曼昆第10版讲义mankiw10e-irm-ch03

|CHAPTER3 NationalIncome:WhereItComesFromandWhereItGoes

LectureNotes|

CHAPTER3

NationalIncome:WhereItComesFromandWhereItGoes

NotestotheInstructor

ChapterSummary

Chapter3presentsanimportantbutrelativelystraightforwardclassicalmodeloftherealsideoftheeconomy.Muchofthematerialinthechapter(suchasmarginalproducts,factordemands,consumptionandinvestmentfunctions,andthelike)islikelytobeareviewofmaterialscoveredinprinciplescourses.Thematerialcanprobablybepresentedintwolecturestostudentswithasuitablegroundingfromprinciples;threelecturesmightbemoreappropriateforless-well-preparedstudents.

Themodelofthechapterprovidesacompletedescriptionofhowtherealsideoftheeconomyworks,inthesensethatitexplainsallthemarketsandtransactionsillustratedinthecircularflowdiagram(Figure3-1).Themodelissetupasfollows:

ProductionCapitalandlaborstocksarefixedand,togetherwiththeproductionfunction,determineGDP.

DistributionGDPispaidtofactorsofproductionaccordingtotheirmarginalproducts.Euler’stheoremensuresthatthesefactorpaymentsexactlyexhaustGDP.

AllocationGDPisallocatedtoconsumption,investment,andgovernmentpurchasesaccordingtoaconsumptionfunction[C=C(Y–T)]),aninvestmentfunction[I=I(r)],andfiscalpolicy.Therealinterestrateadjuststoensureequilibriuminthegoods(equivalentlytheloans)market.

Themodelislongruninthesensethatitassumesthatpricesareflexibleandthatmarketsclear.Atthesametime,however,itpresentsonlyasnapshotoftheeconomyatapointintimebecauseitassumesafixedcapitalstock,laborforce,andtechnology.

Thechapterhasthreeprimarygoals:

Tointroducestudentstosomeofthebasictermsandconceptsthatwillbeusedthroughoutthebook,suchastheproductionfunction,theconsumptionfunction,andtheinvestmentfunction.

Toprovidelong-runanswerstofourquestions:

WhatdeterminesthelevelofGDPandnationalincome?

Whatdetermineshownationalincomeisdistributedtolaborandownersofcapital?

WhatdetermineshowGDPisallocatedtoconsumption,investment,andgovernmentpurchases?

Whatensuresequilibriumoftheflowsinthecircularflowdiagram?

Todevelopamodelthatisbothabasisforfurtheranalysisandabenchmarkforcomparisonasthebookgoesontoconsidertopicssuchasthedeterminationofprices(Chapter5),theopeneconomy(Chapter6),theSolowgrowthmodel(Chapters8and9),andtheIS–LMmodel(Chapters11and12).

Comments

Thelecturenotesintroducenotationforprivatesavingandpublicorgovernmentsavingthatdoesnotappearinthetextbook:SpandSg,respectively.Thisfacilitatespresentationofequilibriumintheloansmarket.Studentsmustclearlyunderstandthedistinctionbetweenpublicandprivatesaving.Forexample,studentsareoftenconfusedbythefactthatdecreasesintaxesdecreasesavingbecausetheyfocusontheeffectonprivatesavingandmisstheeffectonthegovernmentdeficit.

Thelecturenotesemphasizethecircularflowasthereferencepointfortheanalysis.Thehousehold’sbudgetconstraint(C+Sp=Y–T),theequalityofincomeandoutput

(Y=Wages+Profits),thedefinitionofthedeficit(Sg=–DEF=T–G),thegoodsmarketequilibriumcondition(Y=C+I+G),andtheloansmarketequilibriumcondition

(S=Sp+Sg=I)canallbeintroducedintermsofthecircularflowdiagram.

Likethetext,thelecturenotesemphasizetheloanablefundsinterpretationofequilibrium.Aswellasbeingsimpletopresentandillustrateintermsofasavings/investmentdiagram,thisapproachmakesitclearwhytherealinterestrateisthekeyequilibratingvariable.

