中级微观范里安课堂讲义-英文版(上)(上海交通大学赵旭 朱保华)

ChapterOne,TheMarket,TheTheoryofEconomicsdoesnotfurnishabodyofsettledconclusionsimmediatelyapplicabletopolicy.Itisamethodratherthanadoctrine,anapparatusofthemind,atechniqueofthinkingwhichhelpsitspossessortodrawcorrectconclusions-JohnMaynardKeynes,EconomicModeling,Whatcauseswhatineconomicsystems?Atwhatlevelofdetailshallwemodelaneconomicphenomenon?Whichvariablesaredeterminedoutsidethemodel(exogenous)andwhicharetobedeterminedbythemodel(endogenous)?,ModelingtheApartmentMarket,Howareapartmentrentsdetermined?Supposeapartmentsarecloseordistant,butotherwiseidenticaldistantapartmentsrentsareexogenousandknownmanypotentialrentersandlandlords,ModelingtheApartmentMarket,Whowillrentcloseapartments?Atwhatprice?Willtheallocationofapartmentsbedesirableinanysense?Howcanweconstructaninsightfulmodeltoanswerthesequestions?,EconomicModelingAssumptions,Twobasicpostulates:RationalChoice:Eachpersontriestochoosethebestalternativeavailabletohimorher.Equilibrium:Marketpriceadjustsuntilquantitydemandedequalsquantitysupplied.,ModelingApartmentDemand,Demand:Supposethemostanyonepersoniswillingtopaytorentacloseapartmentis$500/month.Thenp=$500QD=1.Supposethepricehastodropto$490beforea2ndpersonwouldrent.Thenp=$490QD=2.,ModelingApartmentDemand,Theloweristherentalratep,thelargeristhequantityofcloseapartmentsdemandedpQD.Thequantitydemandedvs.pricegraphisthemarketdemandcurveforcloseapartments.,MarketDemandCurveforApartments,p,QD,ModelingApartmentSupply,Supply:Ittakestimetobuildmorecloseapartmentssointhisshort-runthequantityavailableisfixed(atsay100).,MarketSupplyCurveforApartments,p,QS,100,CompetitiveMarketEquilibrium,“low”rentalpricequantitydemandedofcloseapartmentsexceedsquantityavailablepricewillrise.“high”rentalpricequantitydemandedlessthanquantityavailablepricewillfall.,CompetitiveMarketEquilibrium,Quantitydemanded=quantityavailablepricewillneitherrisenorfallsothemarketisatacompetitiveequilibrium.,CompetitiveMarketEquilibrium,p,QD,QS,100,CompetitiveMarketEquilibrium,p,QD,QS,pe,100,CompetitiveMarketEquilibrium,p,QD,QS,pe,100,Peoplewillingtopaypeforcloseapartmentsgetcloseapartments.,CompetitiveMarketEquilibrium,p,QD,QS,pe,100,Peoplewillingtopaypeforcloseapartmentsgetcloseapartments.,Peoplenotwillingtopaypeforcloseapartmentsgetdistantapartments.,CompetitiveMarketEquilibrium,Q:Whorentsthecloseapartments?A:Thosemostwillingtopay.Q:Whorentsthedistantapartments?A:Thoseleastwillingtopay.Sothecompetitivemarketallocationisby“willingness-to-pay”.,ComparativeStatics,Whatisexogenousinthemodel?priceofdistantapartmentsquantityofcloseapartmentsincomesofpotentialrenters.Whathappensiftheseexogenousvariableschange?,ComparativeStatics,Supposethepriceofdistantapartmentrises.Demandforcloseapartmentsincreases(rightwardshift),causingahigherpriceforcloseapartments.,MarketEquilibrium,p,QD,QS,pe,100,MarketEquilibrium,p,QD,QS,pe,100,Higherdemand,MarketEquilibrium,p,QD,QS,pe,100,Higherdemandcauseshighermarketprice;samequantitytraded.,ComparativeStatics,Supposethereweremorecloseapartments.Supplyisgreater,sothepriceforcloseapartmentsfalls.,MarketEquilibrium,p,QD,QS,pe,100,MarketEquilibrium,p,QD,QS,100,Highersupply,pe,MarketEquilibrium,p,QD,QS,pe,100,Highersupplycausesalowermarketpriceandalargerquantitytraded.