101A_lec6 - Economics 101A(Lecture 6 Stefano DellaVigna...

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Economics 101A (Lecture 6) Stefano DellaVigna February 5, 2009
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Outline 1. From Preferences to Utility (and viceversa) 2. Common Utility Functions 3. Utility maximization
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1 From preferences to utility Nicholson, Ch. 3 Economists like to use utility functions u : X R u ( x ) is ‘liking’ of good x u ( a ) >u ( b ) means: I prefer a to b. Def. Utility function u represents preferences º if, for all x and y in X, x º y if and only if u ( x ) u ( y ) . Theorem. If preference relation º is rational and continuous, there exists a continuous utility function u : X R that represents it.
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[Skip proof] Example: ( x 1 ,x 2 ) º ( y 1 ,y 2 ) i f x 1 + x 2 y 1 + y 2 Draw: Utility function that represents it: u ( x )= x 1 + x 2 But. .. Utility function representing º is not unique Take 3 u ( x ) or exp( u ( x )) u ( a ) >u ( b ) ⇐⇒ exp( u ( a )) > exp( u ( b ))
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If u ( x ) represents preferences º and f is a strictly increasing function, then f ( u ( x )) represents º as well.
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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_lec6 - Economics 101A(Lecture 6 Stefano DellaVigna...

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