Theclassicalmodelofthischapterprovidesabenchmark.Manyoftheothermodelsinthebooktakethismodelasastartingpoint,andwereferbacktothisanalysismanytimes.Manyoftheconceptsintroducedinthischapter(forexample,consumptionandinvestmentfunctions)areusedthroughoutthebook.

UseoftheWebsite

Sincetheclassicalmodelprovidesabenchmark,itisprobablyagoodideatogivethestudentsmanyanalyticalexercisesusingthismodel.Thecurve-shiftingexercisesarerelativelysimplesothattheexercisesofthischapterallowthestudentstofamiliarizethemselveswiththesoftware.

UseoftheEWebsite

UsetheEwebsitetodownloaddataforthepast40yearsonnationalincome,nationalsaving,thegovernmentbudgetsurplus,andthecurrentaccountsurplus.Computeprivatesavingbysubtractingthegovernmentbudgetsurplusandthecurrentaccountsurplusfromnationalsaving.Now,expressprivatesaving,thegovernmentbudgetsurplus,andthecurrentaccountsurplusasashareofnationalincome.Discusshowtheshareshavechangedovertime.

ChapterSupplements

Thischapterincludesthefollowingsupplements:

3-1 HowLongIstheLongRun?PartI

3-2 WhatIsCapital?

3-3 Labor’sShareofOutputintheUnitedKingdom

3-4 Economists’Terminology

3-5 PublicandPrivateSaving

3-6 WarsandInterestRates

3-7 AFirstLookatNominalandRealInterestRates

LectureNotes

Introduction

Wenowmovefrommeasurementtothedeeperquestionoftheexplanationofthebehavioroftheeconomy.Thischapterdevelopsabasicmodelofthelong-runbehaviorofawell-functioningeconomy(oneinwhichpricesareflexible,soallmarketsarealwaysinequilibrium).Thisclassicalmodelexplains

Supplement3-1,“HowLongIstheLongRun?PartI”

1. Thedeterminantsofthelevelofoutput(income),

2. Howincomeisdistributed,

3. Howoutputisallocatedamongalternativeuses,and

4. Whatensuresthatthesupplyofanddemandforgoodsareequal.

Figure3-1

ThestartingpointisthecircularflowofincomefromChapter2,complicatedsomewhatbytheadditionofthegovernmentbutkeptsimplebyrestrictingattentiontoaclosedeconomy(netexportsequalszero).SomeaccountingrelationshipsfromChapter2showuphere.Fromthegoodsmarket(rememberingthatNX=0),

Y=C+I+G.

Lookingatfirms,wehave

Profits+Wages=Y,

andconsideringthegovernment,weobtainthedefinitionofthegovernmentdeficit:

DEF=G–T.

Finally,fromthefinancialmarkets(lettingSprepresentprivatesaving),

Sp=DEF+I.

3-1 WhatDeterminestheTotalProductionofGoodsandServices?

TheFactorsofProduction

Supplement3-2,“WhatIsCapital?”

Theeconomyhascertainresources,mostnotablyitslaboranditsstockofmachinesandfactories(itscapitalstock).Firmsintheeconomyuselaborandcapitalasinputstoproducegoodsandservices(GDP).Tokeepthingssimple,wetakeKandLasfixedandexogenous

().Wedonotyetwishtoexplainvariationsinemploymentorinthecapitalstock.

TheProductionFunction

Weexpresstheeconomy’sabilitytoproducegoodsandservicesfromitsresourcesas

Y=F(K,L).

ThissayssimplythattheamountofGDPaneconomycanproducedependsonitscapitalstockKanditslaborL.Morecapitalormorelaborallowtheeconomytoproducemoreoutput.Anexampleofaproductionfunctionis

Y=(KL)1/2.

Thus,ifK=40andL=10,Y=(400)1/2=20.

