Consumer_Theory_1_S08

# Consumer_Theory_1_S08 - Preferences and Utility Chapter 3...

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Preferences and Utility Chapter 3 Representation of Individual Preferences Ordinal Ranking of alternatives from best to worst • Characterization of Utility Function Cardinal Ranking , assigning numbers to alternatives – Higher numbers for better alternatives • Graphical Representation: Indifference Curves Marginal Rate of Substitution – Individual tradeoff between consuming one good vs. another

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Preference Relations (1) • Suppose consumer has to choose between different alternatives: w, x, y, z… • Examples: Alternatives may be sports teams, favorite cities, favorite movies etc. Consumer Choice: Alternatives may be “Consumption bundles”, i.e. quantities of different commodities that are consumed (Food, Housing, Education, Travel, Books etc.) • Where x n denotes the quantity of the n-th commodity. ( ) N x x x x ,..., , 2 1 =
Preference Relations (2) Axioms of Rational Choice 1. Completeness: For any alternatives y and z: either y is at least as good as z, or z is at least as good as y, or both (y and z are equally attractive). Any pair of alternatives can be compared 2. Transitivity: For any alternatives x, y, and z, if x is at least as good as y and y is at least as good as z, then x is at least as good as z. Internal consistency of comparisons Completeness and Transitivity together imply that there exists an Ordinal Ranking of alternatives from best to worst.

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Preference Relations (3) 3. Continuity Axiom: If y is strictly better than z, then alternatives “near y” are also strictly better than z. Completeness, Transitivity and Continuity imply that there exists a cardinal ranking: we can assign numbers to each alternative (higher numbers for better alternatives). For consumption bundles: call cardinal ranking utility function U(x) Example of a preference ordering that satisfies completeness and transitivity, but not continuity: Lexicographic Preferences •( x 1 ,y 1 ) is preferred to (x 2 ,y 2 ), if x 1 > x 2 , or x 1 = x 2 and y 1 > y 2 Like the ordering of names in Phonebook
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Consumer_Theory_1_S08 - Preferences and Utility Chapter 3...

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