101A_lec8 - Economics 101A(Lecture 8 Stefano DellaVigna...

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Unformatted text preview: Economics 101A (Lecture 8) Stefano DellaVigna February 12, 2009 Outline 1. Indirect Utility Function II 2. Comparative Statics (Introduction) 3. Income Changes 4. Price Changes 5. Expenditure Minimization 1 Indirect utility function • Nicholson, Ch. 4, pp. 124-127 (106—108, 9th) • De f ne the indirect utility v ( p , M ) ≡ u ( x ∗ ( p , M )) , with p vector of prices and x ∗ vector of optimal solutions. • v ( p , M ) is the utility at the optimimum for prices p and income M • Some comparative statics: ∂v ( p , M ) /∂M =? • Hint: Use Envelope Theorem on Lagrangean func- tion • What is the sign of λ ? • λ = u x i /p > • ∂v ( p , M ) /∂p i =? • Properties: — Indirect utility is always increasing in income M — Indirect utility is always decreasing in the price p i 2 Comparative Statics (introduction) • Nicholson, Ch. 5, pp. 141-151 (121—131, 9th) • Utility maximization yields x ∗ i = x ∗ i ( p 1 , p 2 , M ) • Quantity consumed as a function of income and price • What happens to quantity consumed x ∗ i as prices or income varies? •...
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This note was uploaded on 09/05/2009 for the course ECON 101a taught by Professor Staff during the Spring '08 term at Berkeley.

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101A_lec8 - Economics 101A(Lecture 8 Stefano DellaVigna...

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