Iftheeconomyweresuddenlytohaveexactlytwicetheamountofallitsinputs,wewouldexpectthatitcouldproduceexactlytwiceasmuchoutputsimplybyusingthenewresourcesinexactlythesamewayastheoldresources.Ifafactorycanproduce20automobilesusing40machinesand10workers,thenitshouldbepossibletoproduce40automobileswith80machinesand20workerssimplybybuildingasecondfactoryidenticalinallrespectstothefirstone.Moregenerally,iftheamountofallinputsisincreasedbysomeconstantpercentage,outputshouldbechangedbythesamepercentage.Thismeansthattheproductionfunctionshouldexhibitconstantreturnstoscale.Thisiswrittenmathematicallyas

zY=F(zK,zL)

foranypositivenumberz.Doublingtheamountofinputsfromtheearlierexample,sothatK=80andL=20,gives

Y=(1,600)1/2=40,

illustratingthatthisfunctiondoeshaveconstantreturnstoscale.

TheSupplyofGoodsandServices

SincewearesupposingthatKandLarefixed,itfollowsthatwecancalculateGDPimmediatelyfromtheproductionfunction

.

iscalledthenaturalrateofoutput.Atanypointintime,thelong-runornaturalrateofoutputisdeterminedbytheavailableresourcesandtechnology.

3-2 HowIsNationalIncomeDistributedtotheFactorsofProduction?

Theoveralldeterminationofincomeisstraightforward.Moreinteresting,perhaps,isthequestionofhowthisincomeisdividedupbetweenworkers,whosupplylaborandreceivewages,andtheownersofcapital,whosupplycapitalandobtainprofits.Themoderneconomicexplanationistheneoclassicaltheoryofdistribution,whichexplainshowmuchworkersarepaidperunitoflaborandhowmuchownersofcapitalarepaidperunitofcapital.

FactorPrices

Figure3-2

Asallmarketsareinequilibriumintheclassicalmodel,themarketsforlaborandcapital—factorsofproduction—determinefactorprices.Thepriceofeachofthesefactorsisdeterminedbydemandandsupply.Sincefactorsuppliesarefixed,thesupplycurvesarevertical,soourmaintaskistoexplainfactordemands.

TheDecisionsFacingaCompetitiveFirm

Thedemandforfactorscomesfromthefirmsintheeconomythatusethemtoproducegoods.Wesupposethattherearemanyidenticalcompetitivefirms.Thismeansthattheyaresmallrelativetothemarketsinwhichtheytrade,andsotheytakeasgivenandasoutsidetheircontrolboththepriceatwhichtheycanselloutputandthecostoffactorsofproduction.Eachfirmhasaproductionfunction

Y=F(K,L).

Wetreatlaborandcapitalsymmetrically:householdsownbothlaborandcapital,whichtheysell(rent)tofirms.Inreality,theownershipofcapitalisindirect,sincefirmsowncapital,butthesefirmsare,inturn,ownedbyhouseholds.Firmsobtainrevenuesfromsellingtheirgoodsandincurthecostoflaborandcapital.Thedifferencebetweentheirrevenuesandtheircostistheirprofit.Profitdependsonthepriceatwhichtheycanselltheiroutput(thepriceofaunitofGDP,orP),therentalpriceofcapitalindollars(R),andthedollarwagerate(W):

Profit=PY–RK–WL

=PF(K,L)–RK–WL.

Thefirm’sproblemistochooseKandLtomaximizeitsprofits.

TheFirm’sDemandforFactors

SupposethatafirmwithKunitsofcapitalandLunitsoflaborhiresanextraworker.Theextraoutputitobtainsiscalledthemarginalproductoflabor(MPL):

MPL=F(K,L+1)–F(K,L).

Figure3-3

Figure3-4

Ifthenumberofmachinesisfixedbutthefirmemploysmoreandmoreworkers,eachadditionalworkerwillprobablycontributelessextraoutput.Productionfunctionsgenerallyexhibitdiminishingmarginalproduct.

Firmscomparetheextrarevenuefromonemoreworker(P×MPL)withthecostofthatworker,whichisthenominal(dollar)wage(W).IfP×MPL>W,thefirmwillwanttohiremoreworkers,andconversely,ifP×MPL<W,thefirmwillwanttohirefewerworkers.ThefirmhastheoptimalnumberofworkerswhenP×MPL=W,orwhenthemarginalproductoflaborequalstherealwage(W/P):

MPL=W/P.

Therealwagerepresentsthecompensationofworkersintermsofgoods—unitsofrealGDP—ratherthanintermsofdollars.

