《微观经济学microeconomics》英文版课件

微观经济学

Microeconomics

微观经济学

Microeconomics1ECON501LectureNote1

PreferenceandChoiceECON501LectureNote1Prefere2StructurePreferencerelationChoicerulesThelinkbetweenpreferenceandchoiceStructurePreferencerelation3PreferenceRelationsTheRationalPreferenceCompletenessTransitivityUtilityFunctionDefinition:afunctionuisautilityfunctionrepresentingpreferencerelationif

ApreferencerelationcanberepresentedbyautilityfunctiononlyifitisrationalPreferenceRelationsTheRation4ChoiceRulesAchoicestructureBudgetsetsAchoiceruleTheweakaxiomofrevealedpreference(WARP):ifxisrevealedatleastasgoodasy,thenycannotberevealedpreferredtoxChoiceRulesAchoicestructure5TheLinkBetweenPreferenceandChoiceIfthepreferencerelationisrational,thenthechoicestructuresatisfiestheweakaxiom.IfthechoicestructuresatisfiestheWARPandβincludesallsubsetsofXofuptothreeelements,thenthereisacorrespondingrationalpreferencerelation.TheLinkBetweenPreferencean6ECON501LectureNote2

ConsumerTheory1(TextbookChapter2and3)ECON501LectureNote2Consume7StructureConsumerChoice(Chapter2)BudgetsetWalrasiandemandfunctionComparativestaticsTheweakaxiomofrevealedpreferenceandthelawofdemandPreference(Chapter3)ThebasicpropertiesofpreferenceExistenceofutilityfunctionStructureConsumerChoice(Chap8TheBudgetsetCommoditiesThephysicalconstraintsandtheconsumptionsetTheeconomicconstraint:TheWalrasianbudgetset(Definition2.D.1)ConvexityofWalrasianbudgetset:proofTheBudgetsetCommodities9Consumer’sChoiceTheconsumer’sproblem:tochooseaconsumptionbundlexfromtheWalrasianbudgetset.Consumer’sChoiceTheconsumer’10WalrasianDemandFunctionAssumption:Itishomogeneousofdegreeofzero(Definition2.E.1):individual’schoicedependsonlyonthesetoffeasiblepoints.ItsatisfiesWalras’law(Definition2.E.2):theconsumerfullyexpendshiswealth.Exercise2.E.1WalrasianDemandFunctionAssum11ComparativeStatics–WealthEffectsTheconsumer’sEngelfunctionThewealtheffectNormalgoodsandinferiorgoodsComparativeStatics–WealthE12ComparativeStatics–PriceEffectsThedemandcurve(Figure2.E.2)Theoffercurve(Figure2.E.3and2.E.4)ThepriceeffectComparativeStatics–PriceEf13TheWeakAxiomofRevealedPreference(Definition2.F.1)TheWalrasiandemandfunctionsatisfiedtheweakaxiomofrevealedpreferenceif:Intuition:Figure2.F.1TheWeakAxiomofRevealedPre14TheImplicationofWARPTwoeffectsofpricechange:substitutioneffectandincomeeffect(Slutsky)compensatedpricechangesProposition2.F.1:TheWalrasiandemandfunctionsatisfiedtheWARPifandonlyif:foranycompensatedpricechangefrominitial(p,w)to(p’,w’)=(p’,p’x(p,w)),wehaveThelawofdemandTheImplicationofWARPTwoeff15BasicPropertiesofPreferenceRational(Definition3.B.1)Monotone(Definition3.B.2)Localnonsatiated(Definition3.B.3)Convex(Definition3.B.4)Homothetic(Definition3.B.6)Quasilinear(Definition3.B.7)Continuous(Definition3.C.1)BasicPropertiesofPreference16ExistenceofAUtilityFunctionProposition3.C.1:supposethattherationalpreferencerelationonXiscontinuous,thenthereisacontinuousutilityfunctionthatrepresentthispreference

