中级宏观经济学ppt课件 (2).ppt

PartIIAOne PeriodModeloftheMacroeconomy 1 StaticvsDynamicdecisionmaking Staticdecisionmakinginvolvesplanningoverasingleperiod Chapter4 5 Dynamicdecisionmakinginvolvesplanningovermorethanoneperiod Chapter6 7 8 9 Chapter4firstdescribesthemicrobehaviorofarepresentativeconsumerandarepresentativefirm Chapter5thenassemblestheseinamacromodelinordertoaddresssomeimportantmacroissues 2 Assumptionsontheenvironment Thereareonlytwogoodsthatconsumersdesire Consumptiongood whichisanaggregationofallconsumergoodsintheeconomy Leisure whichisanytimespentotherthanworkinginthemarket Allconsumersarealikeintermsofpreferences ability timeconstraintandbudgetconstraint Ifallconsumersareidentical thentheeconomywillbehaveasiftherewereonlyoneconsumer onethatwerefertoastherepresentativeconsumer 3 Assumptionsontheenvironment therepresentativeconsumerisaprice taker meaningthathe shetreatsmarketpricesasgiven andactsasifhis heractionshavenoeffectonthoseprices Theeconomyweconsiderisabartereconomy meaningthatalltradeinvolvesexchangesofgoodsforgoodsintheabsenceofmoney Whyimposesuchunrealisticassumptions RecallthediscussionsinChapter1 4 TheRepresentativeConsumer sOptimizationProblem Objective tomakehimself herselfaswelloffaspossiblegiventheconstraintshe shefaces TwoIngredientsinthisproblem Consumer spreferencesConsumer sbudgetconstraint 5 Preferences Thepreferencesoftherepresentativeconsumeriscapturedbytheutilityfunction whereCisthequantityofconsumption listhequantityofleisureAnyparticularpairofconsumptionandleisure C l iscalledaconsumptionbundle Foreachconsumptionbundle theutilityfunctionUassignsarealnumbersothatdifferentbundlescanberanked 6 Considertwodistinctbundles C1 l1 and C2 l2 C1 l1 isstrictlypreferredto C2 l2 ifU C1 l1 U C2 l2 consumerisindifferentbetweenthetwobundlesifU C1 l1 U C2 l2 AssumptionsonPreferences 1 MoreisalwayspreferredtolessAconsumeralwaysprefersaconsumptionbundlethatcontainsmoreconsumption moreleisure orboth U1 C l 0andU2 C l 0 7 2 Consumerprefersamorediversifiedconsumptionbundle Iftheconsumerisindifferentbetween C1 l1 and C2 l2 thensomemixtureofthetwowillbepreferabletoeitherone ThisimpliesthatU isstrictlyquasiconcave Example Consideranewbundle C3 l3 whereC3 C1 1 C2 l3 l1 1 l2and liesbetween0and1 afraction thenU C3 l3 U C1 l1 U C2 l2 3 Consumptionandleisurearenormalgoods Agoodisnormal inferior foraconsumerifthequantityofthegoodthathe shepurchasesincreases decreases whenincomeincreases 8 GraphicalRepresentationofPreferences Anindifferencecurveconnectsasetofpoints withthesepointsrepresentingconsumptionbundlesamongwhichtheconsumerisindifferent Afamilyofindifferencecurvesiscalledindifferencemap 9 PropertiesofIndifferenceCurves ConsideraconsumptionbundleB Sinceaconsumerprefersmoretoless anybundlethatisindifferenttoBmustliewithinquadrantIIandIV Implication Anindifferencecurveslopesdownward B I II III IV Leisure Consumption 10 PropertiesofIndifferenceCurves ConsideranytwobundlesAandB sinceaconsumerprefersamorediversifiedbundleCtoeitherAorB thesetofbundlesthatareindifferenttoAandBmustliebelowthestraightlineAB Implication Anindifferencecurveisconvex thatisbowed intowardtheorigin A B C Leisure Consumption 11 MarginalRateofSubstitution Marginalrateofsubstitutionistherateatwhichtheconsumerisjustwillingtosubstituteleisureforconsumptiongood Itisalsominustheslopeoftheindifferencecurve Convexityofindifferencecurveisequivalenttodiminishingmarginalrateofsubstitution Quasiconcavityofutilityfunction 12 MarginalRateofSubstitution TheMRSatAislarger intermsofabsolutemagnitude thantheMRSatB AsweincreaselandreduceC i e movingfromAtoBalongI1 theconsumerneedstobecompensatedmoreintermsofltogiveupanotherunitofC Theconsumerrequiresthisextraconsumptionbecauseofapreferencefordiversity 13 MarginalRateofSubstitution MathematicalDerivations