Sincelaborandcapitalaretreatedsymmetrically,anexactlyanalogousargumentleadstotheconclusionthatthefirmemployscapitaluptothepointwherethemarginalproductofcapital(MPK)equalstherealrentalprice(R/P),whereRrepresentsthedollarcostofaunitofcapital:

MPK=F(K+1,L)–F(K,L)=R/P.

TheDivisionofNationalIncome

Sinceeachfactorofproductionispaidanamountequaltoitsmarginalcontributiontooutput,totalrealpaymentstolaborequal(W/P)×L=MPL×L,andtotalrealpaymentstocapitalequal(R/P)×K=MPK×K.TotaloutputequalsY.Realeconomicprofitisthedifferencebetweenrealoutputandtotalrealpaymentstofactorsofproduction;itequalstheearlierexpressionforprofitdividedthroughbyP:

RealEconomicProfit=Y–[(R/P)×K]–[(W/P)×L].

Iftheproductionfunctionisconstantreturnstoscale,realeconomicprofitiszero.Provingthisingeneralrequirescalculus,butitcanbeillustratedintermsoftheearlierexample,whereK=40,L=10,andF(K,L)=(KL)1/2=:

SoMPK×K+MPL×L=0.25(40)+1(10)=10+10=20=Y.

CaseStudy:TheBlackDeathandFactorPrices

Avividexampleofhowfactorquantitiesaffectfactorpricescomesfromthe1300s,whenthebubonicplaguewasrifeinEurope.Withinafewyears,thepopulationfellbyalmostone-third.Accordingtotheneoclassicaltheoryofdistribution,thedeclineintheamountoflaborshouldhavecausedrealwagestorise,asindeedtheydid.Apeasantwhomanagedtosurvivetheplagueendedupprosperingfinancially!Andthereductioninlaborshouldhavecausedthereturntoland,theothermajorfactorofproductionatthetime,todecline.Withfewerworkerstofarmtheland,anadditionalunitoflandwouldhaveyieldedlessadditionaloutput.Again,thepredictionofthetheoryisconfirmed,asrealrentsfellbyover50percentandthelandedclassexperiencedreducedincomes.

TheCobb–DouglasProductionFunction

Figure3-5

OnefeatureofU.S.dataisthatfactorshares—thedivisionofincomebetweencapitalandlabor—havebeenmoreorlessconstantovertime.EconomistPaulDouglas,wholaterwentontobecomeaU.S.senatorfromIllinois,notedthisconstancyoffactorsharesin1927.Supposethattheeconomyiscompetitivesothatfactorsarepaidtheirmarginalproducts.Whatproductionfunctionthenimpliesthatfactorsharesareconstant?Inotherwords,whatproductionfunctionimpliesthattheratioofcapitalpaymentstoincomeandtheratiooflaborpaymentstoincomeareconstant?

TheanswersuppliedbymathematicianCharlesCobbwasthatthefunctionhastobeoftheform

Y=AKαL1–α,

whereAisanarbitrarypositiveconstant,sothatthefactorsharesareconstantandequaltoαand(1–α):

(MPK×K)/Y=α

MPL×L=(1–α).

RegardlessoftheactualvaluesofKandL,thisfunctionwillsatisfytheseequations.ItbecameknownastheCobb–Douglasproductionfunctionandiswidelyusedineconomics.Sincelabor’sshareoftotaloutputintheUnitedStatesisapproximately0.7,theproductionpossibilitiesoftheU.S.economycanbeapproximatedbythefunction

Y=K0.3L0.7.

Theearlierexample[Y=(KL)1/2]isaspecialcaseoftheCobb–Douglasproductionfunction,whereA=1andα=1/2.Goingbacktothatexample,wecanseethat

(MPK×K)/Y=(MPL×L)/Y=1/2,

soitdoesindeedexhibitconstantfactorshares.

