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Unformatted text preview: Lecture 5 1minute review Demand Functions X ( p x ,p y ,M ) CobbDouglas CES Quasilinear 1 Quasilinear utility function U ( x,y ) = x + log y income = M prices = p x ,p y Lagrangian L ( x,y, ) = x + log y ( p x x + p y y M ) 2 Three equations 1 p x = 0 1 y p y = 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 What is the problem? Corner solutions FOC need not hold at corner solutions 4 5 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 Quasilinear case if ( M/p x ) 1 < 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 x = 0 , y = M p y if M p x 1 < 7 8 9 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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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.
 Fall '07
 McDevitt
 Utility

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