中级微观经济学

Chapter

2005 ChapterChapterWalterNicholson,Microeconomic8thEdition,Southwestern,2002（中文 ModernApproach,6thEdition,Norton,2003JamesM.HendersonandR.E.Quandt,ApproachMcGraw-HillBookCo1980。(该书第八章垄断10第十一章市场失灵与ter Chapter ChapterChapterChapter

2003 ChapterChapterChapterone1.1Defining1.2EconomicTheoriesand1.3TheMathematicsof1.4Demand-SupplyOutlineofThisChapterThischaptermainlyprovidesomebackgroundforthestudyofmicroeconomics.WhatisThegeneralapproachusedinHoweconomistsdeviseandverifysimplemodelsofeconomicactivity.PositiveAnalysisandNormativeThebasicSupply-DemandSeveralMathematicalMethodsthatcanbeusedtosolvemaximization(andminimization)problem.ReadingsaboutthisNicholson:Chapter1,2,P1-Zhang:Chapter1,P1-Chapterone1.1Defining1.2EconomicTheoriesand1.3TheMathematicsof1.4Demand-SupplyDefiningThestudyoftheallocationofscarceresourcesamongalternativeendusesAlternativeAlternativeendDefiningMicroeconomicsEconomicsiscomposedoftwobranches:DefiningMicroeconomicsMicroeconomicsdealsBehaviorofindividualunits——WhenMaximizingHowwechoosewhattoBehaviorofindividualunits——WhenMaximizingHowwechoosewhattoDefiningMicroeconomicsMicroeconomicsdealsMarkets:TheinteractionofconsumersandproducersOutputMarket(ProductInputMarket(FactorDefiningMacroeconomicsdealsAnalysisofaggregateissues（总量的问题）:DefiningTheLinkage(关系BetweenMicroandMicroeconomicsisthefoundationofmacroeconomicanalysisChapterone1.1Defining1.2EconomicTheoriesand1.3TheMathematicsof1.4Demand-SupplyTheoriesandTheoriesandTheoriesareusedtoexplainobservedphenomenaintermsofasetofbasicrulesandassumptions.ForTheTheoryoftheTheTheoryofConsumerTheoriesandMicroeconomicAnalysis—— SimpletheoreticaldescriptionsthatcapturetheessentialsofhowtheeconomyworksTheoriesandGeneralFeaturesofEconomic1.TheCeterisParibusOtherthings2OptimizationAssumption（最优化假设Consumers——Maximizingtheirownwell-Firms——MaximizingGovernmentregulator——MaximizingpublicTheoriesandGeneralFeaturesofEconomic3.PositiveandNormativePositiveAnalysis(实证分析)istheuseoftheoriesandmodelstoexplainhowresourcesactuallyareallocatedinaneconomyTrytoanswer:Whatis（是什么ForWhatwillbetheimpactofanimportquota（进口配额）onforeigncars?TheoriesandPositiveandNormativeNormativeanalysis（规范分析）istheoriesthatmakevaluejudgmentsabouthowtheeconomicresourceshouldbeallocatedTrytoanswer:“Whatoughttobe?”（应该ForWhethershouldanimportquota（beusedonforeigncarsornot?ThePositive-NormativeDistinctionbetweentheoriesthatseektoexplaintheworldasitisandtheoriesthatpostulatethewaytheworldshouldTomanyeconomists,thecorrectrolefortheoryistoexplainthewaytheworldis(positive)ratherthanthewayitshouldbePositiveeconomicsistheprimaryofthe

