《微观经济学microeconomics》英文版全套课件

微观经济学

Microeconomics

ECON501LectureNote1

PreferenceandChoiceStructurePreferencerelationChoicerulesThelinkbetweenpreferenceandchoicePreferenceRelationsTheRationalPreferenceCompletenessTransitivityUtilityFunctionDefinition:afunctionuisautilityfunctionrepresentingpreferencerelationif

ApreferencerelationcanberepresentedbyautilityfunctiononlyifitisrationalChoiceRulesAchoicestructureBudgetsetsAchoiceruleTheweakaxiomofrevealedpreference(WARP):ifxisrevealedatleastasgoodasy,thenycannotberevealedpreferredtoxTheLinkBetweenPreferenceandChoiceIfthepreferencerelationisrational,thenthechoicestructuresatisfiestheweakaxiom.IfthechoicestructuresatisfiestheWARPandβincludesallsubsetsofXofuptothreeelements,thenthereisacorrespondingrationalpreferencerelation.ECON501LectureNote2

ConsumerTheory1(TextbookChapter2and3)StructureConsumerChoice(Chapter2)BudgetsetWalrasiandemandfunctionComparativestaticsTheweakaxiomofrevealedpreferenceandthelawofdemandPreference(Chapter3)ThebasicpropertiesofpreferenceExistenceofutilityfunctionTheBudgetsetCommoditiesThephysicalconstraintsandtheconsumptionsetTheeconomicconstraint:TheWalrasianbudgetset(Definition2.D.1)ConvexityofWalrasianbudgetset:proofConsumer’sChoiceTheconsumer’sproblem:tochooseaconsumptionbundlexfromtheWalrasianbudgetset.WalrasianDemandFunctionAssumption:Itishomogeneousofdegreeofzero(Definition2.E.1):individual’schoicedependsonlyonthesetoffeasiblepoints.ItsatisfiesWalras’law(Definition2.E.2):theconsumerfullyexpendshiswealth.Exercise2.E.1ComparativeStatics–WealthEffectsTheconsumer’sEngelfunctionThewealtheffectNormalgoodsandinferiorgoodsComparativeStatics–PriceEffectsThedemandcurve(Figure2.E.2)Theoffercurve(Figure2.E.3and2.E.4)ThepriceeffectTheWeakAxiomofRevealedPreference(Definition2.F.1)TheWalrasiandemandfunctionsatisfiedtheweakaxiomofrevealedpreferenceif:Intuition:Figure2.F.1TheImplicationofWARPTwoeffectsofpricechange:substitutioneffectandincomeeffect(Slutsky)compensatedpricechangesProposition2.F.1:TheWalrasiandemandfunctionsatisfiedtheWARPifandonlyif:foranycompensatedpricechangefrominitial(p,w)to(p’,w’)=(p’,p’x(p,w)),wehaveThelawofdemandBasicPropertiesofPreferenceRational(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)ExistenceofAUtilityFunctionProposition3.C.1:supposethattherationalpreferencerelationonXiscontinuous,thenthereisacontinuousutilityfunctionthatrepresentthispreference