CaseStudy:LaborProductivityastheKeyDeterminantofRealWages

Table3-1

Theneoclassicaltheoryofdistributionstatesthatthemarginalproductoflaborwillequaltherealwage.TheCobb–Douglasproductionfunctionhasthepropertythatthemarginalproductoflaborisproportionaltoaveragelaborproductivity(Y/L).Sothetheorypredictsthatgrowthofrealwagesshouldequalgrowthofaveragelaborproductivity.FortheUnitedStates,thedataconfirmthisprediction.Overthepasthalfcentury,averagelaborproductivityandrealwageshaveeachrisenabout2percentperyear.Furthermore,duringshorterperiodsoftime,whengrowthinlaborproductivityhasbeenhigherorlowerthanthelong-termaverage,realwageslikewisehaveriseninlinewithproductivity.

FYI:TheGrowingGapBetweenRichandPoor

Supplement3-3,“Labor’sShareofOutputintheUnitedKingdom”

Incomeinequalitybetweenhigh-wageworkersandlow-wageworkersismuchgreatertodaythanitwasinthe1970s.Oneexplanationarguesthatskill-biasedtechnologicalchangehasincreasedthedemandforskilledworkersfasterthantheeducationsystemhassuppliedsuchworkers.Asaresult,thewagesofskilledworkershavegrownrelativetothoseofunskilledworkers.ArecentbookbyeconomistsClaudiaGoldinandLawrenceKatz,discussedinChapter3ofthetextbook,highlightsthisexplanation.Theyarguethatskill-biasedtechnologicalprogresshascontinuedinrecentdecadessimilartowhathadhappenedthroughoutmuchofthetwentiethcenturybuteducationalattainmenthasslowed,puttingupwardpressureontherelativewagesofskilledworkers.

3-3 WhatDeterminestheDemandforGoodsandServices?

Sofar,wehavelookedatthetoppartofthecircularflowandfoundthat,givenfactorsuppliesKandL,totaloutputisY=F(K,L)andtherealwageandrealrentalrateofcapitalaredeterminedbythemarginalproductoflaborandcapital.Wenowexaminethedemandforoutput,which,asthecircularflowdiagramillustrates,comesfromconsumption,investment,andgovernmentspending.Tosimplifyouranalysis,weignorenetexportsandfocusonaclosedeconomythatdoesnottradewiththerestoftheworld.Chapter6extendsourframeworktotheopeneconomy.

Consumption

Consumptionisthelargestsourceofdemandandsoisanaturalstartingpoint.IndividualsreceivewageandprofitincometotalingY.Someofthisincomeispaidtogovernmentintheformoftaxes.Thegovernmentalsogivestransferpayments(forexample,unemploymentinsurance,SocialSecurity)toindividuals.Foraggregatepurposes,onlythenetflowfromindividualstothegovernmentmatters:

T=Taxes–TransferPayments.

Disposableincome(after-taxincome)isY–T.

Theconsumptiondecisionisadecisionbetweenconsumingnoworsavingtoconsumeatsometimeinthefuture.Consequently,thedecisiondependsonexpectationsaboutfutureeconomicconditionsaswellasoncurrentcircumstances.Fornow,however,wepostponedetaileddiscussionoftheseissuesuntilChapter16andconcentrateonthesimpleststoryofconsumerbehavior.

Theprimarydeterminantofconsumptionisdisposableincome,andtherelationshipbetweenconsumptionanddisposableincomeisknownastheconsumptionfunction:

C=C(Y–T).

Thisnotationsimplymeansthatconsumptiondependsondisposableincome.Anexampleofaconsumptionfunctionis

C=a+b(Y–T),

whereaandbareparameters.

Figure3-6

Theamountthatconsumptionchangeswhendisposableincomechangesisthemarginalpropensitytoconsume(MPC).Intheexampleabove,theMPCisaconstantequaltob.Moregenerally,itmightbedifferentatdifferentincomelevels.Sinceweexpectthatsomeonewhogetsanextradollarwillsavesomeofitandspendsomeofit,weexpecttheMPCtobeanumberbetweenzeroandone.

Investment

Supplement3-4,“Economists’Terminology”

Themaindeterminantofinvestmentistheinterestrate.(Wesupposethatthereisasingleinterestrateintheeconomy.Thisisareasonableassumptionbecause,althoughtherearemanydifferentinterestratesintheeconomy,theytendtomovefairlycloselytogether.)