Chapter ChapterChapterHowEconomistsVerifyTheoreticalModelsTwomethodsareDirectApproach（直接验证法）:TestingAssumptions:VerifyingeconomicmodelsbyexaminingvalidityoftheassumptionsonwhichtheyarebasedIndirectApproach(间接检验法)TestingPredictions:Verifyingeconomicmodelsbyaskingiftheycanaccuratelypredictreal-worldeventsTestingOneapproachwouldbetodetermineiftheassumptionsarereasonableTheobviousproblemisthatpeoplehavedifferingopinionregardingreasonableEmpiricalevidencecanalsobeResultsofsuchmethodshavehadproblemssimilartothosefoundinopinionTestingEconomists,suchasMiltonFriedmanarguethatalltheoriesrequireunrealisticassumptionsThetheoryisonlyusefulifitcanbeusedtopredictreal-worldeventsEveniffirmsstatetheydon’tmaximizeprofits,iftheirbehaviorcanbepredictedbyusingthisassumption,thetheoryisChapterone1.1Defining1.2EconomicTheoriesand1.3BasicDemand-Supply1.4TheMathematicsofAPopularEconomic“Evenyourparrotcanbecomeaneconomist—justteachittosay‘supplyanddemand.’”TheBasicSupply-DemandTheSupply-DemandAmodeldescribinghowagood’spriceisdeterminedbythebehavioroftheindividual’swhobuythegoodandthefirmsthatsellit.Economistsarguethatmarketbehaviorcangenerallybeexplainedbythismodelthatcapturestherelationshipbetweenconsumers’preferencesandfirms’costs.BasicAssumptions(基本假设)abouttheSupply-DemandModelRationalBehaviorAssumption（理EachpersontriestochoosethebestalternativeavailabletohimorherScarceResourceAssumption（资源Marginalism（边际主义）andMarshall’sModelofSupplyandDemandRicardo’smodelwasunabletoexplainthefallintherelativepricesofgoodduringthenineteenthcenturysoamoregeneralmodelwasneededEconomistsarguedthewillingnessofpeopletopayforagoodwilldeclineastheyhavemoreofitMarginalismandMarshall’sModelofSupplyandDemandPeoplewillbewillingtoconsumemoreofagoodonlyifthepriceislowerThefocusofthemodelwasonthevalueofthelast,ormarginal,unitpurchasedAlfredMarshall(1842-1924)showedhowtheforcesofdemandandsupplyFIGURE1.3:TheMarshallSupply-DemandCross

perMarginalismandMarshall’sModelofSupplyandDemandThedemandcurveshowstheamountpeoplewanttobuyateachpriceandisnegativelyslopedreflectingthemarginalismprincipleTheupwardslopingsupplycurvereflectstheideaofincreasingcostofmakingonemoreunitofagoodastotalproductionMarginalismandMarshall’sModelofSupplyandDemandSupplyreflectsincreasingmarginalcostsanddemandreflectsdecreasingmarginalusefulnessMarketInFigure1.3,thedemandandsupplycurveintersectatthemarketequilibriumpointP*,Q*P*istheequilibriumprice:ThepriceatwhichthequantitydemandedbybuyersofagoodisequaltothequantitysuppliedbysellersofthegoodFIGURE1.3:TheMarshallSupply-DemandCross

Equilibrium

perMarketBothdemandersandsuppliersaresatisfiedatthisprice,sothereisnoincentiveforeithertoaltertheirbehaviorunlesssomethingelsehappensMarshallcomparedtherolesofsupplyanddemandinestablishingmarketequilibriumtothetwobladesofapairofscissorsworkingtogetherinordertomakeacutNonequilibriumIfsomethingcausesthepricetobesetaboveP*,demanderswouldwishtobuylessthanQ*whilesupplierswouldproducemorethanQ*IfsomethingcausesthepricetobesetbelowP*,demanderswouldwishtobuymorethanQ*whilesupplierswouldproducelessthanQ*ChangeinMarketEquilibrium:IncreasedDemandFigure1.4showsthecasewherepeople’sdemandforthegoodincreasesasrepresentedbytheshiftofthedemandcurvefromDtoD’AnewequilibriumisestablishedwheretheequilibriumpricehasincreasedtoP**FIGURE1.4:AnincreaseinDemandAltersEquilibriumPriceand perChangeinMarketEquilibrium:decreaseinSupplyInFigure1.5thesupplycurvehasshiftedleftwardreflectingadecreaseinsupplybroughtaboutbecauseofanincreaseinsuppliercosts(sayanincreaseinwages)AtthenewequilibriumpriceP**consumersrespondbyreducingquantitydemandedalongtheDemandcurveDFIGURE1.5:AshiftinSupplyAltersEquilibriumPriceandQuantity

