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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 ff ects 9. Normal and inferior goods 10. Compensated and uncompensated demand (Hicksian, Marshallian) 11. Application: Gi ff 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 ff = monetary payo ff 2
Psychic trade-o ff is MRS Monetary trade-o ff 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 ? The slope of the indi ff erence curves is given by the MRS 1.1.1 Interior and corner solutions [Optional] There are two types of solution to this problem. 1. Interior solution 2. Corner solution 3

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