ECON501LectureNote3

ConsumerTheory2(TextbookChapter3)StructureUtilityMaximizationProblemUtilitymaximizationWalrasiandemandfunctionIndirectutilityfunctionExpenditureMinimizationProblemExpenditureminimizationExpenditurefunctionHicksiandemandfunctionUtilityMaximizationProblemTheproblem:TheLagrangianfortheconsumer’sconstrainedoptimization:Firstordercondition:Solution:WalrasiandemandfunctionUtilityMaximization--ExampleExample3.D.1:thetransformedCobb-DouglasUtilityFunctionWalrasianDemandFunctionAssumption:supposeacontinuousutilityfunctionrepresentingalocallynonsatiatedpreferencerelationPropertiesofWalrasiandemandfunction:ItishomogeneousofdegreeofzeroItsatisfiesWalras’lawConvexityofpreferenceimpliesconvexityofx(p,w),strictconvexityofpreferencesimpliesthatx(p,w)issingle-valuedProofIndirectUtilityFunctionDefinition:Properties:HomogeneousofdegreeofzeroStrictlyincreasinginwandnonincreasinginpQuasiconvexinpandwContinuousProofExpenditureMinimizationProblemTheproblem:Thefirstordercondition:Thesolution:Hicksiandemandfunctionh(p,u)ExpenditureFunctionExpenditurefunctionProperties:HomogeneousofdegreeofoneinpStrictlyincreasinginuandnondecreasinginpConcaveinpContinuousinpanduProofHicksianDemandFunctionPropertiesHomogenousofdegreeofzeroinpNoexcessutilityConvexity/uniquenessProofExample3.E.1:HicksiandemandfunctionandexpenditurefunctionfortheCobb-DouglasutilityfunctionECON501LectureNote4ConsumerTheory3StructureDualityIdentitiesofDuality(p.60)HicksianDemandandExpenditureFunction(p.68)WalrasianDemandandIndirectUtilityFunction(p.73)HicksianandWalrasianDemand(p.71)SummaryofDuality(p.75)WelfareEvaluation(p.80)DualityLetx*bethesolutiontotheutilitymaximizationproblemThenx*isalsothesolutiontotheexpenditureproblem

IdentitiesofDualityTheidentities(p.60)HicksianDemandandExpenditureFunctionProposition3.G.1(p.68):[Proof]WalrasianDemandandIndirectUtilityFunctionRoy’sidentity(Proposition3.G.4,p.73):[Proof]TheCompensatedLawofDemand(p.62)(Proposition3.E.4)TheHicksiandemandfunctionsatisfiesthecompensatedlawofdemand:forallp’andp’’[Proof]TheHecksianandWalrasianDemandFunction(Proposition3.G.3,p.71)TheSlutskyEquation[Proof]RelationshipbetweentheUMPandtheEMPSlutskyEquationRoy’sidentityWelfareEvaluationTheequivalentvariation(EV)Thecompensatingvariation(CV)ECON501LectureNote5ProducerChoice1StructureTechnologyandProductionSetProfitMaximizationProblemDefinitionofProductionSet(p.128)Productionset:Transformationfunction:Transformationfrontier:Themarginalrateoftransformation:TechnologieswithDistinctInputsandOutputs(p.129)Productionfunction:ThemarginalrateoftechnicalsubstitutionofinputlforinputkPropertiesofProductionSet(p.130)NonemptyClosedNofreelunchPossibilityofinactionFreedisposalIrreversibilityReturntoscale:nonincreasing,nondecreasing,constantAdditivity(freeentry)ConvexityProfitMaximization(p.135)Problem:Thefirstordercondition:Alternativeway:single-outputtechnologyProfitFunctionProfitfunction:Properties:(p.138)HomogeneousofdegreeofoneinpConvexinpNondecreasinginoutputprice,andnonincreasingininputpriceDemandfunction(supplyfunction)Properties:(p.138)HomogeneousofdegreeofzeroinpIfYisconvex,theny(p)isconvexsetforallp;ifYisstrictlyconvex,theny(p)issinglevalueHotellingLemma:

TheLawofSupply(p.138)Thelawofsupply:quantitiesrespondinthesamedirectionaspricechange[Proof]ECON501LectureNote6ProducerChoice2StructureCostMinimizationProblemDuality:ProductionFunctionandCostFunctionCostMinimizationProblem(p.139)ProblemFirstordercondition:ConditionalfactordemandfunctionCostfunctionExample:theCobb-DouglasproductionfunctionCostFunction(p.141)PropertiesNondecreasinginqHomogeneousofdegreeofoneinwConcaveinwContinuousinwIff(.)ishomogeneousofdegreeofone,thenc(.)ishomogeneousofdegreeofoneinqConditionalFactorDemandFunctionPropertyHomogeneousofdegreezeroinwIff(.)ishomogeneousofdegreeone,thenz(.)ishomogeneousofdegreeofoneinqShepard’slemma:

ProfitMaximizationProblemProblem:Firstordercondition:LongRunandShortRunCostFunctionMarginalcostAveragecostTheshortruncostfunctionThelinkagebetweenlongrunandshortruncostDuality:CostandProductionFunctionRecoveringtheproductionfunctionfromthecostfunctionDualityIsoquant:Theslopeofisoquant:Isocostcurve:Theslopeofisocost:ECON501LectureNote7ChoiceUnderUncertaintyStructureExpectedUtilityTheoryLotteryPreferenceoverLotteryTheExpectedUtilityFunctionTheExpectedUtilityTheoremMoneyLotteriesandRiskAversionMoneyLotteryRiskAversion:DefinitionRiskAversion:MeasurementLottery(p.168)Asimplelottery(Definition6.B.1)Acompoundlottery(Definition6.B.2)AreducedlotteryPreferenceoverLotteriesProperties(p.171)CompleteTransitiveContinuousIndependenceaxiomTheExpectedUtilityFunction(Definition6.B.5)TheutilityfunctionUhasanexpectedutilityformif:(Proposition6.B.1)AutilityfunctionUhasanexpectedutilityformifandonlyifitislinear:(Proposition6.B.2)SupposethatUisav.N-Mexpectedutilityfunction,thenU’isanotherv.N-Mfunctionifandonlyif:TheExpectedUtilityTheorem(Proposition6.B.3):supposethattherationalpreferencerelationonthespaceoflotterysatisfiesthecontinuityandindependenceaxioms,thenthisrelationadmitsautilityrepresentationoftheexpectedutilityform.ProofMoneyLotteriesMoneyLotteries:v.N-Mexpectedutilityfunction:RiskAversion:DefinitionThedecisionmakerisriskaverseifandonlyifThecertaintyequivalentofF(.)TheprobabilitypremiumRiskAversionEquivalentStatements(p.187)Thedecisionmakerisriskaverse.u(.)isconcave.

Example:insuranceMeasurementofRiskAversion(p.190)TheArrow-Prattcoefficientofabsoluteriskaversion(Definition6.C.3)Comparisonsacrossindividual(Proposition6.C.2)ComparisonsacrosswealthlevelsThecoefficientofrelativeriskaversion(Definition6.C.5)ECON501LectureNote9GameTheory1StructureTheStructureofGameTheExtensiveFormRepresentationofaGameStrategiesTheNormalFormRepresentationofaGameDominantandDominatedStrategiesRationalizableStrategiesTheStructureofGameTheplayerTherulesTheoutcomesThepayoffTheExtensiveFormRepresentationofGame(p.221)Thegametree:examplesPerfectinformationStrategies(p.228)Definition7.D.1:astrategyisacompletecontingentplanthatspecifieshowtheplayerwillactineverypossibledistinguishablecircumstancePurestrategy,Si:adeterministicstrategyTheNormalFormRepresentation(p.230)Definition7.D.2:ExamplesDominantandDominatedStrategies(p.236)Example:Prisoner’sDilemmaDefinition8.B.1,8B.2and8.B.3AstrictlydominantstrategyAstrictlydominatedstrategyAweaklydominatedstrategyIterateddeletionofstrictlydominatedstrategies,basedonprincipalofrationality,RationalizableStrategies(p.242)Definition8.C.1:strategysiisabestresponseforplayeritohisrivals’strategiesif