perFIGURE1.5:AshiftinSupplyAltersEquilibriumPriceandQuantity Q**

perHowWeVerifytheSupply-DemandModelsTwomethodsareTestingAssumptions:VerifyingeconomicmodelsbyexaminingvalidityoftheassumptionsonwhichtheyarebasedTestingPredictions:Verifyingeconomicmodelsbyaskingiftheycanaccuratelypredictreal-worldeventsAnExperimentalDoubleAuction（双方拍BuyersattributedmarginalSellersattributedmarginalBuyersonlyknowownSellersonlyknowowncostshighestbidslowestaskstradingprices….madeDoubleAuction:Buyers’DoubleAuction:Sellers’

DoubleAuction:AggregateDemandandSupply:(marginalvaluesgivedemandfunction&Marginalcostsgivesupplyfunction)

DoubleAuction:--

DoubleAuction:--

DoubleAuction:

Competitive

Chapterone1.1Defining1.2EconomicTheoriesand1.3BasicDemand-Supply1.4TheMathematicsofTheMathematicsof（数学的最优化问题OptimizationofEconomicTypeofUnconstrainedOptimization无约束的最优化UnconstrainedOptimization（有约束的最优化UnconstrainedFunctionofOneVaribale(一元函数Forexample dxxSecond-OrderCondition二阶条件ford2 dx2

x Unconstrained2.FunctionofSeveralVariables（多元F.O.CforMax.(Min.)S.E.CForHessianMatrix(海赛矩阵)forthisfunctionisnegative(positive)semidefinite(负半定)（正半ConstrainedConstrainedMAX.S.t.ConstructLagrangeChapterChapterTheLastSeptember.4,ChapterChapterConsumerBehaviorandDemandTheory(消费者行为与需求理论2005ThisChapterwill2.1Preferenceand2.2UtilityMaximizationand2.3IncomeandSubstitution2.4MarketDemandandReadingsaboutthisNicholson:Chapter2-Zhang:ChapterOutlineofToday’s2.1PreferenceandAssumptionofConsumer’sFromPreferencetoUtilityCharacteristicofIndifferenceConsumerConsumer’sRationalityinBasicbehavioralpostulate:Maximizinghiswell-Consumer’soptimizationisconstrainedbyhisincomeortimeDecision-makerchoosesbestavailableSo,tomodelconsumerchoicemustmodelconsumerpreferencesDefiningWhenanindividualreportsthat“XispreferredtoY,”itistakentomeanthatallthingsconsidered,heorshefeelbetteroffundersituationXthanundersituationY.Note:X,orYiscalledabundleofconsumptiongoods消费品束或组合)HowtoExpressPreferenceRelations(1)BundlesofconsumptionX(x1

x2

Y(y1

y2IfbundleXispreferredto

(x1,

x2)

y2IfbundleYispreferredto

y2)

(x1

x2IfconsumerindifferentbetweenXand

y2)

(x1,

x2Forexample,x1=5bananas,x2=6oranges,y1=3coconutsandy2=2packetsofbiscuitsHowtoExpressPreferenceConsumerscancomparetwodifferentconsumptionbundles,Xandy:strictpreference（严格偏好 XfYweakpreference（弱偏好）Xindifference:X~PreferenceIfXYandYX,thenIfXYbutnotYX,thenXHowtoExpressPreferenceTheseareordinalrelations（序Onlyrankalternativebundlesbyorder(e.g.first,second,…)Donotspecifymagnitude（数量）ofpreferenceAssumptionsofConsumer’s Assumption1:Completeness（完备性假设）IfXandYareanysituations,theindividualcanalwaysspecifyexactlyoneofthefollowingthree“XispreferredtoY”,

(x1,x2)f(

y2“YispreferredtoX”,

(x1

x2)p

y1

y2“XandYareequallyattractive”,

~(

y2CompletepreferencesmeansconsumercanalwaysmakeaclearchoiceoveranytwobundlesAssumptionsofConsumer’sAssumption2:Transitivity（传递性假设）ifanindividualreportsthat“XispreferredtoYandthatYispreferredtoZ,thenheorshemustalsoreportthat“XispreferredtoZ” (1