ExistenceofAUtilityFunctio17ECON501LectureNote3

ConsumerTheory2(TextbookChapter3)ECON501LectureNote3Consume18StructureUtilityMaximizationProblemUtilitymaximizationWalrasiandemandfunctionIndirectutilityfunctionExpenditureMinimizationProblemExpenditureminimizationExpenditurefunctionHicksiandemandfunctionStructureUtilityMaximization19UtilityMaximizationProblemTheproblem:TheLagrangianfortheconsumer’sconstrainedoptimization:Firstordercondition:Solution:WalrasiandemandfunctionUtilityMaximizationProblemTh20UtilityMaximization--ExampleExample3.D.1:thetransformedCobb-DouglasUtilityFunctionUtilityMaximization--Exampl21WalrasianDemandFunctionAssumption:supposeacontinuousutilityfunctionrepresentingalocallynonsatiatedpreferencerelationPropertiesofWalrasiandemandfunction:ItishomogeneousofdegreeofzeroItsatisfiesWalras’lawConvexityofpreferenceimpliesconvexityofx(p,w),strictconvexityofpreferencesimpliesthatx(p,w)issingle-valuedProofWalrasianDemandFunctionAssum22IndirectUtilityFunctionDefinition:Properties:HomogeneousofdegreeofzeroStrictlyincreasinginwandnonincreasinginpQuasiconvexinpandwContinuousProofIndirectUtilityFunctionDefin23ExpenditureMinimizationProblemTheproblem:Thefirstordercondition:Thesolution:Hicksiandemandfunctionh(p,u)ExpenditureMinimizationProbl24ExpenditureFunctionExpenditurefunctionProperties:HomogeneousofdegreeofoneinpStrictlyincreasinginuandnondecreasinginpConcaveinpContinuousinpanduProofExpenditureFunctionExpenditur25HicksianDemandFunctionPropertiesHomogenousofdegreeofzeroinpNoexcessutilityConvexity/uniquenessProofExample3.E.1:HicksiandemandfunctionandexpenditurefunctionfortheCobb-DouglasutilityfunctionHicksianDemandFunctionProper26ECON501LectureNote4ConsumerTheory3ECON501LectureNote4Consumer27StructureDualityIdentitiesofDuality(p.60)HicksianDemandandExpenditureFunction(p.68)WalrasianDemandandIndirectUtilityFunction(p.73)HicksianandWalrasianDemand(p.71)SummaryofDuality(p.75)WelfareEvaluation(p.80)StructureDuality28DualityLetx*bethesolutiontotheutilitymaximizationproblemThenx*isalsothesolutiontotheexpenditureproblem

DualityLetx*bethesolution29IdentitiesofDualityTheidentities(p.60)IdentitiesofDualityTheident30HicksianDemandandExpenditureFunctionProposition3.G.1(p.68):[Proof]HicksianDemandandExpenditur31WalrasianDemandandIndirectUtilityFunctionRoy’sidentity(Proposition3.G.4,p.73):[Proof]WalrasianDemandandIndirect32TheCompensatedLawofDemand(p.62)(Proposition3.E.4)TheHicksiandemandfunctionsatisfiesthecompensatedlawofdemand:forallp’andp’’[Proof]TheCompensatedLawofDemand33TheHecksianandWalrasianDemandFunction(Proposition3.G.3,p.71)TheSlutskyEquation[Proof]TheHecksianandWalrasianDem34RelationshipbetweentheUMPandtheEMPSlutskyEquationRoy’sidentityRelationshipbetweentheUMPa35WelfareEvaluationTheequivalentvariation(EV)Thecompensatingvariation(CV)WelfareEvaluationTheequivale36ECON501LectureNote5ProducerChoice1ECON501LectureNote5Producer37StructureTechnologyandProductionSetProfitMaximizationProblemStructureTechnologyandProduc38DefinitionofProductionSet(p.128)Productionset:Transformationfunction:Transformationfrontier:Themarginalrateoftransformation:DefinitionofProductionSet(39TechnologieswithDistinctInputsandOutputs(p.129)Productionfunction:ThemarginalrateoftechnicalsubstitutionofinputlforinputkTechnologieswithDistinctInp40PropertiesofProductionSet(p.130)NonemptyClosedNofreelunchPossibilityofinactionFreedisposalIrreversibilityReturntoscale:nonincreasing,nondecreasing,constantAdditivity(freeentry)ConvexityPropertiesofProductionSet(41ProfitMaximization(p.135)Problem:Thefirstordercondition:Alternativeway:single-outputtechnologyProfitMaximization(p.135)42ProfitFunctionProfitfunction:Properties:(p.138)HomogeneousofdegreeofoneinpConvexinpNondecreasinginoutputprice,andnonincreasingininputpriceProfitFunctionProfitfunction43Demandfunction(supplyfunction)Properties:(p.138)HomogeneousofdegreeofzeroinpIfYisconvex,theny(p)isconvexsetforallp;ifYisstrictlyconvex,theny(p)issinglevalueHotellingLemma:

