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Unformatted text preview: Recap Expenditure minimization Hicksian (compensated) demands
HD0 in prices decreasing in own price Expenditure functions
Substitute Hicksian demands into expenditures HD1 in prices increasing in prices increasing in utility Shephard's lemma Expenditure functions and Indirect utility functions
E (p1 , p2 , u) = V (p1 , p2 , I) = 1 p1 p2 u (1  )1 (1  )1 I 1 p1 p2 Indirect utility functions and Expenditure functions
E (p1 , p2 , u) = V (p1 , p2 , I) = 1 p1 p2 u (1  )1 (1  )1 I 1 p1 p2 Income and substitution effects Income and substitution effects 2
How do we get points A, B, and C? Example: Cobb Douglas 1 u(x1 , x2 ) = x1 x2 p1 x1 + p2 x2 = I p1 x1 + p2 x2 = I Example: Cobb Douglas 2 Example: Cobb Douglas 3 Example: Perfect Compliments
u(x1 , x2 ) = min{x1 , x2 } p1 x1 + p2 x2 = I p1 x1 + p2 x2 = I Example: Perfect Compliments 2 Ordinary and Hicksian demands
x1 (p1 , p2 , E (p1 , p2 , u)) = h1 (p1 , p2 , u) The Slutsky equation
x1 + p1 x1 E E h1 = p1 p1 x1 h1 =  p1 p1 x1 I E p1 The Slutsky equation 2
x1 + p2 x1 E E h1 = p2 p2 x1 h1 =  p2 p2 x1 I E p2 Inverse demand curves Inverse demand curves 2 Inverse demand curves 3 ...
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 Fall '09
 CUR
 Microeconomics, Utility

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