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Unformatted text preview: 1 Ch 3. Preferences Consumers choose the best things they can afford. Ch 2 clarified what was meant by &can afford¡, and this chapter will be prepared for examining the meaning of &the best things¡. 3.1 Consumer Preferences A consumer is assumed to derive satisfaction from consuming a bundle of two goods. Given two bundles, X = (x 1 , x 2 ) and Y = (y 1 , y 2 ) , she can rank them according to their desirability by deciding that one bundle is better than the other or that she is in different between the two. We introduce some operational notions to describe the consumer¢s behavior:  X f Y , meaning that X is strictly preferred to Y , i.e., she strictly prefers X to Y and will choose X rather than Y if possible.  X ～ Y , indicating that she is indifferent between X and Y since she is just as satisfied by consuming X as she is by consuming Y .  X f Y , suggesting that she thinks that X is at least as good as Y and she weakly prefers X to Y . The relations among these notations are: i ) If X f Y and Y f X, then X ～ Y. ii) If X f Y with out X ～ Y, then X f Y. Some fundamental assumptions (called &axioms¡ here) are made to ensure the consistency of consumer preferences: i) Complete : any two bundles can be compared. For any two bundles, X f Y , or Y f X, or X ～ Y. ii) Reflexive : any bundle is at least as good as itself: X f X ; this seems uninteresting but important. iii) Transitive : if X f Y and Y f Z, then X f Z . This suggests that X f Y and Y f Z implies X f Z , and that X ～ Y and Y ～ Z implies X ～ Z . 2 Axiom 1 rules out the unreasonable case where X f Y and at the same time Y f X , and enables a consumer to make a choice between any two bundles. Axiom 2 is trivial. Axiom 3 is a bit problematic (you may ignore this), but is important if economists are to develop a theory of reasonable people&s choices. 3.2 Indifference Curves (ICs) It is convenient to describe preferences graphically by using ICs. See figure 3.1 The set of all consumption bundles X f X o is called the weakly preferred set . The bundles on this set&s boundary, for which the consumer is indifferent to X o , form the indifference curve (IC). We call this curve the IC through X o , and hence X& ～ X¡ for any X& on this IC. Important to know the fact that ICs representing distinct levels of preference cannot cross . That is, the following situation in figure 3.2 can not happen under axiom 3. Proof by contradiction: let X and Y stand for distinct levels of preference ( X is on IC 1 and Y is on IC 2 ), implying that X ～ Y cannot arise. Suppose IC 1 and IC 2 intersect at Z o X X f X o IC X& X Y Z IC 1 IC 2 3 so that X ～ Z and Y ～ Z. But, this implies by axiom 3 that X ～ Y , a contradiction....
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This note was uploaded on 02/19/2009 for the course ECIF ECIF201 taught by Professor Gu during the Spring '09 term at University of Manchester.
 Spring '09
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