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slide18-oct12 - REVEALED PREFERENCE Siyang Xiong Rice...

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REVEALED PREFERENCE Siyang Xiong Rice University October 14, 2011 Xiong (Rice University) ECON 401 October 14, 2011 1 / 7
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Revealed Preference By the previous two theorems, assuming rational preference, it is without loss of generality to describe the consumer°s preference by " ° ." Let 2 X denote the power set of X , i.e., 2 X is the set of all subsets of X . Consider c : 2 X n f ? g ! 2 X : (i) c ( A ) ± A ; (ii) c ( A ) 6 = ? . We say c ( ² ) is a choice function i/ both (i) and (ii) are satis±ed. interpretation: when the consumer is facing the set of choice A , the set of bundles he will choose is c ( A ) . Xiong (Rice University) ECON 401 October 14, 2011 2 / 7
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Revealed Preference: example X = f x ; y ; z g ; 2 X = f ? ; f x g ; f y g ; f z g ; f x ; y g ; f y ; z g ; f x ; z g ; f x ; y ; z gg ; consider the following choice function c : c ( f x g ) = f x g ; c ( f y g ) = f y g ; c ( f z g ) = f z g ; c ( f x ; y g ) = f x g ; c ( f y ; z g ) = f y g ; c ( f x ; z g ) = f z g ; c ( f x ; y ; z g ) = f x ; z g . Xiong (Rice University) ECON 401 October 14, 2011 3 / 7
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Revealed Preference Consider a particular way to construct choice function.
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