,

TransitivitymeansaconsumerschoicesmustbelogicallyconsistentAssumptionsofConsumer’s xAssumption4:NonSatiationorMoreisgood.（非饱和性假设）Aneconomicgoodisonethatyieldspositivebenefitstopeople.Thus,ofagoodis,bydefinition,better.(多多益AssumptionsofConsumer’sAssumption5Continuity（连续ifanindividualreportsthat“XispreferredtoY”thensituationssuitably“closeto”XmustalsobepreferredtoY”Continuity:smallbundlechangescauseonlysmallchangestothepreferenceFromPreferencetoUtilityIfconsumerpreferencesNon-Continuous(noThen,canberepresentedbyacontinuousutilityfunction.AutilityfunctionU(xrepresentsapreferencerelationifandonlyif(当且仅当):x’> U(x’)>x’<x” U(x’)<x’ U(x’)=TheutilityfunctionmustpreservethepreferenceorderingUtilityUtilityisanordinal(ordering)IfU(x)=6andU(y)=2,thenx>yButxnotpreferredthreetimesasmuchasyGeneralExpressionforUtilityweassumethatapersonreceivesutilityfromtheconsumptionofngoodsX1,X2,….Xn,whichwecanshowinfunctionalnotationbyUtilityU(X1,X2LXn;otherTheotherthingsthatappearafterthesemicolonareassumedtobeheldconstant. DefiningMarginalUtility(边际效用Marginalutility（MU）:ChangeinutilityfromsmallchangeinonecommodityholdingothercommoditiesMU1

u(

x2,Lxn

u(

x2,LxnMU1

u(x1,x2,Lxn

MU2

u(x1,x2,Lxn

u(x1,x2,Lxn Non-uniquenessofUtilityU(A)=5andU(B)=4U(A)=1,000,000andU(B)=IneithercasethenumbersimplythatAispreferredtoB.Itshowthatwecanexpressthesamepreferencerelationsbythedifferentutilityfunctions.Non-uniquenessofUtilityEachofthethreeutilityfunctionsranksthebundlesinsameThepreferenceorderingunaffectedbyamonotonictransformation(单调变换)oftheutilityfunctionNon-uniquenessofUtility（3）ThereisnouniqueutilityfunctionrepresentationofapreferencerelationSupposeU(x1,x2)=Againconsiderbundles(4,1),(2,3),U(2,3)=6>U(4,1)=U(2,2)=Or,supposeV(x1,x2)=U2=x2xThenV(2,3)=36>U(4,1)=U(2,2)=Vpreservessameorder,reflectssameNon-uniquenessofUtilityOrW(x1,x2)=2U+10=2x1x2Forsamebundles(4,1),(2,3),W(2,3)=22>U(4,1)=U(2,2)=Again,preservessameordering,representssamepreferencesTrueforanymonotonic(strictlyincreasing)transformation（严格递增的单调变换）ofU(x1,x2)MonotonicTransformationoftheMonotonic Non- TheThebelowareexamplesofCobb-Douglasu(x1

x2)

u(x1

x2

u(x,x)x2x2(xx)2

u(x,x)xcxd

canddareconstantsreflectingtheimportanceofthatcommodityNoteforlater:Wecanalwaysfindamonotonictransformationsuchthat

