Topic3:NationalIncome:

WhereitComesFromandWhereitGoes(chapter3) revised9/21/09

slide1IntroductionInthelastlecturewedefinedandmeasuredsomekeymacroeconomicvariables.Nowwestartbuildingtheoriesaboutwhatdeterminesthesekeyvariables.Inthenextcouplelectureswewillbuilduptheoriesthatwethinkholdinthelongrun,whenpricesareflexibleandmarketsclear.CalledClassicaltheoryorNeoclassical.

slide2TheNeoclassicalmodelIsageneralequilibriummodel:InvolvesmultiplemarketseachwithownsupplyanddemandPriceineachmarketadjuststomakequantitydemandedequalquantitysupplied.slide3NeoclassicalmodelThemacroeconomyinvolvesthreetypesofmarkets:Goods(andservices)MarketFactorsMarketorLabormarket,neededtoproducegoodsandservicesFinancialmarket

Arealsothreetypesofagentsinaneconomy:HouseholdsFirmsGovernmentslide4Financial

MarketGoods

MarketLabor

MarketHouseholdsGovernmentFirmssavingborrowingborrowingconsumptiongovernmentspendinginvestmentproductionworkhiring

ThreeMarkets–Threeagentsslide5Neoclassicalmodel Agentsinteractinmarkets,wheretheymaybedemanderinonemarketandsupplierinanother1)Goodsmarket:

Supply:firmsproducethegoods

Demand:byhouseholdsforconsumption,governmentspending,andotherfirmsdemandthemforinvestmentslide6Neoclassicalmodel2)Labormarket(factorsofproduction)

Supply:Householdsselltheirlaborservices.

Demand:Firmsneedtohirelabortoproducethegoods.3)Financialmarket

Supply:householdssupplyprivatesavings:incomelessconsumption

Demand:firmsborrowfundsforinvestment;governmentborrowsfundstofinanceexpenditures.slide7NeoclassicalmodelWewilldevelopasetofequationstocharac-terizesupplyanddemandinthesemarketsThenusealgebratosolvetheseequationstogether,andseehowtheyinteracttoestablishageneralequilibrium.Startwithproduction…slide8Financial

MarketGoods

MarketLabor

MarketHouseholdsGovernmentFirmssavingborrowingborrowingconsumptiongovernmentspendinginvestmentproductionworkhiring

ThreeMarkets–Threeagentsslide9Part1:Supplyingoodsmarket:ProductionSupplyinthegoodsmarketdependsonaproductionfunction: denotedY=F(K,

L)WhereK= capital:tools,machines,andstructuresusedinproductionL= labor:thephysicalandmentaleffortsofworkersslide10Theproductionfunctionshowshowmuchoutput(Y)theeconomycanproducefrom

K

unitsofcapitalandL

unitsoflabor.reflectstheeconomy’sleveloftechnology.Generally,wewillassumeitexhibitsconstantreturnstoscale.slide11ReturnstoscaleInitiallyY1

=F(K1

,

L1

)Scaleallinputsbythesamemultiplez:

K2=zK1andL2=zL1

forz>1 (Ifz=1.25,thenallinputsincreaseby25%)Whathappenstooutput,Y2=F(K2

,

L2

)?Ifconstantreturnstoscale,Y2=zY1

Ifincreasingreturnstoscale,Y2>zY1

Ifdecreasingreturnstoscale,Y2<zY1

slide12Exercise:determinereturnstoscaleDeterminewhetherthefollowingproductionfunctionhasconstant,increasing,ordecreasingreturnstoscale:slide13Exercise:determinereturnstoscale

slide14AssumptionsofthemodelTechnologyisfixed.Theeconomy’ssuppliesofcapitalandlaborarefixedatslide15DeterminingGDPOutputisdeterminedbythefixedfactorsuppliesandthefixedstate

oftechnology:Sowehaveasimpleinitialtheoryofsupplyinthegoodsmarket:slide16Financial

