Rice_ECO501_lectures - Rice University ECO 501...

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Unformatted text preview: Rice University ECO 501 & & & & & & & & & & & & & & & & & & Lecture Notes: Microeconomic Theory I & & & & & & & & & & & & & & & & & & Christian Roessler Fall 2008 Contents 1 Preference 3 1.1 Consumption Set . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Rational Preference . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Utility Functions . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Utility 8 2.1 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Quasiconcavity . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Demand I: Utility Maximization Problem 15 3.1 Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 The Utility Maximization Problem (UMP) . . . . . . . . . . . 16 3.3 Indirect Utility Function . . . . . . . . . . . . . . . . . . . . . 21 4 Demand II: Expenditure Minimization Problem 23 4.1 EMP and Hicksian Demand . . . . . . . . . . . . . . . . . . . 23 4.2 Expenditure Function . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5 Comparative Statics 30 5.1 Wealth E/ects . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 Price E/ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.3 Law of Demand . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.4 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.5 Money Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.6 Welfare Comparisons . . . . . . . . . . . . . . . . . . . . . . . 36 6 Choice-Based Approach 41 6.1 Choice Structures . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.2 Weak Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.3 Relationship with the Law of Demand . . . . . . . . . . . . . 47 6.4 Strong Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7 Integrability 55 7.1 Slutsky and Hicks Compensation . . . . . . . . . . . . . . . . 55 7.2 Aside: Dot Product . . . . . . . . . . . . . . . . . . . . . . . . 57 7.3 Substitution Matrix . . . . . . . . . . . . . . . . . . . . . . . . 58 1 7.4 Substitution Matrix with Preference . . . . . . . . . . . . . . . 62 7.5 Integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 8 Aggregation 71 8.1 Aggregate Demand Function . . . . . . . . . . . . . . . . . . . 71 8.2 Representative Consumer . . . . . . . . . . . . . . . . . . . . . 76 8.3 Failure of the Weak Axiom . . . . . . . . . . . . . . . . . . . . 80 9 Expected Utility 84 9.1 Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 9.2 Preference over Lotteries . . . . . . . . . . . . . . . . . . . . . 86 9.3 Expected Utility Theorem . . . . . . . . . . . . . . . . . . . . 88 9.4 Paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 9.5 State-Space Approaches . . . . . . . . . . . . . . . . . . . . . 98 10 Risk 100 10.1 Money Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . 100 10.2 Risk Attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . 10110....
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This note was uploaded on 10/25/2011 for the course ECON 501 taught by Professor Zobuz during the Spring '11 term at Istanbul Technical University.

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Rice_ECO501_lectures - Rice University ECO 501...

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