Definition:thestrategiesthatsurvivetheiteratedremovalofstrategiesthatareneverbeabestresponseareknownasplayer’srationalizablestrategiesExample8.C.1ECON501LectureNote10GameTheory2StructureNashEquilibriumBayesianNashEquilibriumSequentialRationality,BackwardInduction,andSubgamePerfectionNashEquilibrium(p.246)Definition8.D.1:astrategyprofiles=(s1,…,sI)constitutesaNashequilibriumifforeveryi=1,…,I,ExamplesIntuitionBayesianNashEquilibrium(p.253)Agameofimperfectinformation:naturemakesthefirstmove,choosingrealizationsoftherandomvariablesthatdetermineeachplayer’spreferencetype,andeachplayerobservestherealizationofonlyhisownrandomvariable.Definition8.E.1:BayesianNashequilibrium:ExamplesSequentialRationality(p.268)Example:incrediblethreatTheprincipleofsequentialrationality:aplayer’sstrategyshouldspecifyoptimalactionsateverypointinthegametreeBackwardinductioninfinitegamesofperfectinformationSubgameperfectNashequilibrium:aprofileofstrategiesisaSPNEifitinducesaNashequilibriumineverysubgame.ExamplesECON501LectureNote11MarketPowerStructureMonopolyPricingStaticModelsofOligopolyTheBertrandModelofPriceCompetitionTheCournotModelofQuantityCompetitionTheStackelbergModelofQuantityLeadershipThePriceLeadershipTheRepeatedBertrandModelMonopolyPricing(p.384)Monopolist’sdecisionproblemWelfarelossofmonopolyExampleBertrandModelofPriceCompetition(p.388)Thetwofirmssimultaneouslynametheirp1andp2.salesforfirmjaregivenby

Proposition12.C.1:ThereisauniqueNashequilibriumintheBertrandduopolymodel:bothfirmssettheirpricesequaltocost.CournotModelofQuantityCompetition(p.389)Firmj’smaximizationproblemgivenfirmk’soutputlevel:Proposition12.C.2:inanyNEoftheCournotduopolymodel,themarketpriceisgreaterthanc(thecompetitiveprice)andsmallerthanthemonopolyprice.ExampleStackelbergModelofQuantityLeadershipTheleader’s(firm1)problem:Thefollower’s(firm2)problem:Theleader’sprofitwillbehigherthanCournotmodel,andlessthancollusionprofit.MarketpricewillbelowerthanCournotmodel,andhigherthancompetitiveprice.PriceLeadershipThefollower’s(firm2)problem:Theleader’s(firm1)problem:theleaderfacesthe“residualdemandcurve”TheInfinitelyRepeatedBertrandDuopolyGame(p.400)SetupofgameNashreversionstrategy:firmscooperateuntilsomeonedeviation,andanydeviationtriggersapermanentretaliationinwhichbothfirmssettheirpriceequaltocost.Proposition12.D.1:TheNashreversionstrategyconstituteaSPNEoftheinfinitelyrepeatedBertrandduopolygameifandonlyifECON501LectureNote12GeneralEquilibrium1StructureParetoOptimalityCompetitive(Walrasian)EquilibriumPureExchangeOne-Consumer,One-ProducerEconomyParetoOptimality(p.312)Structure:Iconsumers.JproducersandLgoods,aneconomicallocation:Feasibility:Definition10.B.2:AfeasibleallocationisParetooptimalifthereisnootherallocationsuchthat:WalrasianEquilibrium(p.314)Definition10.B.3:Theallocation(x*,y*)andpricevectorp*constituteacompetitiveequilibriumifthefollowingconditionsaresatisfiedProfitMaximization:foreachfirm,y*solvesUtilityMaximization:foreachconsumer,x*solvesMarketclearing:foreachgoodlPureExchange(p.515)Basicsetup:noproductionUtilityMaximization:foreachconsumer,x*solvesMarketClearingTheWalrasianequilibrium:pricep*andallocationx*suchthatx*maximizestheconsumers’utilityunderbudgetconstraintPureExchange:theEdgeworthBoxTheEdgeworthboxTheoffercurveTheWalrasianequilibriumintheEdgeworthboxExamplePureExchange:WelfarePropertiesofWalrasian

EquilibriaDefinition15.B.2:ParetooptimalintheEdgeworthboxParetosetandthecontractcurveTheOne-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-ProducerEconomyConsumptionmarketclearing:Labormarketclearing:AWalrasianequilibrium:theallocation(x1*,x2*)andpricevector(p*,w*)whichmaximizetheconsumer’sutilityandproducer’sprofitandclearbothconsumptionmarketandlabormarket.ECON501LectureNote13GeneralEquilibrium2StructureBasicSetupTheEquilibriuminFactorMarketThe