MarketGoods

MarketLabor

MarketHouseholdsGovernmentFirmssavingborrowingborrowingconsumptiongovernmentspendinginvestmentproductionworkhiring

ThreeMarkets–Threeagentsslide17Part2:EquilibriuminthefactorsmarketEquilibriumiswherefactorsupplyequalsfactordemand.Recall:Supplyoffactorsisfixed.Demandforfactorscomesfromfirms.slide18DemandinfactorsmarketAnalyzethedecisionofatypicalfirm.Itbuyslaborinthelabormarket,wherepriceiswage,W.Itrentscapitalinthefactorsmarket,atrateR.Ituseslaborandcapitaltoproducethegood,whichitsellsinthegoodsmarket,atpriceP.slide19DemandinfactorsmarketAssumethemarketiscompetitive: Eachfirmissmallrelativetothemarket,soitsactionsdonotaffectthemarketprices. Ittakespricesinmarketsasgiven-W,R,P.slide20DemandinfactorsmarketItthenchoosestheoptimalquantityofLaborandcapitaltomaximizeitsprofit.Howwriteprofit:Profit =revenue-laborcosts-capitalcosts =PY-WL-RK =PF(K,L)-WL-RKslide21DemandinthefactorsmarketIncreasinghiringofLwillhavetwoeffects:1)Benefit:raiseoutputbysomeamount2)Cost:raiselaborcostsatrateWToseehowmuchoutputrises,weneedthemarginalproductoflabor(MPL)slide22Marginalproductoflabor(MPL)Anapproximatedefinition(usedintext):

Theextraoutputthefirmcanproduceusingoneadditionallabor(holdingotherinputsfixed):

MPL

=

F

(K,

L+1)

–

F

(K,

L)slide23YoutputTheMPLandtheproductionfunctionLlabor1MPL1MPL1MPLAsmorelaborisadded,MPL

SlopeoftheproductionfunctionequalsMPL:riseoverrunslide24DiminishingmarginalreturnsAsafactorinputisincreased,itsmarginalproductfalls(otherthingsequal).Intuition:

LwhileholdingKfixedfewermachinesperworkerlowerproductivityslide25MPLwithcalculusWecangiveamoreprecisedefinitionofMPL: Therateatwhichoutputrisesforasmallamountofadditionallabor(holdingotherinputsfixed): MPL=[F

(K,L+DL)–F

(K,L)]/DL

whereDis‘delta’andrepresentschangeEarlierdefinitionassumedthatDL=1. F

(K,L+1)–F

(K,L)Wecanconsidersmallerchangeinlabor.slide26MPLasaderivativeAswetakethelimitforsmallchangeinL:

Whichisthedefinitionofthe(partial)derivativeoftheproductionfunctionwithrespecttoL,treatingKasaconstant. Thisshowstheslopeoftheproductionfunctionatanyparticularpoint,whichiswhatwewant.slide27TheMPLandtheproductionfunctionLlaborYoutputMPLisslopeoftheproductionfunction(riseoverrun)F

(K,L+DL)–F

(K,L))slide28fL:F(L):L:DerivativeasmarginalproductYL6

40.50.751.59639411993

slide29Returntofirmproblem:hiringLFirmchoosesLtomaximizeitsprofit.HowwillincreasingLchangeprofit?

Dprofit =Drevenue-Dcost

=P*MPL-W Ifthisis: >0 shouldhiremore <0 shouldhireless =0 hiringrightamountslide30FirmproblemcontinuedSothefirm’sdemandforlaborisdeterminedbythecondition:

P*MPL=W HiresmoreandmoreL,untilMPLfallsenoughtosatisfythecondition.Alsomaybewritten:

MPL=W/P,whereW/Pisthe‘realwage’slide31RealwageThinkaboutunits:W=$/hourP=$/goodW/P

=($/hour)/($/good)=goods/hourTheamountofpurchasingpower,measuredinunitsofgoods,thatfirmspayperunitofworkslide32Example:derivinglabordemandSupposeaproductionfunctionforallfirmsintheeconomy:slide33Labordemandcontinuedslide34Labormarketequilibriumslide35Financial