Demandfunction(supplyfuncti44TheLawofSupply(p.138)Thelawofsupply:quantitiesrespondinthesamedirectionaspricechange[Proof]TheLawofSupply(p.138)Thel45ECON501LectureNote6ProducerChoice2ECON501LectureNote6Producer46StructureCostMinimizationProblemDuality:ProductionFunctionandCostFunctionStructureCostMinimizationPro47CostMinimizationProblem(p.139)ProblemFirstordercondition:ConditionalfactordemandfunctionCostfunctionExample:theCobb-DouglasproductionfunctionCostMinimizationProblem(p.48CostFunction(p.141)PropertiesNondecreasinginqHomogeneousofdegreeofoneinwConcaveinwContinuousinwIff(.)ishomogeneousofdegreeofone,thenc(.)ishomogeneousofdegreeofoneinqCostFunction(p.141)Propert49ConditionalFactorDemandFunctionPropertyHomogeneousofdegreezeroinwIff(.)ishomogeneousofdegreeone,thenz(.)ishomogeneousofdegreeofoneinqShepard’slemma:

ConditionalFactorDemandFunc50ProfitMaximizationProblemProblem:Firstordercondition:ProfitMaximizationProblemPro51LongRunandShortRunCostFunctionMarginalcostAveragecostTheshortruncostfunctionThelinkagebetweenlongrunandshortruncostLongRunandShortRunCostFu52Duality:CostandProductionFunctionRecoveringtheproductionfunctionfromthecostfunctionDualityIsoquant:Theslopeofisoquant:Isocostcurve:Theslopeofisocost:Duality:CostandProductionF53ECON501LectureNote7ChoiceUnderUncertaintyECON501LectureNote7ChoiceU54StructureExpectedUtilityTheoryLotteryPreferenceoverLotteryTheExpectedUtilityFunctionTheExpectedUtilityTheoremMoneyLotteriesandRiskAversionMoneyLotteryRiskAversion:DefinitionRiskAversion:MeasurementStructureExpectedUtilityTheo55Lottery(p.168)Asimplelottery(Definition6.B.1)Acompoundlottery(Definition6.B.2)AreducedlotteryLottery(p.168)Asimplelotte56PreferenceoverLotteriesProperties(p.171)CompleteTransitiveContinuousIndependenceaxiomPreferenceoverLotteriesPrope57TheExpectedUtilityFunction(Definition6.B.5)TheutilityfunctionUhasanexpectedutilityformif:(Proposition6.B.1)AutilityfunctionUhasanexpectedutilityformifandonlyifitislinear:(Proposition6.B.2)SupposethatUisav.N-Mexpectedutilityfunction,thenU’isanotherv.N-Mfunctionifandonlyif:TheExpectedUtilityFunction(58TheExpectedUtilityTheorem(Proposition6.B.3):supposethattherationalpreferencerelationonthespaceoflotterysatisfiesthecontinuityandindependenceaxioms,thenthisrelationadmitsautilityrepresentationoftheexpectedutilityform.ProofTheExpectedUtilityTheorem(P59MoneyLotteriesMoneyLotteries:v.N-Mexpectedutilityfunction:MoneyLotteriesMoneyLotteries60RiskAversion:DefinitionThedecisionmakerisriskaverseifandonlyifThecertaintyequivalentofF(.)TheprobabilitypremiumRiskAversion:DefinitionThed61RiskAversionEquivalentStatements(p.187)Thedecisionmakerisriskaverse.u(.)isconcave.