u(x,

)xaabove

UtilityFunctionsandIndifferenceCurve(无差异曲线)Utilityisanordinal(ordering)IfU(x)=6andU(y)=2,thenx>ButxnotpreferredthreetimesasmuchasIndifferencecurve(set):allequallypreferredEqualpreferencesameutilityTherefore,allbundlesonanindifferencecurvehavesameutilitylevelUtilityFunctionsandIndifferenceCurvesSupposebundles(4,1)and(2,2)areontheindifferencecurvewithutilitylevelUBundle(2,3)isintheindifferencecurvewithutilitylevelU6.ImpliesindifferenceUtilityFunctionsandIndifference UtilityFunctionsandIndifferenceOrcouldvisualizeinthreePlotconsumptionbundlesinhorizontalPlottheutilitylevelonaverticalStartwithseveralAddindifferencecurvesthroughAddmoreindifferencecurvestorepresentallpreferencesoverallconsumptionUtilityFunctionsandIndifferenceCurves3-Dplot（三维图）ofconsumptionutilitylevelsfor3bundlesU(2,3)=U(2,2)=U(4,1)=UtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceLetorangetogreenrepresentincreasingutilitylevelsCancompletelyrepresentstheconsumer’spreferencesin3-DThisisan“indifferencemap”thatfullyrepresentsautilityfunctionUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceCurvesUtilityFunctionsandIndifferenceTheCharacteristicsoftheIndifferenceCurve1.Therearemany(orcountless)indifferencecurvesintheX-Yplane,inwhicheachpointmusthaveanindifferencecurvepassingthroughit(byassumption5)2.Anindifferencecurveaboveandtotherightofanotherrepresentspreferredcombinationofcommodities.(byassumption4).TheCharacteristicoftheIndifferenceCurve3.Anindifferencecurvehasnegativeslope(byassumption4).4.Indifferencecurvecanneverintersect(byassumption3and4)5.TheShapeofindifferencecurveisconvextotheOrigin（凸向原点）.byDiminishingmarginalratesofsubstitution.Theslopeofandifferencecurvediminishesaswemovefromlefttorightalongitslength.FigureforTwoIndifferenceCurvesCannotIntersectTransitivityandNon-satiationofpreferencesimpliesindifference cannottheMarginalRateofMarginalRateofSubstitution(MRS):Therateatwhichanindividualiswillingtoreduceconsumptionofonegoodwhenheorshegetsonemoreunitofanothergoodinordertoholdhisorherutilityconstant.MRSisalsothenegativeoftheslopeofanindifferencecurve.TheMRSbetweenpointsAandBonU1inFigureofnextpageis(approximately)2.FIGURE:IndifferenceCurveandMRS

dd

U/U/ MarginalUtilitiesandtheTheequationofanindifferencecurveisU(x1,x2)k,aconstantTotallydifferentiatingthisidentity

dx1

x2

dx2

0,

MU(x1

U/x2

MU(x2ExampleofMarginalUtilitiesandMRSSupposeU(x1,x2)=x1x2.

(1)(x2)x2(x1)(1)

dd

U/U/

x2ExampleofMarginalUtilitiesandMRSU(x,x)=xx x MRS(1,8)=8/1= MRS(6,6)=6/6=U=U= MRSforQuasi-linearUtilityQuasi-linearutilityU(x1,x2)=f(x1)+U

f(x U

U/

d1

U/MRSforQuasi-linearUtility MRS

EachcurveisashiftedcopyoftheMRS=MRSisalonganylineforwhichx1is MonotonicTransformationsandMRSMonotonictransformationofUdoesnotchangeunderlyingpreferencestructureExample:U(x1,x2)=x1x2withMRS= ConsiderV=U2,orV(x1,x2)=x2x V/ 2x MRS

V/ 2x2x whichisthesameastheMRSforMonotonictransformationdoesnotchangeSpecialUtilityFunctionsandTheirIndifferenceDiminishingMRSAlonganIndifferenceExample:PerfectSupposegoodsareperfectsubstitutes，forexample,CokeandPepsi;redpencilandbluepencil,etc.ConsumercaresonlyabouttotalofbothSo,preferencescanberepresentedbyutilityfunctionoftheformV(x1,x2)=x1+AlonganIC,utilityisconstant(k),x2=k–Linearwithslopeof-PerfectSubstitutesx1+x2=x1+x2=x1+x2=V(x1,x2)=x1+ Perfectsubstitutes(Linearu(x1,x2)ax1

MU1

MU2Example:PerfectSupposegoodsareperfectcomplements,e.g.LeftShoeandRightConsumercanusegoodsonlyinGoodsconsumedinfixedCanberepresentedbyutilityfunctionW(x1,x2)=min{x1,x2}.Gives“rightangle”（直角）IC’sverticesonraythroughthePerfectComplementsIndifferenceCurves

