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slide16-sept28

# slide16-sept28 - PREFERENCES Siyang Xiong Rice University...

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PREFERENCES Siyang Xiong Rice University September 27, 2011 Xiong (Rice University) ECON 401 September 27, 2011 1 / 14

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consumer preferences Suppose we are given a choice set X . Let x ; y ; z denote elements in X , i.e., x ; y ; z 2 X . I have a binary relation (more speci°cally, preference) on elements in X . For example, x is strictly preferred y : x ° y : I am indi/erent between x and y : x ± y : x is weakly preferred y : x ² y : Xiong (Rice University) ECON 401 September 27, 2011 2 / 14
binary relation Let B denote the binary relation (i.e., ° , ± or ² ): xBy Some property of binary relation: Relexive : xBx for all x 2 X ; Irrelexive : : xBx for all x 2 X ; Symmetric : xBy implies yBx for all x ; y 2 X ; Asymmetric : xBy implies : yBx for all x ; y 2 X ; Transitive : xBy and yBz implies xBz for all x ; y ; z 2 X ; Negatively Transitive : : xBy and : yBz implies : xBz for all x ; y ; z 2 X ; Complete : either xBy or yBx for all x ; y 2 X ; Acyclic : x 1 Bx 2 Bx 3 ::: x n ° 1 Bx n implies x 1 6 = x 2 . Xiong (Rice University) ECON 401 September 27, 2011 3 / 14

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de°ne preferences: method #1 start with " ² ", then " ± " is de°ned as follows. x ± y i/ both x ² y and y ² x : " ° " is de°ned as follows. x ° y i/ x ² y and : y ² x : Xiong (Rice University) ECON 401 September 27, 2011 4 / 14
de°ne preferences: method #2 start with " ° ", then " ² " is de°ned as follows.

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slide16-sept28 - PREFERENCES Siyang Xiong Rice University...

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