: ∂h i ( p , v ( p , M )) ∂p i = • Income e f ect: − x ∗ i ( p 1 , p 2 , M ) ∂x ∗ i ( p , M ) ∂M = • Sum them up to get ∂x ∗ i ( p , M ) ∂p i = • It works! 2 Complements and substitutes • Nicholson, Ch. 6, pp. 182187 (161—166, 9th) • How about if price of another good changes?...
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This note was uploaded on 09/02/2010 for the course ECON 101a taught by Professor Staff during the Fall '08 term at Berkeley.
 Fall '08
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