Lec03-Axioms_Consumer_Pref_Theory_Choice

# Lec03-Axioms_Consumer_Pref_Theory_Choice - Lecture 3 Axioms...

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Lecture 3 - Axioms of Consumer Preference and the Theory of Choice David Autor 14.03 Microeconomic Theory and Public Policy, Fall 2005 Agenda : 1. Consumer preference theory (a) Notion of utility function (b) Axioms of consumer preference (c) Monotone transformations 2. Theory of choice Ingredients Characteristics of the solution Interior vs corner solutions (b) Constrained maximization for consumer (c) Interpretation of the Lagrange multiplier Road map : Theory 1. Consumer preference theory 2. Theory of choice 3. Individual demand functions 4. Market demand 1

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Applications 1. Dead weight loss of Christmas 2. Food stamps and other taxes and transfers 3. Gi/en goods: Theory and evidence 1 Consumer Preference Theory A ² is determined by a personal utility function . 1.1 Cardinal and ordinal utility Cardinal Utility Function According to this approach U ( A ) is a cardinal number, that is: U : consumption bundle ±! R 1 measured in ±utils² Ordinal Utility Function More general than cardinal utility function U provides a ±ranking²or ±preference ordering²over bundles. U : ( A; B ) ±! 8 < : A P B B P A A I B Used in demand³consumer theory Cardinal vs Ordinal Utility Functions The problem with cardinal utility functions comes from the di¢ culty in ´nding the appro- priate measurement index (metric). Example: Is 1 util for person 1 equivalent to 1 util for person 2? By being unit-free ordinal utility functions avoid these problems. 2
, that is, how they choose among competing alternatives. We do not need to know how many ±utils²people experience from each choice to answer this question; we just need to know how they rank choices. 1.2 Axioms of Consumer Preference Theory Created for purposes of: 1. Using mathematical representation of utility functions 3. Deriving ±well-behaved²demand curves When we get through the entire corpus of consumer theory, you may be surprised to real- ize that all of the results and predictions we will have derived rest entirely (with no further assumptions) on the small set of axioms below. For any two bundles A and B, a consumer can establish a preference ordering. That is, for any comparison of bundles, she will choose one and only one of the following: 1. A P B 2. B P A 3. A I B Without this property, preferences are unde´ned.

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## This note was uploaded on 04/11/2008 for the course ECON 14.03 taught by Professor Autor during the Spring '08 term at MIT.

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Lec03-Axioms_Consumer_Pref_Theory_Choice - Lecture 3 Axioms...

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