PS7(09)

PS7(09) - ECN 712 Fall 2009 Professor Schlee Problem Set...

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ECN 712 Fall 2009 Professor Schlee Problem Set VII, Due Tuesday, 27 October 1. Let X be a finite set of outcomes, L the set of probablity distributions over X and % a (complete and transititve) preference relation on L . Assume, as we did in the lecture, that no two (sure) elements of X are indifferent. We proved that if % is continuous, monotone and satisfies the independence axiom, then there is an expected utility representation of % . Now go in the other direction: Suppose that there is an expected utility representation of the preference relation % ; does it follow that % is continuous, monotone and satisfies independence? 2. Let X = { x 1 ,...,x n } be a set of outcomes ( n 3), with x 1 the outcome “death.” Define % as follows: for any q,p ∈ L , if q 1 > p 1 , then p ± q ; if q 1 = p 1 , then there is a real-valued function u on { x 2 ,...,x n } such that p % q precisely when n X i =2 u ( x i ) p i n X i =2 u ( x i ) q i . where
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