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micro-fall2007-6 - Households Preferences An important...

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Households Preferences An important property of the utility function The indi/erence curves remain unchanged under any monotonic transformation of the utility function. Let f : R ! R be a strictly increasing function. Then, ( i ) f ( u ( x )) = f ( u ( z )) () u ( x ) = u ( z ) . ( ii ) MRS ( x ) : = ° dx 2 dx 1 = f 0 ( ± ) u ( ± ) x 1 f 0 ( ± ) u ( ± ) x 2 = u ( ± ) x 1 u ( ± ) x 2 Ani Guerdjikova Fall 2007 74 / 80
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Households Preferences Properties of the preference relation A representation of preferences by means of a utility function is possible if following assumptions are satis°ed: 1 Completeness For all x , z 2 X ° either x % z ° or z % x ° or x % z and z % x Ani Guerdjikova Fall 2007 75 / 80
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Households Preferences Properties of the preference relation A representation of preferences by means of a utility function is possible if following assumptions are satis°ed: 1 Completeness For all x , z 2 X ° either x % z ° or z % x ° or x % z and z % x 2 Transitivity For all x , y , z 2 X , x % y and y % z imply x % z .
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