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Money,Interest,andIncome
.IntroductionMoneyplaysacentralroleinthedeterminationofincomeandemploymentInterestratesareasignificantdeterminantofaggregatespendingFedcontrolsthemoneysupplyintheUnitedStatesThestockofmoney,interestrates,andtheFedwerenoticeablyabsentfromthemodeldevelopedinthelastchapterThischapter:IntroducesmoneyandmonetarypolicyBuildsanexplicitframeworkofanalysiswithinwhichtostudytheinteractionofgoodsmarketsandassetsmarketWhatdeterminesinterestrates?Whatistheroleofinterestratesinthebusinesscycle?11-2IntroductionFigure11-1showstheinterestrateonTreasurybills=thepaymentreceivedbysomeonewholendstotheU.S.governmentEx.Ataninterestrateof5%,a$100loantothegovernmentwillearn$5ininterest11-3IntroductionInterestrates:ArehighjustbeforearecessionDropduringtherecessionRiseduringtherecovery11-4Introduction
11-5Figure11-2showsthestronglinkbetweenmoneyandoutputgrowthIS-LMmodelisthecoreofshort-runmacroeconomicsMaintainsthedetailsofearliermodel,butaddstheinterestrateasanadditionaldeterminantofaggregatedemandIncludesthegoodsmarketandthemoneymarket,andtheirlinkthroughinterestratesandincomeStructureoftheIS-LMModel
11-6TheGoodsMarketandtheISCurveTheIScurveshowscombinationsofinterestrates andlevelsofoutputsuchthatplannedspendingequalsincomeDerivedintwosteps:LinkbetweeninterestratesandinvestmentLinkbetweeninvestmentdemandandADInvestmentisnolongertreatedasexogenous,butdependentuponinterestrates(endogenous)InvestmentdemandislowerthehigherareinterestratesInterestratesarethecostofborrowingmoneyIncreasedinterestratesraisethepricetofirmsofborrowingforcapitalequipmentreducethequantityofinvestmentdemand11-7InvestmentandtheInterestRate
11-8Theinvestmentspendingfunctioncanbespecifiedas:(1)whereb>0i=rateofinterestb=theresponsivenessofinvestmentspendingtotheinterestrate=autonomousinvestmentspendingInvestmentandtheInterestRate11-9Figure11-4illustratestheinvestmentscheduleofequation(1)NegativeslopereflectsassumptionthatareductioniniincreasesthequantityofIInvestmentandtheInterestRate
11-10
(1)ThepositionoftheIscheduleisdeterminedby:Theslope,bIfinvestmentishighlyresponsivetoi,theinvestmentscheduleisalmostflatIfinvestmentrespondslittletoi,theinvestmentscheduleisclosetoverticalLevelofautonomousspendingAnincreaseinshiftstheinvestmentscheduleoutAdecreaseinshiftstheinvestmentscheduleinTheInterestRateandAD:TheISCurveNeedtomodifytheADfunctionofthelastchaptertoreflectthenewplannedinvestmentspendingschedule
(2)AnincreaseinireducesADforagivenlevelofincomeAtanygivenlevelofi,candeterminetheequilibriumlevelofincomeandoutputasinChapter10Achangeiniwillchangetheequilibrium
11-11TheInterestRateandAD:TheISCurve
11-12
(2)Foragiveninterestrate,i1,thelastterminequation(2)isconstantcandrawtheADfunctionwithaninterceptofTheequilibriumlevelofincomeisY1atpointE1Plotthepair(i1,Y1)inthebottompanelaspointE1
apointontheIScurveCombinationofiandYthatclearsthegoodsmarketTheInterestRateandAD:TheISCurve
11-13
(2)Consideralowerinterestrate,i2ShiftstheADcurveupwardtoAD’withaninterceptofGiventheincreaseinAD,theequilibriumshiftstopointE2,withanassociatedincomelevelofY2Plotthepair(i2,Y2)inpanel(b)foranotherpointontheIScurveTheInterestRateandAD:TheISCurve
11-14WecanapplythesameproceduretoalllevelsofitogenerateadditionalpointsontheIScurveAllpointsontheIScurverepresentcombinationsofiandincomeatwhichthegoodsmarketclears
goodsmarketequilibriumscheduleFigure11-5showsthenegativerelationshipbetweeniandYDownwardslopingIScurveTheInterestRateandAD:TheISCurveWecanalsoderivetheIScurveusingthegoodsmarketequilibriumcondition:
(4)
where(5),themultiplierfromChapter1011-15TheSlopeoftheISCurveThesteepnessoftheIScurvedependson:HowsensitiveinvestmentspendingistochangesiniThemultiplier,
GSupposeinvestmentspendingisverysensitivetoitheslope,b,islargeAgivenchangeiniproducesalargechangeinAD(largeshift)AlargeshiftinADproducesalargechangeinYAlargechangeinYresultingfromagivenchangeiniIScurveisrelativelyflatIfinvestmentspendingisnotverysensitivetoi,theIScurveisrelativelysteep
11-16TheRoleoftheMultiplier
11-17Figure11-6showstheADcurvescorrespondingtodifferentmultipliersThecoefficientconthesolidblackADcurveissmallerthanthatonthedashedADcurvemultiplierlargeronthedashedADcurvesAgivenreductioninitoi2raisestheinterceptoftheADcurvesbythesameverticaldistanceBecauseofthedifferentmultipliers,incomerisestoY’2onthedashedlineandY2onthesolidlineTheRoleoftheMultiplierThesmallerthesensitivityofinvestmentspendingtotheinterestrateANDthesmallerthemultiplier,thesteepertheIScurveThiscanbeseeninequation(5):Wecansolveequation(5)fori:11-18ThePositionoftheISCurve