Investmentdependsontheinterestratebecauseinvestmentdecisionsaremadewithaneyetothefuture.Firmsfaceanumberofdifferentinvestmentopportunitiesorprojectswithdifferingreturns.Firmscomparethereturnontheseprojectswiththecostofborrowingtofinancethem—inotherwords,withtheinterestrate.Theinterestrateisthecostofinvestment.

Theinterestratesthatarequotedinthenewspapersarenominalinterestrates,meaningthattheyarequotedindollarterms.Anominalinterestrateof10percentmeansthatifyouborrow$100thisyear,youmustrepay$110nextyear.Buteconomicsemphasizesthatpeopleultimatelycarenotaboutthedollarcostofthingsbutratheraboutwhatthosedollarsrepresentintermsofrealgoods.Inatimeofinflation,thenominalinterestratedoesnotmeasurethetruerealcostofborrowing.Toseethis,supposethattheinflationrateisalso10percent,andthepriceofatypicalgoodtodayis$1.Then$100willbuy100unitstoday.Butnow,ifyouhavetorepay$110nextyear,thatstillonlyrepresents100unitsofGDP,since10percentinflationmeansthatthenewpricelevelis1.1.Thenominalcostoftheloanis10percent,buttherealinterestrateiszero.

Figure3-7

Firmslookattherealinterestratewhenmakingtheirinvestmentdecisions.Theycomparetherealreturnonaninvestmentproject(howmanyextragoodscanbeproducedtomorrowifgoodsaregivenuptoday)withtherealcost.Thus,wewritetheinvestmentfunction:

I=I(r),

whererdenotestherealinterestrate.

GovernmentPurchases

Thefinalcomponentofexpenditureisgovernmentspending.Thisisthepurchasebyfederal,state,andlocalgovernmentsofgoodsandservices.Itdoesnotincludetransferpayments;thesecontributeindirectlytothedemandforgoodsandservicesthroughtheireffectonconsumption.Governments’choicesofGandTdeterminetheirfiscalpolicy.Onemeasureofagovernment’sfiscalpolicystanceisthedeficit(DEF=G–T).Ifthegovernmenttakesactionstoincreasethedeficit(increasingGordecreasingT),thisisknownasanexpansionarypolicy;theconverseisacontractionarypolicy.ThecurrentanalysistakesGandTasexogenous().

FYI:TheManyDifferentInterestRates

Thetextbookspeaksthroughoutof“the”interestrate.Yetweknowthat,intherealworld,therearemanydifferentinterestrates.Interestratesdifferbecauseoftermtomaturity,creditrisk,andtaxtreatment.Butformostmacroeconomicanalysis,wecanignorethesedistinctionsbecausedifferentinterestratestendtomovetogether.

3-4 WhatBringstheSupplyandDemandforGoodsandServicesintoEquilibrium?

Fromthecircularflowdiagram,thesupplyofgoods,Y,equalsthedemandforgoods(C+I+G).ButYisdeterminedbythetechnology,togetherwiththestocksofcapitalandlabor,whileC,I,andGdependonthechoicesofhouseholds,firms,andgovernment.Whatguaranteesthatsupplyequalsdemand?Frommicroeconomics,weshouldexpectthatsomepricewillmatchupsupplyanddemand.

AnaturalcandidatefortheequilibratingpricemightseemtobeP,sinceitrepresentsthepriceofaunitofGDPintermsofdollars.But,infact,neitherthesupplynoranycomponentofthedemandforgoodsdependsonthegeneralpricelevelbecausepeoplecareaboutrealvalues.If,say,thepricelevelincreases,theneverythingcostsmoreindollarterms,butrealpricesarenotaffected.Instead,thepricethatensuresequilibriuminthegoodsmarketisactuallytherealinterestrate.(WewillseeinChapter7thatthepricelevelisactuallydeterminedinthemoneymarket.SincePisthepriceofgoodsintermsofdollars,1/Pisthepriceofdollarsintermsofgoods,ortherealpriceofmoney.)