,ComparativeStatics,Supposepotentialrentersincomesrise,increasingtheirwillingness-to-payforcloseapartments.Demandrises(upwardshift),causinghigherpriceforcloseapartments.,MarketEquilibrium,p,QD,QS,pe,100,MarketEquilibrium,p,QD,QS,pe,100,Higherincomescausehigherwillingness-to-pay,MarketEquilibrium,p,QD,QS,pe,100,Higherincomescausehigherwillingness-to-pay,highermarketprice,andthesamequantitytraded.,TaxationPolicyAnalysis,Localgovernmenttaxesapartmentowners.Whathappenstopricequantityofcloseapartmentsrented?Isanyofthetax“passed”torenters?,TaxationPolicyAnalysis,Marketsupplyisunaffected.Marketdemandisunaffected.Sothecompetitivemarketequilibriumisunaffectedbythetax.Priceandthequantityofcloseapartmentsrentedarenotchanged.Landlordspayallofthetax.,ImperfectlyCompetitiveMarkets,Amongstmanypossibilitiesare:amonopolisticlandlordaperfectlydiscriminatorymonopolisticlandlordacompetitivemarketsubjecttorentcontrol.,AMonopolisticLandlord,WhenthelandlordsetsarentalpricepherentsD(p)apartments.Revenue=pD(p).Revenueislowifp0RevenueislowifpissohighthatD(p)0.Anintermediatevalueforpmaximizesrevenue.,MonopolisticMarketEquilibrium,p,QD,Lowprice,Lowprice,highquantitydemanded,lowrevenue.,MonopolisticMarketEquilibrium,p,QD,Highprice,Highprice,lowquantitydemanded,lowrevenue.,MonopolisticMarketEquilibrium,p,QD,Middleprice,Middleprice,mediumquantitydemanded,largerrevenue.,MonopolisticMarketEquilibrium,p,QD,QS,Middleprice,Middleprice,mediumquantitydemanded,largerrevenue.Monopolistdoesnotrentallthecloseapartments.,100,MonopolisticMarketEquilibrium,p,QD,QS,Middleprice,Middleprice,mediumquantitydemanded,largerrevenue.Monopolistdoesnotrentallthecloseapartments.,100,Vacantcloseapartments.,PerfectlyDiscriminatoryMonopolisticLandlord,Imaginethemonopolistkneweveryoneswillingness-to-pay.Charge$500tothemostwilling-to-pay,charge$490tothe2ndmostwilling-to-pay,etc.,DiscriminatoryMonopolisticMarketEquilibrium,p,QD,QS,100,p1=$500,1,DiscriminatoryMonopolisticMarketEquilibrium,p,QD,QS,100,p1=$500,p2=$490,1,2,DiscriminatoryMonopolisticMarketEquilibrium,p,QD,QS,100,p1=$500,p2=$490,1,2,p3=$475,3,DiscriminatoryMonopolisticMarketEquilibrium,p,QD,QS,100,p1=$500,p2=$490,1,2,p3=$475,3,DiscriminatoryMonopolisticMarketEquilibrium,p,QD,QS,100,p1=$500,p2=$490,1,2,p3=$475,3,pe,Discriminatorymonopolistchargesthecompetitivemarketpricetothelastrenter,andrentsthecompetitivequantityofcloseapartments.,RentControl,Localgovernmentimposesamaximumlegalprice,pmax20.,ShapesofBudgetConstraints-QuantityDiscounts,Supposep2isconstantat$1butthatp1=$2for0x120andp1=$1forx120.Thentheconstraintsslopeis-2,for0x120-p1/p2=-1,forx120andtheconstraintis,ShapesofBudgetConstraintswithaQuantityDiscount,m=$100,50,100,20,Slope=-2/1=-2(p1=2,p2=1),Slope=-1/1=-1(p1=1,p2=1),80,x2,x1,ShapesofBudgetConstraintswithaQuantityDiscount,m=$100,50,100,20,Slope=-2/1=-2(p1=2,p2=1),Slope=-1/1=-1(p1=1,p2=1),80,x2,x1,ShapesofBudgetConstraintswithaQuantityDiscount,m=$100,50,100,20,80,x2,x1,BudgetSet,BudgetConstraint,ShapesofBudgetConstraintswithaQuantityPenalty,x2,x1,BudgetSet,BudgetConstraint,ShapesofBudgetConstraints-OnePriceNegative,Commodity1isstinkygarbage.Youarepaid$2perunittoacceptit;i.e.p1=-$2.p2=$1.Income,otherthanfromacceptingcommodity1,ism=$10.Thentheconstraintis-2x1+x2=10orx2=2x1