_Lecture_07

# _Lecture_07 - Lecture 7 1-minute review Pictures demand...

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Lecture 7 1-minute review Pictures demand curve Engel curve income expansion path Computations Cobb-Douglas CES elasticity Slutsky equation 1

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Three applications 1. investment over time 2. labor supply 3. insurance 2
Example 1: Investment over time I have income M this year Consume this year? Save for retirement? Interest rate changes? Assume retirement is next year no other income in retirement x = consumption this year, y = consumption next year p y = 1 1+ r ; r = interest rate 3

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4
Assume U ( x,y ) = x c c + ρ y c c ( ρ < 1 represents impatience: prefer to consume today) Lagrangian L = ± x c c ! + ρ ± y c c ! - λ ( p x x + p y y - M ) Equations x c - 1 - λp x = 0 y c - 1 - λp y = 0 p x x + p y y - M = 0 5

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x c - 1 1 = ρ ± y c - 1 1 / (1 + r ) ! y = [ ρ (1 + r )] 1 / (1 - c ) x x + ²³ 1 1 + r ´ [ ρ (1 + r )] 1 / (1 - c ) µ x = M x = M 1 + 1 1+ r · ρ 1 / (1 - c ) (1 + r ) 1 / (1 - c ) = M 1 + ρ 1 / (1 - c ) (1 + r ) c/ (1 - c ) 6
r ? Save more or less?

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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_07 - Lecture 7 1-minute review Pictures demand...

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