Rubinstein2005-page59 - . The preFerence represented by x 1...

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October 21, 2005 12:18 master Sheet number 57 Page number 41 Consumer Preferences 41 Monotonicity: The relation % satisfes monotonicity iF For all x , y X , iF x k y k For all k , then x % y , and iF x k > y k For all k , then x  y . In some cases, we will Further assume that the consumer is strictly happier with any additional quantity oF any commodity. Strong Monotonicity: The relation % satisfes strong monotonicity iF For all x , y X iF x k y k For all k and x 6= y , then x  y . OF course, in the case that preFerences are represented by a util- ity Function, preFerences satisFying monotonicity (or strong mono- tonicity) are represented by monotonic increasing (or strong monotonic increasing) utility Functions. Examples: The preFerence represented by min { x 1 , x 2 } satisfes monotonicity but not strong monotonicity
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Unformatted text preview: . The preFerence represented by x 1 + x 2 satisfes strong mono-tonicity . The preFerence relation | x x | satisfes nonsatiation , a related property that is sometimes used in the literature: For every x X and For any > 0 there is some y X that is less than away From x so that y x . Every monotonic preFerence re-lation satisfes nonsatiation, but the reverse is, oF course, not true. Continuity We will use the topological structure oF < K + (induced From the stan-dard distance Function d ( x , y ) = p ( x k y k ) 2 ) to apply the defni-tion oF continuity discussed in Lecture 2. We say that the preFerences...
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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