MarketGoods

MarketLabor

MarketHouseholdsGovernmentFirmssavingborrowingborrowingconsumptiongovernmentspendinginvestmentproductionworkhiring

ThreeMarkets–Threeagentsslide36MPLandthedemandforlaborEachfirmhireslabor

uptothepointwhereMPL=W/PUnitsofoutputUnitsoflabor,LMPL,LabordemandRealwageslide37DeterminingtherentalrateWehavejustseenthatMPL

=W/PThesamelogicshowsthatMPK

=R/P

:diminishingreturnstocapital:MPK

asK

TheMPK

curveisthefirm’sdemandcurve

forrentingcapital.FirmsmaximizeprofitsbychoosingK

suchthatMPK=R/P

.slide38Howincomeisdistributed:totallaborincome=totalcapitalincome= Wefoundthatifmarketsarecompetitive,thenfactorsofproductionwillbepaidtheirmarginalcontributiontotheproductionprocess.slide39Euler’stheorem:Underourassumptions(constantreturnstoscale,profitmaximization,andcompetitivemarkets)…totaloutputisdividedbetweenthepaymentstocapitalandlabor,dependingontheirmarginalproductivities,withnoextraprofitleftover.national

incomelabor

incomecapital

incomeslide40MathematicalexampleConsideraproductionfunctionwithCobb-Douglasform:

Y=AK

L1-

whereAisaconstant,representingtechnology

Showthishasconstantreturnstoscale: multiplyfactorsbyZ:

F(ZK,ZY)=A(ZK)

(ZL)1-

=AZ

K

Z1-

L1-

=AZ

Z1-

K

L1-

=ZxAK

L1-

=ZxF(K,L)slide41MathematicalexamplecontinuedComputemarginalproducts:

MPL=(1-

)AK

L-

MPK=

AK-1L1-

Computetotalfactorpayments:

MPLxL+MPKxK =(1-

)AK

L-

xL+

AK-1L1-

xK =(1-

)AK

L1-

+

AK

L1-

=AK

L1-

=Y Sototalfactorpaymentsequalstotalproduction.slide42Financial

MarketGoods

MarketLabor

MarketHouseholdsGovernmentFirmssavingborrowingborrowingconsumptiongovernmentspendinginvestmentproductionworkhiring

ThreeMarkets–Threeagentsslide43OutlineofmodelAclosedeconomy,market-clearingmodelGoodsmarket:Supplyside:productionDemandside:C,I,andGFactorsmarketSupplysideDemandsideLoanablefundsmarketSupplyside:savingDemandside:borrowingDONE

DONE

Next

DONE

slide44Demandforgoods&servicesComponentsofaggregatedemand:C=consumerdemandforg&sI=demandforinvestmentgoodsG=governmentdemandforg&s (closedeconomy:noNX)slide45Consumption,Cdef:disposableincomeistotalincomeminustotaltaxes:Y–TConsumptionfunction:C=C(Y–T) Showsthat(Y–T)

C

def:Themarginalpropensitytoconsume(MPC)istheincreaseinCcausedbyanincreaseindisposableincome.SoMPC=derivativeoftheconsumptionfunctionwithrespecttodisposableincome.MPCmustbebetween0and1.slide46TheconsumptionfunctionCY–TC

(Y–T)runriseTheslopeoftheconsumptionfunctionistheMPC.slide47Consumptionfunctioncont.Supposeconsumptionfunction:

C=10+0.75Y

MPC=0.75 Forextradollarofincome,spend0.75dollarsconsumption Marginalpropensitytosave=1-MPCslide48Investment,ITheinvestmentfunctionisI=I(r), wherer

denotestherealinterestrate,

thenominalinterestratecorrectedforinflation.Therealinterestrateis

thecostofborrowing

theopportunitycostofusingone’s ownfunds

tofinanceinvestmentspending. So,

r

I

slide49TheinvestmentfunctionrII

(r

)Spendingoninvestmentgoods

isadownward-slopingfunctionoftherealinterestrateslide50Governmentspending,GGincludesgovernmentspendingongoodsandservices.Gexcludestransferpayments

