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Unformatted text preview: x and superior to y . Since Y is dense, there exists z 1 ∈ Y such that x Â z 1 Â y . Similarly, there exists z 2 ∈ Y such that z 1 Â z 2 Â y . Finally, U ( x ) ≥ v ( z 1 ) (by the de±nition of U and x Â z 1 ), v ( z 1 ) > v ( z 2 ) (since v represents % on Y and z 1 Â z 2 ), and v ( z 2 ) ≥ U ( y ) (by the de±nition of U and z 2 Â y ). Bibliographic Notes Recommended readings : Kreps 1990, 30–32; MasColell et al. 1995, chapter 3, C. Fishburn (1970) covers the material in this lecture very well. The example of lexicographic preferences originated in Debreu (1959) (see also Debreu 1960, in particular Chapter 2, which is available online at http://cowles.econ.yale.edu/P/cp/p00b/p0097.pdf.)...
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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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