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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:“loanablefunds” 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
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