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UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
1
Chapter10
1. FactsofGrowth
ξ Theemphasisisonoutputpercapitaratherthanthenumbersfortotaloutput.Theevolutionofacountry’sstandardoflivingisgivenbytheevolutionofitsoutputpercapita,nottheevolutionofitstotaloutput.
ξ OutputpercapitaequalsGDPdividedbypopulation.
gt =Yt −Yt−1Yt
ξ LongtermgrowthisacompositionofshortormediumtermbusinesscyclesofaneconomyandusuallyillustratedthroughrealGDP.
ξ Sofar,inconstructingoutputnumbersforcountriesotherthantheUnitedStates,thestraightforwardmethodoftakingthatcountry’sGDPexpressedinthatcountry’scurrency,andthenusingthecurrentexchangeratetoexpressitintermsofdollarswouldcausecomplicationssuchas:
o Exchangeratecanvaryalot
o Thepricesofbasicgoodsdifferfromcountrytocountry.Sodoestheaverageconsumptionofanindividual.Ingeneral,loweracountry’soutputpercapita,thelowerthepricesoffoodandbasicservicesinthatcountry.
ξ Hence,tocompareGDPacrosscountries,weuseacommonsetofpricesforallcountries.AdjustedrealGDPnumbersaremeasuresofpurchasingpoweracrosscountries,alsocalledpurchasingpowerparity(PPP)numbers.
ξ Historicalobservations:
o ThepictureforOECDcountriesismuchthesameasallstartinhighlevelsofoutputpercapitaandthenthereisaclearconvergence.
o ConvergenceisalsovisibleformostAsianCountries.Japanleadingthepackwiththefourtigers(Korea,Singapore,HongKongandTaiwanclosebehind)
o ThepictureisverydifferentforAfricancountries
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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2. AggregateProductionFunction
ξ Outputwassimplyproportionaltotheamountoflaborusedbyfirms–morespecifically,proportionaltothenumberofworkersemployedbyfirms.
ξ Solongasourfocuswasonfluctuationsinoutputandemployment,theassumptionwasacceptable.But,asthefocusshiftstogrowth,thatassumptionwillnolongerdo.Itimpliesthatoutputperworkerisconstant,rulingoutgrowthaltogether.
ξ Therefore,nowweassumetherearetwoinputs–capitalandlabor–andthattherelationbetweenaggregateoutputandtwoinputare:
Y = AF(K ,N ) Y=aggregateoutput.
K=capital—thesumofallthemachines,plants,andoffice
buildingsintheeconomy.
N=labor—thenumberofworkersintheeconomy.
A=productivityfactor.
ξ Thefunction,F,whichtellsushowmuchoutputisproducedforgivenquantitiesofcapitalandlabor,istheaggregateproductionfunction.
o AggregateOutput,YisdependentonAggregatecapital,KandAggregateemployment,N.
o Note:thefunction,F,dependsonthestateoftechnology.TheHigherthestateoftechnology,thehigher foragivenKandagivenN.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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3. ReturnstoScaleandreturnstoFactors
ξ Whenthenumberofworkersandtheamountofcapitalinaneconomyincreasebyx,outputshouldalsodouble.
xY = F(xK , xN ) ξ Whatwouldhappenifonlyoneofthetwoinputsisincreased?
o Initially,therewouldbelargeincreasesincapitalbutascapitalincreasesfurthertheincrementalincreaseincapitalleadsonlytoasmallerandsmallerincreaseinoutput.Thisisknownasthedecreasingreturnstocapital
Decreasingreturnstocapitalreferstothepropertythatincreasesincapitalleadtosmallerandsmallerincreasesinoutputasthelevelofcapitalincreases.
o Similarly,thesameconceptappliestolabor.
Decreasingreturnstolaborreferstothepropertythatincreasesinlabor,givencapital,leadtosmallerandsmallerincreasesinoutputastheleveloflaborincreases.
4. OutputperWorkerandCapitalPerWorker
YN
= AF(KN, NN) = AF(K
N,1) = Af (k)
ξ Theamountofoutputperworker,Y/Ndependsontheamountofcapitalperworker,K/N.
o Ascapitalperworkerincreases,sodoesoutputperworker.
o Thiscanbeillustratedgraphically
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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ξ Thecurveisdrawnsothatincreasesincapitalleadtosmallerandsmallerincreasesinoutput.Thisfollowsfromthepropertythattherearedecreasingreturnstocapital.
ξ AtpointA,wherecapitalperworkerislow,anincreaseincapitalperworker,representedbythehorizontaldistanceAB,leadstoanincreaseinoutputperworkerequaltotheverticaldistanceA’B’.
ξ AtpointC,wherecapitalperworkerislarger,thesameincreaseincapitalperworker,presentedbythehorizontaldistanceCDleadstoamuchsmallerincreaseinoutputperworker,onlyC’D’.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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4.1 Sourcesofgrowth
ξ Increaseinoutputperworker(Y/N)cancomefromincreasesin:
o Capitalperworker(K/N)i.e.capitalaccumulation
o ImprovementsintheStateoftechnologythatshifttheproductionfunction,F,andleadtomoreoutputperworker(B’>A’)givencapitalperworker(A)i.e.viaTechnologicalprogress.
