Lec04-Theory_Choice_Indiv_Demand

Lec04-Theory_Choice_Indiv_Demand - Lecture 4 - Theory of...

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Lecture 4 - Theory of Choice and Individual Demand David Autor 14.03 Microeconomic Theory and Public Policy, Fall 2005 Agenda 1. Utility maximization 2. Indirect utility function 3. Application: Gift giving — Waldfogel paper 4. Expenditure function 5. Relationship between Expenditure function and Indirect utility function 6. Demand functions 7. Application: Food stamps — Whitmore paper 8. Income and substitution e f ects 9. Normal and inferior goods 10. Compensated and uncompensated demand (Hicksian, Marshallian) 11. Application: Gi f en goods — Jensen and Miller paper Roadmap: 1
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Axioms of consumer preference Primal Dual Min p x x+ p y y s.t. U(x,y) > U Indirect Utility function U*= V(p x , p y , I) Expenditure function E*= E(p x , p y , U) Max U(x,y) s.t. p x x+ p y y< I Marshallian demand X = d x (p x , p y , I) = (by Roy’s identity) Hicksian demand X = h x (p x , p y , U) = (by Shepard’s lemma) Slutsky equation I V p V x / / x p E 1 Theory of consumer choice 1.1 Utility maximization subject to budget constraint Ingredients : Utility function (preferences) Budget constraint Price vector Consumer’s problem Maximize utility subject to budget constraint Characteristics of solution : Budget exhaustion (non-satiation) For most solutions: psychic trade-o f =monetarypayo f 2
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Psychic trade-o f is MRS Monetary trade-o f is the price ratio From a visual point of view utility maximization corresponds to the following point: (Note that the slope of the budget set is equal to p x p y ) B A D C x y IC 1 IC 2 IC 3 What’s wrong with some of these points? We can see that A P B , A I D , C P A . Why should one choose A ? Thes lopeo ftheind i f erence curves is given by the MRS 1.1.1 Interior and corner solutions [Optional] There are two types of solution to this problem.
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y x Typical case The one below is an example of a corner solution. In this speci f cexamp letheshapeo f the indi f erence curves means that the consumer is indi f erent to the consumption of good y . Utility increases only with consumption of x . y
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x y In the graph above preference for y is su ciently strong relative to x that the the psychic trade-o f is always lower than the monetary trade-o f . This must be the case for many products that we don’t buy. Another type of “corner” solution results from indivisibility. 1 10 y x I = 500 p x = 450 p y = 50 Why can’t we draw this budget set, i.e. connect dots? This is because only 2 points can be drawn. This is a sort of “integer constraint”. We normally abstract from indivisibility. 5
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Going back to the general case, how do we know a solution exists for consumer, i. e. how do we know the consumer can choose? We know because of the completeness axiom. Every bundle is on some indi
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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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Lec04-Theory_Choice_Indiv_Demand - Lecture 4 - Theory of...

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