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_Lecture_05REV(2)

# _Lecture_05REV(2) - Lecture 5 1-minute review Demand...

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Lecture 5 1-minute review Demand Functions X ( p x , p y , M ) Cobb-Douglas CES Quasi-linear 1

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Quasi-linear utility function U ( x, y ) = x + log y income = M prices = p x , p y Lagrangian L ( x, y, λ ) = x + log y - λ ( p x x + p y y - M ) 2
Three equations 1 - p x λ = 0 1 y - p y λ = 0 p x x + p y y - M = 0 Solve x = M p x - 1 , y = p x p y What if M p x - 1 < 0?? 3

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What is the problem? Corner solutions FOC need not hold at corner solutions 4
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To take care of this difficulty: – just check possible corner solutions separately Fortunately: corner solutions will always jump out like this if you look carefully. 6
Finish Quasi-linear case if ( M/p x ) - 1 < 0 must have corner solution : x = 0 or y = 0 in this case x = 0, y = M/p y Full solution x = M p x - 1 , y = p x p y if M p x - 1 0 x = 0 , y = M p y if M p x - 1 < 0 7

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What happens to demand for x when price of x ↑ ↓ ? Two effects • ↓ ↑ buying power: income effect shift in choice: substitution effect 10
Isolate substitution effect by asking: What would consumer do if we exactly compensated change in buying power?

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_Lecture_05REV(2) - Lecture 5 1-minute review Demand...

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