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Chapter

Notes on Microecon.pdf


Department
Economics
Course Code
ECON401
Professor
John Burbidge

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Notes on Microeconomic Theory
Nolan H. Miller
August 18, 2006

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Contents
1 The Economic Approach 1
2ConsumerTheoryBasics 5
2.1 CommoditiesandBudgetSets............................... 5
2.2 DemandFunctions ..................................... 8
2.3 ThreeRestrictionsonConsumerChoices......................... 9
2.4 AFirstAnalysisofConsumerChoices .......................... 10
2.4.1 ComparativeStatics ................................ 11
2.5 Requirement1Revisited:WalrasLaw.......................... 11
2.5.1 WhatstheFunnyEqualsSignAllAbout?.................... 12
2.5.2 Back to Walras’ Law: Choice Response to a Change in Wealth . . . . . . . . 13
2.5.3 TestableImplications ............................... 14
2.5.4 Summary:HowDidWeGetWhereWeAre? .................. 15
2.5.5 WalrasLaw:ChoiceResponsetoaChangeinPrice .............. 15
2.5.6 ComparativeStaticsinTermsofElasticities................... 16
2.5.7 WhyBother?.................................... 17
2.5.8 Walras’ Law and Changes in Wealth: Elasticity Form . . . . . . . . . . . . . 18
2.6 Requirement 2 Revisited: Demand is Homogeneous of Degree Zero. . . . . . . . . . . 18
2.6.1 Comparative Statics of Homogeneity of Degree Zero . . . . . . . . . . . . . . 19
2.6.2 AMathematicalAside... ............................. 21
2.7 Requirement3Revisited:TheWeakAxiomofRevealedPreference.......... 22
2.7.1 CompensatedChangesandtheSlutskyEquation................ 23
2.7.2 Other Properties of the Substitution Matrix . . . . . . . . . . . . . . . . . . . 27
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Nolan Miller Notes on Microeconomic Theory ver: Aug. 2006
3 The Traditional Approach to Consumer Theory 29
3.1 BasicsofPreferenceRelations............................... 30
3.2 FromPreferencestoUtility ................................ 35
3.2.1 UtilityisanOrdinalConcept........................... 36
3.2.2 SomeBasicPropertiesofUtilityFunctions ................... 37
3.3 TheUtilityMaximizationProblem(UMP)........................ 42
3.3.1 WalrasianDemandFunctionsandTheirProperties............... 47
3.3.2 TheLagrangeMultiplier.............................. 49
3.3.3 TheIndirectUtilityFunctionandItsProperties ................ 50
3.3.4 RoysIdentity.................................... 52
3.3.5 The Indirect Utility Function andWelfareEvaluation ............. 54
3.4 TheExpenditureMinimizationProblem(EMP)..................... 55
3.4.1 AFirstNoteonDuality.............................. 57
3.4.2 Properties of the Hicksian Demand Functions and Expenditure Function . . . 59
3.4.3 The Relationship Between the Expenditure Function and Hicksian Demand . 62
3.4.4 TheSlutskyEquation ............................... 65
3.4.5 Graphical Relationship of the Walrasian and Hicksian Demand Functions . . 67
3.4.6 TheEMPandtheUMP:SummaryofRelationships .............. 71
3.4.7 WelfareEvaluation................................. 72
3.4.8 BringingItAllTogether.............................. 78
3.4.9 WelfareEvaluationforanArbitraryPriceChange ............... 83
4 Topics in Consumer Theory 87
4.1 HomotheticandQuasilinearUtilityFunctions...................... 87
4.2 Aggregation......................................... 89
4.2.1 TheGormanForm................................. 90
4.2.2 AggregateDemandandAggregateWealth.................... 92
4.2.3 DoesindividualWARPimplyaggregateWARP?................ 94
4.2.4 RepresentativeConsumers............................. 96
4.3 TheCompositeCommodityTheorem........................... 98
4.4 So Were They Just Lying to Me When I Studied Intermediate Micro? . . . . . . . . 99
4.5 ConsumptionWithEndowments .............................101
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