Example:insuranceRiskAversionEquivalentStatem62MeasurementofRiskAversion(p.190)TheArrow-Prattcoefficientofabsoluteriskaversion(Definition6.C.3)Comparisonsacrossindividual(Proposition6.C.2)ComparisonsacrosswealthlevelsThecoefficientofrelativeriskaversion(Definition6.C.5)MeasurementofRiskAversion(63ECON501LectureNote9GameTheory1ECON501LectureNote9GameThe64StructureTheStructureofGameTheExtensiveFormRepresentationofaGameStrategiesTheNormalFormRepresentationofaGameDominantandDominatedStrategiesRationalizableStrategiesStructureTheStructureofGame65TheStructureofGameTheplayerTherulesTheoutcomesThepayoffTheStructureofGameTheplaye66TheExtensiveFormRepresentationofGame(p.221)Thegametree:examplesPerfectinformationTheExtensiveFormRepresentat67Strategies(p.228)Definition7.D.1:astrategyisacompletecontingentplanthatspecifieshowtheplayerwillactineverypossibledistinguishablecircumstancePurestrategy,Si:adeterministicstrategyStrategies(p.228)Definition68TheNormalFormRepresentation(p.230)Definition7.D.2:ExamplesTheNormalFormRepresentation69DominantandDominatedStrategies(p.236)Example:Prisoner’sDilemmaDefinition8.B.1,8B.2and8.B.3AstrictlydominantstrategyAstrictlydominatedstrategyAweaklydominatedstrategyIterateddeletionofstrictlydominatedstrategies,basedonprincipalofrationality,DominantandDominatedStrateg70RationalizableStrategies(p.242)Definition8.C.1:strategysiisabestresponseforplayeritohisrivals’strategiesif

Definition:thestrategiesthatsurvivetheiteratedremovalofstrategiesthatareneverbeabestresponseareknownasplayer’srationalizablestrategiesExample8.C.1RationalizableStrategies(p.71ECON501LectureNote10GameTheory2ECON501LectureNote10GameTh72StructureNashEquilibriumBayesianNashEquilibriumSequentialRationality,BackwardInduction,andSubgamePerfectionStructureNashEquilibrium73NashEquilibrium(p.246)Definition8.D.1:astrategyprofiles=(s1,…,sI)constitutesaNashequilibriumifforeveryi=1,…,I,ExamplesIntuitionNashEquilibrium(p.246)Def74BayesianNashEquilibrium(p.253)Agameofimperfectinformation:naturemakesthefirstmove,choosingrealizationsoftherandomvariablesthatdetermineeachplayer’spreferencetype,andeachplayerobservestherealizationofonlyhisownrandomvariable.Definition8.E.1:BayesianNashequilibrium:ExamplesBayesianNashEquilibrium(p.75SequentialRationality(p.268)Example:incrediblethreatTheprincipleofsequentialrationality:aplayer’sstrategyshouldspecifyoptimalactionsateverypointinthegametreeBackwardinductioninfinitegamesofperfectinformationSubgameperfectNashequilibrium:aprofileofstrategiesisaSPNEifitinducesaNashequilibriumineverysubgame.ExamplesSequentialRationality(p.26876ECON501LectureNote11MarketPowerECON501LectureNote11Market77StructureMonopolyPricingStaticModelsofOligopolyTheBertrandModelofPriceCompetitionTheCournotModelofQuantityCompetitionTheStackelbergModelofQuantityLeadershipThePriceLeadershipTheRepeatedBertrandModelStructureMonopolyPricing78MonopolyPricing(p.384)Monopolist’sdecisionproblemWelfarelossofmonopolyExampleMonopolyPricing(p.384)Monopo79BertrandModelofPriceCompetition(p.388)Thetwofirmssimultaneouslynametheirp1andp2.salesforfirmjaregivenby

