101A_lec9

# 101A_lec9 - Economics 101A(Lecture 9 Stefano DellaVigna...

This preview shows pages 1–6. Sign up to view the full content.

Economics 101A (Lecture 9) Stefano DellaVigna February 17, 2009

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outline 1. Expenditure Minimization II 2. Slutsky Equation 3. Complements and substitutes 4. Do utility functions exist?
1 Expenditure minimization II Nicholson, Ch. 4, pp. 127-132 (109—113, 9th) + Ch. 5, pp. 151-154 Solve problem EMIN (minimize expenditure): min p 1 x 1 + p 2 x 2 s.t. u ( x 1 ,x 2 ) ¯ u Pick budget set which is tangent to indi f erence curve Optimum coincides with optimum of Utility Maxi- mization! Formally: h i ( p 1 ,p 2 , ¯ u )= x i ( p 1 ,p 2 ,e ( p 1 ,p 2 , ¯ u ))

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Expenditure function is expenditure at optimum e ( p 1 ,p 2 , ¯ u )= p 1 h 1 ( p 1 ,p 2 , ¯ u )+ p 2 h 2 ( p 1 ,p 2 , ¯ u ) h i ( p i ) is Hicksian or compensated demand function Is h i always decreasing in p i ?Y e s ! Graphical proof: moving along a convex indi f erence curve
Using f rst order conditions: L ( x 1 ,x 2 )= p 1 x 1 + p 2 x 2 λ ( u ( x 1 ,x 2 ) ¯ u ) ∂L ∂x i = p i λu 0 i ( x 1 ,x 2 )=0 Write as ratios: u 0 1 ( x 1 ,x 2 ) u 0 2 ( x 1 ,x 2 ) = p 1 p 2 MRS = ratio of prices as in utility maximization! However: di

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 20

101A_lec9 - Economics 101A(Lecture 9 Stefano DellaVigna...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online