11-19Figure11-7showstwodifferentIScurvesdifferbylevelsofautonomousspendingInitialADwithandi1
correspondingpointE1onIScurveinFigure11-7(b)Ifautonomousspendingincreasesto,equilibriumlevelofincomeincreasesati1pointE2inpanel11-7(b),shiftingoutISThechangeinincomeasaresultfromachangeinautonomousspendingisTheMoneyMarketandtheLMCurveTheLMcurveshowscombinationsofinterestratesandlevelsofoutputsuchthatmoneydemandequalsmoneysupplyequilibriuminthemoneymarketTheLMcurveisderivedintwosteps:ExplainwhymoneydemanddependsoninterestratesandincomeTheoryofrealmoneybalances,ratherthannominalEquatemoneydemandwithmoneysupply,andfindcombinationsofincomeandinterestratesthatmaintainequilibriuminthemoneymarket(i,Y)pairsmeetingthiscriteriaarepointsonagivenLMcurve11-20DemandforMoneyThedemandformoneyisademandforrealmoneybalancesPeopleareconcernedwithhowmuchtheirmoneycanbuy,ratherthanthenumberofdollarsintheirpocketsThedemandforrealbalancesdependson:Realincome:peopleholdmoneytopayfortheirpurchases,which,inturn,dependonincomeInterestrate:thecostofholdingmoneyThedemandformoneyisdefinedas:(6)
11-21DemandforMoney
11-22(6)TheparameterskandhreflectthesensitivityofdemandforrealbalancestothelevelofYandiThedemandfunctionforrealbalancesimpliesthatforagivenlevelofincome,thequantitydemandedisadecreasingfunctionofiFigure11-8illustratestheinverserelationshipbetweenmoneydemandandi
moneydemandcurveTheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurveThenominalquantityofmoneysupplied,M,controlledbycentralbankRealmoneysupplyis,whereMandPareassumedfixedFigure11-9showscombinationsofiandYsuchthatdemandforrealmoneybalancesexactlymatchesavailablesupply11-23TheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurveStartingatY1,thecorrespondingdemandcurveforrealbalancesisL1showninpanel(a)PointE1istheequilibriumpointinthemoneymarket11-24TheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurvePointE1isrecordedinpanel(b)asapointonthemoneymarketequilibriumschedule,ortheLMcurve(i1,Y1)pairisapointonLMcurve11-25TheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurveIfincomeincreasestoY2,realmoneybalanceshigherateverylevelofi
moneydemandshiftstoL2Theinterestrateincreasestoi2tomaintainequilibriuminmoneymarketThenewequilibriumisatpointE211-26TheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurveRecordE2inpanel(b)asanotherpointontheLMcurvePair(i2,Y2)ishigherupthegivenLMcurve11-27TheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurveTheLMscheduleshowsallcombinationsofinterestratesandlevelsofincomesuchthatthedemandforrealbalancesisequaltothesupplymoneymarketisinequilibriumLMcurveispositivelysloped:AnincreaseintheinterestratereducesthedemandforrealbalancesTomaintainthedemandforrealmoneybalancesequaltothefixedsupply,thelevelofincomehastoriseMoneymarketequilibriumimpliesthatanincreaseintheinterestrateisaccompaniedbyanincreaseinthelevelofincome.11-28TheSupplyofMoney,MoneyMarketEquilibrium,andtheLMCurveTheLMcurvecanbeobtaineddirectlybycombiningthedemandcurveforrealbalancesandthefixedsupplyofrealbalancesForthemoneymarkettobeinequilibrium,supplymustequaldemand:(7)Solvingfori:(7a)11-29TheSlopeoftheLMCurveThesteepertheLMcurve:Thegreatertheresponsivenessofthedemandformoneytoincome,asmeasuredbykThelowertheresponsivenessofthedemandformoneytotheinterestrate,hThesepointscanbeconfirmedbyexperimentingwithFigure11-9orexaminingequation(7a),Agivenchangeinincomehasalargereffectoni,thelargeriskandthesmallerish11-30ThePositionoftheLMCurveRealmoneysupplyconstantalongtheLMcurveachangeintherealmoneysupplywillshifttheLMcurveFigure11-10showstheeffectofanincreaseinmoneysupplyEquilibriumoccursatpointE1withinterestratei1
correspondingpointE1ontheLMcurve11-31ThePositionoftheLMCurveIfrealmoneybalancesincreases,moneysupplycurveshiftstotherightTorestoreequilibriumattheincomelevelY1,theimustdecreasetooInpanel(b),theLMcurveshiftstothedownandtotheright11-32EquilibriumandtheGoods
andMoneyMarket
FlatSRAScurve11-33TheISandLMschedulessummarizetheconditionsthathavetobesatisfiedforthegoodsandmoneymarketstotheinequilibriumAssumptions:PricelevelisconstantFirmswillingtosupplywhateveramountofoutputisdemandedatthatpricelevelChangesintheEquilibriumLevelsofIncomeandtheInterestRate
11-34TheequilibriumlevelsofincomeandtheinterestratechangewheneithertheISortheLMcurveshiftsFigure11-12showseffectsofanincreaseinautonomousspendingShiftsIScurveoutbyifautonomousinvestmentisthesourceofincreasedspendingTheresultingchangeinYissmallerthanthechangeinautonomousspendingduetoslopeofLMcurveDerivingtheADSchedule
11-35TheADschedulemapsouttheIS-LMequilibriumholdingautonomo
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