July 14 Utility Handout

July 14 Utility Handout - PREFERENCE & UTILITY THEORY x y...

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PREFERENCE & UTILITY THEORY A x y means that the consumer thinks that x is at least as good as y, "weak preference" x y "strict preference" xy "indifference" The individual has a preference ordering on X, which is a complete ordering (A1 – A3). A1. Complete . For all x and y in X, either x y or yx or both. A2. Transitive . For all x , y , and z in X, if x y and yz , then x z . & A3. Continuity . For any x , y , and z in X, if x y and , then there must exist some composite of x and z which gives the same utility as y . Existence of a Utility Function . For any preordering satisfying Axioms A1 – A3 defined over a closed, convex set X, there exists a continuous utility function u:X with the following properties: (a)    ux uy x y  (b) x y  B Assume that the set of choices facing the consumer take the form of lotteries - a lottery is denoted    1 p;x,y p x p y    - ie. the consumer receives prize x with prob.
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This note was uploaded on 02/02/2012 for the course ECON 442 taught by Professor Grahamlemke during the Spring '11 term at Binghamton.

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