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Unformatted text preview: { y  y x } and { y  x y } are open sets in X . Problem 2. ( Moderate ) Give an example of preferences over a countable set in which the preferences cannot be represented by a utility function that returns only integers as values. Problem 3. ( Moderate ) Consider the sequence of preference relations ( % n ) n = 1,2, .. , deFned on < 2 + where % n is represented by the utility function u n ( x 1 , x 2 ) = x n 1 + x n 2 . We will say that the sequence % n converges to the preferences % if for every x and y , such that x y , there is an N such that for every n > N we have x n y . Show that the sequence of preference relations % n converges to the preferences which are represented by the function max { x 1 , x 2 } ....
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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.
 Fall '10
 aswa
 Utility

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