SupposeindifferencecurveI1representstheutilitylevel TotallydifferentiatethiswithrespecttoCandlgives 14 ConstraintsfacedbyTheRepresentativeConsumer Twotypesofconstraints timeconstraintbudgetconstraintThetimeconstraintfortheconsumerisgivenbyl Ns hwherehisthetotalnumberofhoursavailable e g 24hoursaday listheleisuretimeandNsisthetimespentworking orlaborsupply 15 BudgetConstraint Sourcesofincome 1 Realwageincome wNswistherealwage i e thepriceofoneunitoflabortimeintermsofconsumptiongoods thenumeraire 2 Realdividendincome sincethefirmsareownedbytherepresentativeconsumer anyprofitsmadebyfirmsaredistributedtohim herasdividends 16 TaxationT alump sumtax i e ataxthatdoesnotdependontheactionsoftheeconomicagentwhoisbeingtaxed RealDisposableIncome wNs TTheconsumerfirstreceivesincomeandpaystaxesintermsofconsumptiongoods andthendecidesonhowmuchtoconsumeoutofthedisposableincome Claim alldisposableincomeisconsumed i e C wNs T w h l T 17 Reasons sincetheconsumeronlylivesforoneperiod thereisnoincentivetosaveanythingsincemoreispreferredtoless anywastageisnotoptimal Theconsumer sbudgetconstraintcanbewrittenasC wl wh TRHS totalimplicitrealdisposableincomeLHS implicitexpenditureonconsumptionandleisureNote wcanalsobeinterpretedasthemarketprice ortheopportunitycost ofleisuretime 18 GraphicalRepresentationoftheBudgetConstraint Budgetconstraint C wl wh Tthusslope w theverticalintercept wh T isthemaximumconsumptionthatcanbeachievedwhentheconsumerconsumesnoleisure Case1 TtheconsumercanstillenjoyC T 0evenifhe shechoosesnottowork 19 GraphicalRepresentationoftheBudgetConstraint Thebudgetconstrainttellsuswhatconsumptionbundlesarefeasibletoconsumegiventhemarketrealwage w dividendincome andtaxes T Theconsumptionbundleswithintheshadedregionsandonthebudgetconstraint arefeasible Thustheshadedregiontogetherwiththebudgetconstraintiscalledthefeasibleset 20 ConsumerOptimization Therepresentativeconsumerisassumedtoberational i e he shealwayschoosesthebestfeasibleconsumptionbundle ortheoptimalconsumptionbundle Best inthesensethatitliesonthehighestpossibleindifferencecurve Feasible inthesensethatitlieswithinthefeasibleset 21 GraphicalSolution Suppose T Claim Histheoptimalconsumptionbundle Reasons anybundleinsidethebudgetconstraintisnotoptimal compareJtoF BispreferredtoanypointonBD ForanypointonAB theconsumercanalwaysimprovebymovingclosertoH 22 MathematicalSolution Appendixp 627 TheconsumertriestosolvethefollowingconstrainedoptimizationproblemmaxU C l C lsubjecttoC w h l TandC 0 h l 0 LagrangianL U C l w h l T C where istheLagrangianmultiplier 23 Weassumethataninteriorsolutioncanbeobtained ThismeanschoosingC 0 l horl 0arenotoptimal sothatwecanignorethelasttwoconstraints Formally wecanimposetherestrictions foranyCandl toguaranteeaninteriorsolution First order Necessary conditions FOCs obtainedbydifferentiatingtheLagrangianwithrespecttoC land U1 C l U2 C l w w h l T C 0 24 FromtheFOCs weobtain AtH whereanindifferencecurveisjusttangenttothebudgetconstraint theaboveequalityholds IfMRS w e g atF theconsumerwouldbebetteroffbyincreasinglandreducingC thusmovingclosertoH 25 ComparativeStatics Appendixp 628 629 TodeterminehowCandlchangeswhenanyof Tandwchanges RecalltheFOCoftheconsumer sproblem whichcanbewrittenasU2 C l wU1 C l 0 Fromthebudgetconstraint w h l T C 0 ThetwoformasystemofequationsintermsofCandl endogenousvariables 26 Totallydifferentiatethetwoequations dC wdl h l dw d dT 0 U12 wU11 dC U22 wU12 dl U1dw 0Inmatrixform DeterminantoftheborderedHessianmatrixAisStrictquasiconcavityofU 0 A 27 UsingCramer sRule wegetTheassumptionthatConsumptionandleisurearenormalgoodsisequivalenttotheconditions U22 wU12 0andU12 wU11 0 1 Changesin and orT 28 GraphicalIllustration Consideranetincreasein T Sincewremainsthesame thebudgetconstraintmakesaparallelshift fromABtoFJ Sincedisposableincome whilepricesremainthesame thereisonlyapureincomeeffectontheconsumer schoices ThenewoptimalconsumptionbundleisK wherebothCandl normalgoods 29 GraphicalIllustration Remark theincreaseinconsumption C2 C1 islessthantheincreaseinnonwageincome distanceAF Sincetheconsumerisworkingless leisure wageincome Thiswilloffsetpartoftheconsumptionincrease 30 2 Changesinw UsingCramer srule Cisnormalgood U22 wU12 0 togetherwith 0andU1 0 31 However wecannotdeterminetheeffectofachangeinwonl Reason itdependsontherelativemagnitudeoftheopposingincomeandsubstitutioneffects Substitutioneffect w opportunitycostofleisure lbecomesmoreexpensiverelativetoC demandforleisure Incomeeffect w wageincome demandforleisure normalgood 32 GraphicalIllustration Suppose Tandw ThebudgetconstraintshiftsfromAFBtoEHB withasteeperslope Thisshowsaspecialcaseinwhichleisureremainsunaffected Puresubstitutioneffect movementfromFtoO onthesameindifferentcurve Pureincomeeffect movementfromOtoH Bothincomeandsubstitutioneffectsactto C 33 Laborsupplycurvewhichspecifieshowmuchlabortheconsumerwishestosupplygivenanyrealwage Algebraically thelaborsupplycurveisNs w h l w wherel w isthedemandfunctionforleisure Substitutioneffect Incomeeffect UpwardslopinglaborsupplycurveNet in T Upwardshiftinlaborsupplycurve 34 Example Candlareperfectcomplements Supposetheconsumer sutilityfunctioncanberepresentedbyU C l min C al whereaisapositiveconstant Notethatmoreisnotalwayspreferredtoless Theconsumercanbebetteroffonlyifhe shereceivesmoreofbothgoods Thus itisalwaysoptimaltochooseC al 35 Example Candlareperfectcomplements CombiningC alandthebudgetconstraintgivesInthiscase Thisisbecausewithperfectcomplements therearenosubstitutioneffects Thusleisure asrealwages 36 TheRepresentativeFirm Thefirmownsproductivecapitalandhirelabortoproduceconsumptiongoods Productiontechnologyiscapturedbytheproductionfunction whichdescribesthetechnologicalpossibilitiesforconvertingfactorinputs capitalKandlaborNd intooutputsY Y zF K Nd wherezistotalfactorproductivity z bothKandNdwillbemoreproductive 37 AssumptionsonProductionFunction Productionfunctionexhibitsconstantreturnstoscale orhomogenousofdegreeone Foranyx 0 xY zF xK xNd Ifallfactorinputsarechangedbyafactorx thenoutputchangesbythesamefactorx Inthiscase aperfectlycompetitiveeconomywithnumeroussmallfirmswillbehaveinexactlythesamewayasonewithasinglerepresentativefirm Increasingreturntoscale zF xK xNd xzF K Nd Decreasingreturntoscale zF xK xNd xzF K Nd 38 Positivemarginalproductofcapital MPK andmarginalproductoflabor MPN MPK MPN istheadditionaloutputthatcanbeproducedwithoneadditionalunitofcapital labor holdingconstantthequantitiesoflabor capital FixthequantityoflaboratN thentheMPKatthequantityoflaborK istheslopeoftheproductionfunctionatpointA 39 Algebraically weassumethat F1 K Nd 0andF2 K Nd 0 Conceptually thissimplymeans moreinputsyieldmoreoutput DiminishingMarginalProductthedecliningMPKandMPNisequivalenttotheconcavityoftheproductionfunction Algebraically thismeansF11 K Nd 0 andF22 K Nd 0 Implicitly weassumethatF istwicedifferentiable 40 MPN asK Algebraically thismeansIncreaseinthequantityofmachineryandequipmentenhancestheproductivityoftheworkers F isquasiconcave 41 Cobb DouglasProductionFunction ProbablythemostcommonlyusedformofproductionfunctionwhichsatisfiesalltheabovepropertiesY zKa Nd bwhere0 1 increasing decreasing returntoscale Ifthereareprofit maximizingprice takingfirmsanda b 1 thenawillbethesharethatcapitalreceivesofnationalincome 42 ChangesinTotalFactorProductivity z Changesinziscriticaltoourunderstandingofthecausesofeconomicgrowthandbusinesscycles Effectsofz 1 output forgivenvaluesofKandNd 2 MPL forgivenvalueofK Factorsthatwouldaffectztechnologicalinnovationweathergovernmentregulationspriceofenergy 43 ProfitMaximizationPr