EquilibriumintheMarketforGoodsandServices:TheSupplyandDemandfortheEconomy’sOutput

Thefollowingequationssummarizethedemandandsupplyofgoodsandservicesfortheeconomy:

Since

,

UsingtheseequationsandnotingthatGandTarefixedbypolicyandYisfixedbythefactorsofproductionandtheproductionfunction,wecanderivethefollowingrelationship:

wherethesupplyofoutputequalsthedemandforoutput.SinceY,C,andGarefixedinthisequation,equilibriummustbeachievedbyadjustmentoftheinterestrate.Ifthesupplyofgoodsandservicesexceedsthedemandforgoodsservices,thentheinterestratewillfall,encouraginginvestmentandincreasingthedemandforgoodsandservices.Conversely,ifthesupplyofgoodsandservicesfallsshortofthedemandforgoodsandservices,thentheinterestratewillrise,reducinginvestmentanddecreasingthedemandforgoodsandservices.

EquilibriumintheFinancialMarkets:TheSupplyandDemandforLoanableFunds

Wecanrewritetheequilibriumconditionas

Nowaddandsubtract:

Thiscanberewrittenas

Inthiscase,isprivatesaving,andispublicsaving.Combiningthesavingtermsintonationalsaving,S,weobtain

Supplement3-5,“PublicandPrivateSaving”

Fromthisequation,wecanseethatwhenthegoodsmarketequilibriumconditionisrewrittenintermsofsavingandinvestment,ithasaninterpretationintermsofequilibriuminthefinancialmarkets.Savingandinvestmentrepresentthesupplyofanddemandforloanablefunds.Individualsandgovernmentssave,makingfundsavailableforinvestment.Iftheinterestrateishigh,therewillnotbeverymuchdemandforinvestment,implyingtoolittleinvestmentrelativetotheamountofsaving.Theinterestratewillthenfall.Theoppositeoccursiftheinterestrateistoolow.

Figure3-8

ChangesinSaving:TheEffectsofFiscalPolicy

Wecannowuseoursimplemodeltocarryoutcomparativestaticexperiments.Amongthemostinterestingarethosethatentailachangeingovernmentpolicyvariables.Supposethatthegovernmentcarriesoutanexpansionaryfiscalpolicybyincreasingspendingorcuttingtaxes.Then,thegovernmentdeficitwillincrease,soSgwillfall.Torestoreequilibriuminthegoodsmarket,theinterestratemustrise:Sincethereisagreaterdemandforgoods,butafixedsupply,theinterestratehastorisetodecreaseinvestmentdemand.Expressedintermsoftheloansmarket,thereislesssavingavailable,sotherewillbelessinvestmentinequilibrium.Thisisknownascrowdingout.

Figure3-9

Noticethatifthereisanincreaseingovernmentspendingof∆G,theremustbeanexactlyequaldecreaseininvestmentspending.Governmentspendingcrowdsoutinvestmentcompletely.

Supplement3-6,“WarsandInterestRates”

AnalogousresultsholdforachangeinT.Givenadecreaseintaxesequalto∆T,disposableincomewillincreaseby∆T,soconsumptionwillincreaseby∆C=MPC×∆T.National

saving,thus,fallsbythisamount.(Equivalently,privatesavingrisesby(1–MPC)∆Tandgovernmentsavingfallsby∆T,sothenetchangeisMPC×∆T.)Ataxcutthusreducessaving,increasestherealinterestrate,andcrowdsoutinvestmentbyanamountequaltoMPC×∆T.

ChangesinInvestmentDemand

Supplement3-7,“AFirstLookatNominalandRealInterestRates”

Figure3-10

Themodelemphasizesthatinvestmentisendogenous,sinceitdependsontheinterestrate,buttheremayalsobeexogenouschangesininvestmentdemand.Forexample,atechnologicalinnovationmightleadfirmstowishtoinvestinnewcapitalgoods(suchascomputers),orgovernmentsmightchangethetaxlawsinwaysthataffectfirms’incentivestoinvest.Thesecanberepresentedasshiftsinthedemandforinvestment.Perhapssurprisingly,themodelpredictsthatactualinvestmentwillbeunchangedinequilibrium.Sinceinvestmentmustequalsaving,andsincethesupplyofsavingisfixedexogenously,thechangein