W(x1,x2)=min{x1,x2}min{x1,x2}=8min{x1,x2}=min{x1,x2}=indifferencecurvesslope

SmokingabadDrinkingagoodIndifferencecurvespositiveslopeNeedmoreSmokingtocompensateforacceptingmoreDrinkingANeutralGood（中性物品Li’sMyExample:Cobb-DouglasUtilityCobb-DouglasutilityfunctionhasU(x1,x2)=x1ax2b,a>0,b>U(x1,x2)=x11/2 (a=b=V(x1,x2)=x1 (a=1,b=Cobb-DouglasIndifferenceAllcurvesareasymptotingto,butnevertouchinganyExample:Cobb-Douglas

u(x,

)xaMarginal

MU

axa1x1a

a)x

x

a Slopeoftheindifferencecurve(Marginalrateof

MRS

1au(u(x1,x2)v(x1)LinearinoneofTheLastLastSeptember.9,ChapterChapterConsumerBehaviorandDemandTheoryChapter22.1Preferenceand2.2UtilityMaximizationand2.3IncomeandSubstitution2.4MarketDemandandOverviewofLastAssumptionsofConsumer’sDefiningHowtoGetIndifferenceCharacteristicofIndifferenceDiminishingMRS（边际替代率递减法OutlineofToday’sBudgetConstraint(预算约束ApplicationofBudgetUtilityMaximization(Consumer’sOptimalChoice)TypesofOptimalUtilityMaximization:AnInitialEconomistsassumethatwhenapersonisfacedwithachoiceamongseveralpossibleoptions,heorshewillchoosetheonethatyieldsthehighestutility-utilitymaximization.Economistsassumethatpeopleknowtheirownmindsandmakechoicesconsistentwiththeirpreferences.ChoicesareConstrained（受约束的PeopleareconstrainedintheirchoicesbythesizeoftheirincomesandotherOfthechoicestheindividualcanafford,thepersonwillchoosetheonethatyieldsthemostutility.BudgetConstraintSet（预算约束集Anindividual’sbudgetconstraintSet(ConsumptionChoiceset)isthesetthatincomeplacesonthecombinationsofgoodsandservicesthatapersoncanbuy.ConsumptionChoice(Budget)Consumptionchoice(orbudget)Allconsumptionchoicesavailableto“Available”–subjecttoBudgetSetsandConsumptionbundle:(x1,x2,…,Commodityprices:p1,p2,…,Budgetsetdefinedbyincomex10,…,xnp1x1+…+pnxnI=consumer’s(disposable)Budgetconstraintassumesallincomeisp1x1+…+pnxn=Isthusupperboundaryofbudgetset（预算约束集的上I/p2

BudgetSet,ConstraintforTwoBudgetconstraintisp1x1+p2x2=IandI BudgetSet,ConstraintforTwoI

Budgetconstraintisp1x1+p2x2=II I/p2

BudgetSet,ConstraintforTwoBudgetconstraintisp1x1+p2x2=I.JustI BudgetSet,ConstraintforTwoI/p2

Budgetconstraintisp1x1+p2x2=I.NotaffordableJustaffordableI BudgetSet,ConstraintforTwoI/p2

Budgetconstraintisp1x1+p2x2=I.NotaffordableJustaffordableAffordablewithcashI BudgetSet,ConstraintforTwoI/p2

Budgetconstraintisp1x1+p2x2=ICollectionofallaffordablebundles

I BudgetSet,ConstraintforTwoSolvep1x1Solvep1x1+p2x2=Ix2:x2=I/p2-I SlopeofBudgetConstraint(2x2=I/p2-SlopeofBudgetLineis-BudgetConstraint(2 Slopeis-EffectsofincreaseinincomebudgetbudgetsetEffectsofincreaseinincomeNewaffordable choices–budgetsetOriginalandnewbudgetparallelbudget

EffectsofdecreaseinincomebudgetsetbudgetsetEffectsofdecreaseinincomeNew,smallerbudgetset

ConsumptionbundlesthatarenolongerOldandnewareparallel.Effectsofp1Decreasefromp1’tobudgetset Effectsofp1decreasefromp1’to