Proposition12.C.1:ThereisauniqueNashequilibriumintheBertrandduopolymodel:bothfirmssettheirpricesequaltocost.BertrandModelofPriceCompet80CournotModelofQuantityCompetition(p.389)Firmj’smaximizationproblemgivenfirmk’soutputlevel:Proposition12.C.2:inanyNEoftheCournotduopolymodel,themarketpriceisgreaterthanc(thecompetitiveprice)andsmallerthanthemonopolyprice.ExampleCournotModelofQuantityComp81StackelbergModelofQuantityLeadershipTheleader’s(firm1)problem:Thefollower’s(firm2)problem:Theleader’sprofitwillbehigherthanCournotmodel,andlessthancollusionprofit.MarketpricewillbelowerthanCournotmodel,andhigherthancompetitiveprice.StackelbergModelofQuantity82PriceLeadershipThefollower’s(firm2)problem:Theleader’s(firm1)problem:theleaderfacesthe“residualdemandcurve”PriceLeadershipThefollower’s83TheInfinitelyRepeatedBertrandDuopolyGame(p.400)SetupofgameNashreversionstrategy:firmscooperateuntilsomeonedeviation,andanydeviationtriggersapermanentretaliationinwhichbothfirmssettheirpriceequaltocost.Proposition12.D.1:TheNashreversionstrategyconstituteaSPNEoftheinfinitelyrepeatedBertrandduopolygameifandonlyifTheInfinitelyRepeatedBertra84ECON501LectureNote12GeneralEquilibrium1ECON501LectureNote12General85StructureParetoOptimalityCompetitive(Walrasian)EquilibriumPureExchangeOne-Consumer,One-ProducerEconomyStructureParetoOptimality86ParetoOptimality(p.312)Structure:Iconsumers.JproducersandLgoods,aneconomicallocation:Feasibility:Definition10.B.2:AfeasibleallocationisParetooptimalifthereisnootherallocationsuchthat:ParetoOptimality(p.312)Struc87WalrasianEquilibrium(p.314)Definition10.B.3:Theallocation(x*,y*)andpricevectorp*constituteacompetitiveequilibriumifthefollowingconditionsaresatisfiedProfitMaximization:foreachfirm,y*solvesUtilityMaximization:foreachconsumer,x*solvesMarketclearing:foreachgoodlWalrasianEquilibrium(p.314)D88PureExchange(p.515)Basicsetup:noproductionUtilityMaximization:foreachconsumer,x*solvesMarketClearingTheWalrasianequilibrium:pricep*andallocationx*suchthatx*maximizestheconsumers’utilityunderbudgetconstraintPureExchange(p.515)Basicset89PureExchange:theEdgeworthBoxTheEdgeworthboxTheoffercurveTheWalrasianequilibriumintheEdgeworthboxExamplePureExchange:theEdgeworthB90PureExchange:WelfarePropertiesofWalrasianEquilibriaDefinition15.B.2:ParetooptimalintheEdgeworthboxParetosetandthecontractcurvePureExchange:WelfarePropert91TheOne-Consumer,One-ProducerEconomy(p.525)Basicsetup:oneconsumer,oneproducer,twogoods,thelaboroftheconsumerandaconsumptiongoodproducedbythefirmsTheconsumer’sutilitymaximizationproblem:Theproducer’sprofitmaximizationproblem:Theoptimallabordemandisz(p,w);theoutputisq(p,w);theprofitisπ(p,w)TheOne-Consumer,One-Producer92TheOne-Consumer,One-ProducerEconomyConsumptionmarketclearing:Labormarketclearing:AWalrasianequilibrium:theallocation(x1*,x2*)andpricevector(p*,w*)whichmaximizetheconsumer’sutilityandproducer’sprofitandclearbothconsumptionmarketandlabormarket.TheOne-Consumer,One-Producer93ECON501LectureNote13GeneralE