Assumegovernmentspendingandtotaltaxesareexogenous:slide51Themarketforgoods&servicesTherealinterestrateadjusts

toequatedemandwithsupply.slide52TheloanablefundsmarketAsimplesupply-demandmodelof

thefinancialsystem.Oneasset:“l(fā)oanablefunds” demandforfunds: investment supplyoffunds: saving “price”offunds: realinterestrateslide53Demandforfunds:InvestmentThedemandforloanablefunds:comesfrominvestment:

Firmsborrowtofinancespendingonplant&equipment,newofficebuildings,etc.Consumersborrowtobuynewhouses.dependsnegativelyonr

,the“price”ofloanablefunds(thecostofborrowing).slide54LoanablefundsdemandcurverII

(r

)Theinvestmentcurveisalsothedemandcurveforloanablefunds.slide55Supplyoffunds:SavingThesupplyofloanablefundscomesfromsaving:Householdsusetheirsavingtomakebankdeposits,purchasebondsandotherassets.Thesefundsbecomeavailabletofirmstoborrowtofinanceinvestmentspending.Thegovernmentmayalsocontributetosavingifitdoesnotspendallofthetaxrevenueitreceives.slide56Typesofsavingprivatesaving(sp)=(Y–T)–Cgovernmentsaving(sg)=T–Gnationalsaving,S

=sp+sg=(Y–T)–C+T–G=Y–C–Gslide57EXERCISE:

CalculatethechangeinsavingSupposeMPC=0.8Foreachofthefollowing,compute

S:

G =100

T =100slide58Answersslide59digression:

BudgetsurplusesanddeficitsWhenT

>

G,

budgetsurplus=(T–

G)=publicsavingWhenT

<

G

,

budgetdeficit=(G–T)

andpublicsavingisnegative.WhenT=

G,

budgetisbalancedandpublicsaving=0.slide60TheU.S.FederalGovernmentBudgetslide61TheU.S.FederalGovernmentDebtFunfact:Intheearly1990s,nearly18centsofeverytaxdollarwenttopayinterestonthedebt.slide62LoanablefundssupplycurverS,INationalsavingdoesnotdependonr,

sothesupplycurveisvertical.slide63LoanablefundsmarketequilibriumrS,II

(r

)EquilibriumrealinterestrateEquilibriumlevelofinvestmentslide64Thespecialroleofrradjuststoequilibratethegoodsmarketandtheloanablefundsmarketsimultaneously: IfL.F.marketinequilibrium,then Y–C–G=I

Add(C+G)tobothsidestoget Y=C+I+G

(goodsmarketeq’m)Thus,Eq’minL.F.marketEq’mingoodsmarketslide65AlgebraexampleSupposeaneconomycharacterizedby:Factorsmarketsupply:laborsupply=1000Capitalstocksupply=1000Goodsmarketsupply:Productionfunction:Y=3K+2LGoodsmarketdemand:Consumptionfunction:C=250+0.75(Y-T)Investmentfunction:I=1000–5000rG=1000,T=1000slide66Algebraexamplecontinued

Giventheexogenousvariables(Y,G,T),findtheequilibriumvaluesoftheendogenousvariables(r,C,I) Findrusingthegoodsmarketequilibriumcondition:Y=C+I+G5000=250+0.75(5000-1000)+1000 -5000r+10005000=5250–5000r-250=-5000rso

r=0.05AndI=1000–5000*(0.05)=750 C=250+0.75(5000-1000)=3250slide67MasteringtheloanablefundsmodelThingsthatshiftthesavingcurvepublicsavingfiscalpolicy:changesinGorTprivatesavingpreferencestaxlawsthataffectsaving(401(k),IRA)slide68CASESTUDY

TheReaganDeficitsReaganpoliciesduringearly1980s:increase