+10.,ShapesofBudgetConstraints-OnePriceNegative,10,Budgetconstraintsslopeis-p1/p2=-(-2)/1=+2,x2,x1,x2=2x1+10,ShapesofBudgetConstraints-OnePriceNegative,10,x2,x1,Budgetsetisallbundlesforwhichx10,x20andx22x1+10.,MoreGeneralChoiceSets,Choicesareusuallyconstrainedbymorethanabudget;e.g.timeconstraintsandotherresourcesconstraints.Abundleisavailableonlyifitmeetseveryconstraint.,MoreGeneralChoiceSets,Food,OtherStuff,10,Atleast10unitsoffoodmustbeeatentosurvive,MoreGeneralChoiceSets,Food,OtherStuff,10,BudgetSet,Choiceisalsobudgetconstrained.,MoreGeneralChoiceSets,Food,OtherStuff,10,Choiceisfurtherrestrictedbyatimeconstraint.,MoreGeneralChoiceSets,Sowhatisthechoiceset?,MoreGeneralChoiceSets,Food,OtherStuff,10,MoreGeneralChoiceSets,Food,OtherStuff,10,MoreGeneralChoiceSets,Food,OtherStuff,10,Thechoicesetistheintersectionofalloftheconstraintsets.,ChapterThree,Preferences,RationalityinEconomics,BehavioralPostulate:Adecisionmakeralwayschoosesitsmostpreferredalternativefromitssetofavailablealternatives.Sotomodelchoicewemustmodeldecisionmakerspreferences.,PreferenceRelations,Comparingtwodifferentconsumptionbundles,xandy:strictpreference:xismorepreferredthanisy.weakpreference:xisasatleastaspreferredasisy.indifference:xisexactlyaspreferredasisy.,PreferenceRelations,Strictpreference,weakpreferenceandindifferenceareallpreferencerelations.Particularly,theyareordinalrelations;i.e.theystateonlytheorderinwhichbundlesarepreferred.,PreferenceRelations,denotesstrictpreference;xymeansthatbundlexispreferredstrictlytobundley.,p,p,PreferenceRelations,denotesstrictpreference;xymeansbundlexispreferredstrictlytobundley.denotesindifference;xymeansxandyareequallypreferred.,p,p,PreferenceRelations,denotesstrictpreferencesoxymeansthatbundlexispreferredstrictlytobundley.denotesindifference;xymeansxandyareequallypreferred.denotesweakpreference;xymeansxispreferredatleastasmuchasisy.,p,p,PreferenceRelations,xyandyximplyxy.,PreferenceRelations,xyandyximplyxy.xyand(notyx)implyxy.,p,AssumptionsaboutPreferenceRelations,Completeness:Foranytwobundlesxandyitisalwayspossibletomakethestatementthateitherxyoryx.,AssumptionsaboutPreferenceRelations,Reflexivity:Anybundlexisalwaysatleastaspreferredasitself;i.e.xx.,AssumptionsaboutPreferenceRelations,Transitivity:Ifxisatleastaspreferredasy,andyisatleastaspreferredasz,thenxisatleastaspreferredasz;i.e.xyandyzxz.,IndifferenceCurves,Takeareferencebundlex.Thesetofallbundlesequallypreferredtoxistheindifferencecurvecontainingx;thesetofallbundlesyx.Sinceanindifference“curve”isnotalwaysacurveabetternamemightbeanindifference“set”.,IndifferenceCurves,x2,x1,x”,x”,xx”x”,x,IndifferenceCurves,x2,x1,zxy,p,p,x,y,z,IndifferenceCurves,x2,x1,x,AllbundlesinI1arestrictlypreferredtoallinI2.,y,z,AllbundlesinI2arestrictlypreferredtoallinI3.,I1,I2,I3,IndifferenceCurves,x2,x1,I(x),x,I(x),WP(x),thesetofbundlesweaklypreferredtox.,IndifferenceCurves,x2,x1,WP(x),thesetofbundlesweaklypreferredtox.,WP(x)includesI(x).,x,I(x),IndifferenceCurves,x2,x1,SP(x),thesetofbundlesstrictlypreferredtox,doesnotincludeI(x).,x,I(x),IndifferenceCurvesCannotIntersect,x2,x1,x,y,z,I1,I2,FromI1,xy.FromI2,xz.Thereforeyz.,IndifferenceCurvesCannotIntersect,x2,x1,x,y,z,I1,I2,FromI1,xy.FromI2,xz.Thereforeyz.ButfromI1andI2weseeyz,acontradiction