NewaffordablechoicesSetexpands–welfareupbudgetset

I/p I/p Effectsofp1decreasefromp1’to

NewaffordableBudgetbudgetset

pivots;slopeflattensfrom-p1’/p2to ApplicationsofBudgetConstraintSetExampleofPriceChanges:SalesProportionaloradvaloremsalestax（从价LeviedatproportionalrateIncreasespricefromptoChangesbudgetconstraint(1+t)p1x1+(1+t)p2x2=p1x1+p2x2=UniformAdValoremSales p1x1+p2x2=pp1 p1UniformAdValoremSalesI p1x1+p2x2=pp1x1+p2x2=(1t)UniformAdValoremSales Equivalentincome

I1I1AnExampleofABudgetSetWithSupposeSupposegood1wererationedsothatmorethanx1couldbeconsumedbygivenp1x p2x x xTaxingConsumptionGreaterThanInInthisbudgetlineconsumermustpayataxonlyontheconsumptionofgood1thatisinexcessofx1sobudgetlinebecomessteepertotherightofx1TheFoodStampProgram（食品券FoodPopularincomesupportCoupons（优待券）giventopoor(usedtobeCanbelegallyexchangedonlyforPopularwithsomedonors(“inkind”PopularwithagriculturalTheFoodStampWhatiseffectonbudgetSupposeI=pF=Priceof“allothergoods”ispG=BudgetconstraintisF+GKeyfactor:Incomeavailablefor“othergoods”doesnotchangewithreceiptoffoodstampsSupposereceivefoodstampsgoodfor40unitsofTheFoodStamp F+G=100,beforefood TheFoodStampProgram（食品券计划F+G=100:beforeBudgetsetafter40foodstampsissued

TheFoodStamp

Welfareupsincebudgetsetisenlarged

TheFoodStampIffoodstampprogramisgenerous,familiesmaybeat“kink”（折弯处）ofbudgetsetWhatiffoodstampscanbetradedonablackmarketfor$0.50each?TheFoodStampBudgetconstraintwithblackmarkettrading,$0.50on

TheFoodStampBlackmarketexpandsbudgetset

Quantity-BasedPrices（以数量为基础PricemaybeafunctionofDiscountsforlargebuyers,Penaltiesforbuying“tooBudgetconstraints“kinked”wherepSupposequantityp2constantat$1andp1=$2for0x120;-p1/p2=-p1=$1forx1>20;-p1/p2=-BudgetConstraints/Quantity

Slope=-

I=20units@p=260units@Slope=- BudgetConstraints/Quantity

I=BudgetBudget BudgetConstraints/QuantityBudgetBudgetUtilityMaximization（效用最大化AnindividualcanaffordallbundlesofXandYthatfallwithinthebudgetconstraintrepresentedbytheshadedareainFigure2.7.PointAisaffordablebutnotalloftheconsumer’sincomewouldbespent.PointBisaffordablebutisnotonthehighestindifferencecurvethatcanbereachedbytheconsumer.FIGURE2.7:GraphicDemonstrationof

UtilityPointDisonahigherindifferencecurvethanC,butisnotaffordablegiventhebudgetconstraint.PointC,wheretheconsumerchoosesX1*,X2*isthepointthatisaffordablethatliesonthehighestindifferencecurve,soitrepresentsutilitymaximization.UtilityMaximization——OptimalAtpointCallincomeisAtpointCindifferencecurveU2istangenttothebudgetlinesothattheSlope

Slope

indifferen

Optimalchoice:Typicallywhereslopeofindifferencecurveequalsslopebudgetline

u(x1,x2

u(x1,x2

p1MU2 Rewritethiscondition

MUThemarginalutilityofthelastpennyspentoneachgoodisthesameAnexamplewithwellbehaved u

p1x1

p2x2MU1

MU2

2x2Usethisinthebudgetconstrainttosolveforthedemandfunctionforx1,x2:x

p1

pp

p2

x

p2

pp

p2TheLagrangeanapproachisanalternativeapproachforConstrainedoptimizationproblemL(

u(x1

x2

p1x1

IUtilityisUtilityistobeThelagrangeThebudgetTakefirstordernecessaryconditionsforThebudgetu(x1,

x2

p1

u(x1,

x2

p2p1x1p2x2ITheseconditionsgivethesamethreeTheseconditionsgivethesamethreeequationsasinpreviousslideTypesoftheOptimalSolutionForMaximizationUtilityOptimalchoicewithwellbehavedOptimalchoicewithwellbehavedinteriorsolutionOptimalchoicewithnotwell-behavedThetangencyconditionwillnotholdbetweentwogoodsifoneisnotconsumed

