Rubinstein2005-page80 - the SA is “cumbersome,” and...

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October 21, 2005 12:18 master Sheet number 78 Page number 62 62 Lecture Five Apparently WA is not a sufficient condition for extending the bi- nary relation ± , as defined above, into a complete and transitive relation (an example with three goods from Hicks 1956 is discussed in Mas-Colell et al. 1995). A necessary and sufficient condition for a demand function x satisfying Walras’s law and homogeneity of degree zero to be rationalized is the following: Strong Axiom of Revealed Preference (SA): If ( x n ) n = 1, ... , N is a sequence of bundles and ( B ( p n , w n )) n = 1, ... , N is a se- quence of budget sets so that for all n N 1, x n ²= x n + 1 and x n is chosen from B ( p n , w n ) which also contains x n + 1 , then x 1 / B ( p N , w N ) . The Strong Axiom is basically equivalent to the assumption that the relation ± derived from revealed behavior is transitive. But ± is not necessarily a complete relation, and thus we are left with the question of whether ± can be extended into preferences. Proving that this is possible is beyond the scope of this course. In any case,
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Unformatted text preview: the SA is “cumbersome,” and using it to determine whether a certain demand function is rationalizable may not be a trivial task. Decreasing Demand The consumer model discussed so far constitutes the standard frame-work for deriving demand. Our intuition tells us that demand for a good falls when its price increases. However, this does not follow from the standard assumptions about the rational consumer’s be-havior which we have discussed so far. The following is an example of a preference relation that induces demand that is nondecreasing in the price of one of the commodities: An Example in Which Demand for a Good May Increase with Price Consider the preferences represented by the following utility func-tion: u ( x 1 , x 2 ) = ± x 1 + x 2 if x 1 + x 2 < 1 x 1 + 4 x 2 if x 1 + x 2 ≥ 1 ....
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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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