.,p,SlopesofIndifferenceCurves,Whenmoreofacommodityisalwayspreferred,thecommodityisagood.Ifeverycommodityisagoodthenindifferencecurvesarenegativelysloped.,SlopesofIndifferenceCurves,Better,Worse,Good2,Good1,Twogoodsanegativelyslopedindifferencecurve.,SlopesofIndifferenceCurves,Iflessofacommodityisalwayspreferredthenthecommodityisabad.,SlopesofIndifferenceCurves,Better,Worse,Good2,Bad1,Onegoodandonebadapositivelyslopedindifferencecurve.,ExtremeCasesofIndifferenceCurves;PerfectSubstitutes,Ifaconsumeralwaysregardsunitsofcommodities1and2asequivalent,thenthecommoditiesareperfectsubstitutesandonlythetotalamountofthetwocommoditiesinbundlesdeterminestheirpreferencerank-order.,ExtremeCasesofIndifferenceCurves;PerfectSubstitutes,x2,x1,8,8,15,15,Slopesareconstantat-1.,I2,I1,BundlesinI2allhaveatotalof15unitsandarestrictlypreferredtoallbundlesinI1,whichhaveatotalofonly8unitsinthem.,ExtremeCasesofIndifferenceCurves;PerfectComplements,Ifaconsumeralwaysconsumescommodities1and2infixedproportion(e.g.one-to-one),thenthecommoditiesareperfectcomplementsandonlythenumberofpairsofunitsofthetwocommoditiesdeterminesthepreferencerank-orderofbundles.,ExtremeCasesofIndifferenceCurves;PerfectComplements,x2,x1,I1,45o,5,9,5,9,Eachof(5,5),(5,9)and(9,5)contains5pairssoeachisequallypreferred.,ExtremeCasesofIndifferenceCurves;PerfectComplements,x2,x1,I2,I1,45o,5,9,5,9,Sinceeachof(5,5),(5,9)and(9,5)contains5pairs,eachislesspreferredthanthebundle(9,9)whichcontains9pairs.,PreferencesExhibitingSatiation,Abundlestrictlypreferredtoanyotherisasatiationpointorablisspoint.Whatdoindifferencecurveslooklikeforpreferencesexhibitingsatiation?,IndifferenceCurvesExhibitingSatiation,x2,x1,Satiation(bliss)point,IndifferenceCurvesExhibitingSatiation,x2,x1,Better,Better,Better,Satiation(bliss)point,IndifferenceCurvesExhibitingSatiation,x2,x1,Better,Better,Better,Satiation(bliss)point,IndifferenceCurvesforDiscreteCommodities,Acommodityisinfinitelydivisibleifitcanbeacquiredinanyquantity;e.g.waterorcheese.Acommodityisdiscreteifitcomesinunitlumpsof1,2,3,andsoon;e.g.aircraft,shipsandrefrigerators.,IndifferenceCurvesforDiscreteCommodities,Supposecommodity2isaninfinitelydivisiblegood(gasoline)whilecommodity1isadiscretegood(aircraft).Whatdoindifference“curves”looklike?,IndifferenceCurvesWithaDiscreteGood,Gas-oline,Aircraft,0,1,2,3,4,Indifference“curves”arecollectionsofdiscretepoints.,Well-BehavedPreferences,Apreferencerelationis“well-behaved”ifitismonotonicandconvex.Monotonicity:Moreofanycommodityisalwayspreferred(i.e.nosatiationandeverycommodityisagood).,Well-BehavedPreferences,Convexity:Mixturesofbundlesare(atleastweakly)preferredtothebundlesthemselves.E.g.,the50-50mixtureofthebundlesxandyisz=(0.5)x+(0.5)y.zisatleastaspreferredasxory.,Well-BehavedPreferences-Convexity.,x2,y2,x2+y2,2,x1,y1,x1+y1,2,x,y,z=,x+y,2,isstrictlypreferredtobothxandy.,Well-BehavedPreferences-Convexity.,x2,y2,x1,y1,x,y,z=(tx1+(1-t)y1,tx2+(1-t)y2),ispreferredtoxandyforall0tU(x”)xx”U(x)U(4,1)=U(2,2)=4.Callthesenumbersutilitylevels.,p,UtilityFunctionseachistheother.,UtilityFunctions,Thereisnouniqueutilityfunctionrepresentationofapreferencerelation.SupposeU(x1,x2)=x1x2representsapreferencerelation.Againconsiderthebundles(4,1),(2,3)and(2,2).,UtilityFunctions,U(x1,x2)=x1x2