MUEvenwhenallincomespentongood1OptimalChoicewithPerfectPerfect

uax

bxSinceMRSisconstant,thetangencyconditiononlyholdsifbothslopesthesameMU1SinceMRSisconstant,thetangencyconditiononlyholdsifbothslopesthesameMRSa ap1

allx1：

x1

,x2

Consumeallx2x2

,x1OptimalChoicewithPerfectOptimalChoiceforPerfectumin(ax1,bx2Tangencyconditionwillnotholdsinceindifferencecurvesnotcontinuous.Slopeiseitherzero,infinityornotdefinedConsumerwillalwaysbeonthecorneroftheindifferencecurveconsuminginfixed

b Usethisconditioninthebudgetconstrainttosolveforx1orx2

Ip1x1

x1

pap

x2

pap preferencesmayleadtomorethanoneoptimalOptimalChoicewithConcave(凹形)consumeatacornertoUsingtheModelofTheutilitymaximizationmodelcanbeusedtoexplainmanycommonFigureinnextpageshowspeoplewiththesameincomestillconsumedifferentbundlesofgoods.DifferencesinPreferencesResultinDifferingperweek

perweek

Soft per

Softdrinksperperper

LI

WangUsingtheModelofFigureinnextpageshowsthefourindifferencecurvemapswithabudgetconstraintandtheutilitymaximizingchoicelabeledE.Panel(a)showsthatpeoplewillnotbuyuselessgoodsand(b)showstheywillnotbuyPanel(c)showsthatpeoplewillbuytheleastexpensiveofthetwoperfectsubstituteswhile(d)showsthatperfectcomplementswillbepurchasedtogether.Utility-MaximizingChoicesforSpecialofperweek

perU1U2

Foodper

Foodper(a)Auseless (b)AneconomicofExxonper

Rightshoesper U1U2

Gallonsof U1

Leftshoesper(c)Perfect (d)PerfectAPPLICATION:QuantityDiscountsandFrequent-FlierProgramsWhenconsumersreceivequantitydiscountsorhavetopayexcessiveusefees,thebudgetlineisnolongerstraight.InFigure1,theconsumerpaysregularpriceforgoodXuptoXDbutreceiveaquantitydiscountbeyondthatasshownbytheflatterbudgetlineafterconsumingXD.FIGURE1:KinkedBudgetResultingfromaQuantityQuantityofY

QuantityofXperAPPLICATION:APPLICATION:QuantityDiscountsandFrequent-FlierProgramsSincetheconsumerisindifferentbetweenpointsAandB,aslightlylargerdiscountwouldcausetheconsumertoreachahigherindifferencecurvebyusingthediscount.Allmajorairlinesusefrequent-flierprogramsthatprovidesuchquantitydiscountsandenabletheairlinestogainrevenuesonseatsthatotherwisewouldremainempty.TheLastSeptember12,ChapterChapterConsumerBehaviorandDemandTheoryChapter22.1Preferenceand2.2UtilityMaximizationand2.3IncomeandSubstitution2.4MarketDemandandOverviewofLastBudgetConstraint(预算约束ApplicationofBudgetUtilityMaximization(Consumer’sOptimalChoice)TypesofOptimalOutlineofTodayHowtoGetIndividualDemandFunction(AlgebraandGraph)Marshallian（马歇尔）demandPrice-ConsumptionCurve（价格消费线）andDemandCurveIncome-ConsumptionCurve（收入消费线）andEngelCurve（恩格尔曲线）ExamplesofrelativestaticASurveyofThisThissectionstudieshowpeoplechangetheirchoiceswhenconditionssuchasincomeorchangesinthepricesofgoodsaffecttheamountthatpeoplechoosetoThissectionthencomparesthenewchoiceswiththosethatweremadebeforeconditionschangedThemainresultofthisapproachistoconstructanindividual’sdemandcurveDefiningIndividualDemandIndividualdemandAnindividualdemandFunctionshowstherelationshipbetween