,soU(2,3)=6U(4,1)=U(2,2)=4;thatis,(2,3)(4,1)(2,2).,p,UtilityFunctions,U(x1,x2)=x1x2(2,3)(4,1)(2,2).DefineV=U2.,p,UtilityFunctions,U(x1,x2)=x1x2(2,3)(4,1)(2,2).DefineV=U2.ThenV(x1,x2)=x12x22andV(2,3)=36V(4,1)=V(2,2)=16soagain(2,3)(4,1)(2,2).VpreservesthesameorderasUandsorepresentsthesamepreferences.,p,p,UtilityFunctions,U(x1,x2)=x1x2(2,3)(4,1)(2,2).DefineW=2U+10.,p,UtilityFunctions,U(x1,x2)=x1x2(2,3)(4,1)(2,2).DefineW=2U+10.ThenW(x1,x2)=2x1x2+10soW(2,3)=22W(4,1)=W(2,2)=18.Again,(2,3)(4,1)(2,2).WpreservesthesameorderasUandVandsorepresentsthesamepreferences.,p,p,UtilityFunctions,IfUisautilityfunctionthatrepresentsapreferencerelationandfisastrictlyincreasingfunction,thenV=f(U)isalsoautilityfunctionrepresenting.,Goods,BadsandNeutrals,Agoodisacommodityunitwhichincreasesutility(givesamorepreferredbundle).Abadisacommodityunitwhichdecreasesutility(givesalesspreferredbundle).Aneutralisacommodityunitwhichdoesnotchangeutility(givesanequallypreferredbundle).,Goods,BadsandNeutrals,Utility,Water,x,Unitsofwateraregoods,Unitsofwaterarebads,Aroundxunits,alittleextrawaterisaneutral.,Utilityfunction,SomeOtherUtilityFunctionsandTheirIndifferenceCurves,InsteadofU(x1,x2)=x1x2considerV(x1,x2)=x1+x2.Whatdotheindifferencecurvesforthis“perfectsubstitution”utilityfunctionlooklike?,PerfectSubstitutionIndifferenceCurves,5,5,9,9,13,13,x1,x2,x1+x2=5,x1+x2=9,x1+x2=13,V(x1,x2)=x1+x2.,PerfectSubstitutionIndifferenceCurves,5,5,9,9,13,13,x1,x2,x1+x2=5,x1+x2=9,x1+x2=13,Allarelinearandparallel.,V(x1,x2)=x1+x2.,SomeOtherUtilityFunctionsandTheirIndifferenceCurves,InsteadofU(x1,x2)=x1x2orV(x1,x2)=x1+x2,considerW(x1,x2)=minx1,x2.Whatdotheindifferencecurvesforthis“perfectcomplementarity”utilityfunctionlooklike?,PerfectComplementarityIndifferenceCurves,x2,x1,45o,minx1,x2=8,3,5,8,3,5,8,minx1,x2=5,minx1,x2=3,W(x1,x2)=minx1,x2,PerfectComplementarityIndifferenceCurves,x2,x1,45o,minx1,x2=8,3,5,8,3,5,8,minx1,x2=5,minx1,x2=3,Allareright-angledwithverticesonarayfromtheorigin.,W(x1,x2)=minx1,x2,SomeOtherUtilityFunctionsandTheirIndifferenceCurves,AutilityfunctionoftheformU(x1,x2)=f(x1)+x2islinearinjustx2andiscalledquasi-linear.E.g.U(x1,x2)=2x11/2+x2.,Quasi-linearIndifferenceCurves,x2,x1,Eachcurveisaverticallyshiftedcopyoftheothers.,SomeOtherUtilityFunctionsandTheirIndifferenceCurves,AnyutilityfunctionoftheformU(x1,x2)=x1ax2bwitha0andb0iscalledaCobb-Douglasutilityfunction.E.g.U(x1,x2)=x11/2x21/2(a=b=1/2)V(x1,x2)=x1x23(a=1,b=3),Cobb-DouglasIndifferenceCurves,x2,x1,Allcurvesarehyperbolic,asymptotingto,butnevertouchinganyaxis.,MarginalUtilities,Marginalmeans“incremental”.Themarginalutilityofcommodityiistherate-of-changeoftotalutilityasthequantityofcommodityiconsumedchanges;i.e.,MarginalUtilities,E.g.ifU(x1,x2)=x11/2x22then,MarginalUtilities,E.g.ifU(x1,x2)=x11/2x22then,MarginalUtilities,E.g.ifU(x1,x2)=x11/2x22then,MarginalUtilities,E.g.ifU(x1,x2)=x11/2x22then,MarginalUtilities,So,ifU(x1,x2)=x11/2x22then,MarginalUtilitiesandMarginalRates-of-Substitution,ThegeneralequationforanindifferencecurveisU(x1,x2)k,aconstant.Totallydifferentiatingthisidentitygives,MarginalUtilitiesandMarginalRates-of-Substitution,rearrangedis,MarginalUtilitiesandMarginalRates-of-Substitution,rearrangedis,And,ThisistheMRS.,Marg.UtilitiesAnexample,SupposeU(x1,x2)=x1x