Note:Becauseofdecreasingreturnstocapital,capitalaccumulationbyitselfcannotsustaingrowth.
4.2 WhyCapitalAccumulationbyitselfcannotsustaingrowth
ξ Thisisbecauseofdecreasingreturnstocapital,sustainingasteadyincreaseinoutputperworkerwillrequirelargerandlargerincreasesinthelevelofcapitalperworker.Atsomestage,theeconomywillbeunwillingorunabletosaveandinvestenoughtofurtherincreasecapital.ATthatstage,outputperworkerwillstopgrowing.
ξ However,thisdoesnotmeansavingscannotincreaseoutputbuthighersavingratecannotpermanentlyincreasethegrowthrateofoutput.
ξ But,highersavingscansustainahigherlevelofoutput.Therefore,acountrywithahighersavingratewillhavehigherlevelofoutputpercapitalthantheother.
F(K/N,1)’
F(K/N,1)
Capitalperworker(K/N)A
B’
A’
Outputperworker,Y/N
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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Chapter11
5. Saving,CapitalAccumulationandOutput
ξ Atthecenterofthedeterminationofoutput:
o Theamountofcapitaldeterminestheamountofoutputbeingproduced
o Theamountofoutputdeterminestheamountofsavingandinturn,theamountofcapitalbeingaccumulatedovertime.
EffectsofCapitalonOutput
YN
= F(KN,1)
ξ Outputperworker(Y/N)isanincreasingfunctionofcapitalperworker(K/N).Undertheassumptionofdecreasingreturnstocapital,theeffectofagivenincreaseincapitalperworkeronoutputperworkerdecreases,astheratioofcapitalperworkergetslarger.Hence,whencapitalperworkerisalreadyveryhigh,furtherincreasesincapitalperworkerhaveonlyasmalleffectonoutputperworker.
ξ Nowfocusingonoutputandcapitalperworkerwecanrewritetheaboveequationas:
YN
= f (KN)
ξ Wherethefunctionf,representsthesamerelationbetweenoutputandcapitalperworkerasthefunctionF:
f (KN) ≡ F(K
N,1)
o Therearetwoassumptions:
Thesizeofthepopulation,participationrateandtheunemploymentrateareall‐constant.ThelaborforceisequaltopopulationtimestheparticipationrateandNisconstant.Under
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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thisassumption,outputperworker,outputpercapitaandoutputitself,allmoveproportionately.
Thereisnotechnologicalprogress,sothefunctionfdoesnotchangeovertime.
ξ Rewritetheaboveequation:
YtN
= f (Kt
N) ≡ F( Kt
N ,1)
Note:highercapitalperworkerleadstohigheroutputperworker.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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6. OutputandInvestment
ξ Wemakethreeassumptionstoderivetherelationbetweenoutputandinvestment:
o Weassumetheeconomyisclosed
I = S + (T −G)
o Weassumepublicsaving,T–G,isequaltozero.
I = S o Weassumethatprivatesavingisproportionaltoincome,so
S = sY
• Theparametersisthesavingrate.Itahsavaluebetweenzeroandone.
o Twoassumptionaboutsavings:
o Thesavingratedoesnotappeartosystemicallyincreaseordecreaseasacountrybecomesricher
o Richercountriesdonotappeartohavesystematicallyhigherorlowerratesthanpoorerones.
o Combiningthesetworelationsgives:
It = sYt
ξ Therefore,investmentisproportionaltooutput.Thehighertheoutput,thehigherissavingandisthehigherisinvestment.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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7. InvestmentandCapitalAccumulation
ξ Thinkofthecapitalstockasbeingmeasuredatthebeginningofeachyear,soKt referstothecapitalstockatthebeginningofyeart,Kt+1 tocapitalstockatthebeginningofyeart+1,andsoon.
ξ Assumethatcapitaldeprecatesatrateδ peryear,Thatis,fromoneyeartothenext,aproportionδ ofthecapitalstockbreaksdownandbecomesuseless.Equivalently,aproportion (1− δ ) ofcapitalstockremainsintactfromoneyeartothenext.
ξ Theevolutionofthecapitalstockisgivenby:
Kt+1 = (1− δ )Kt + It
ξ Replacinginvestmentfromtheequationabove, It = sYt
Kt+1
N= (1− δ )Kt
N+ s
YtN
ξ Note:Capitalperworkeratthebeginningofyeart+1=capitalperworkeratthebeginningofyeart
o Adjustedfordepreciation,plusinvestmentperworkerduringyeart,whichisequaltothesavingratetimesoutputperworkerduringyeart( ).
ξ Expandthetermsabove:
Kt+1
N−Kt
N= s
YtN
− δ Kt
N
ξ Thechangeinthecapitalstockperworker–representedbythedifference
betweenthetwotermsontheleft–isequaltosavingperworker( s YtN)–minus
depreciation(δ Kt
N).
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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7.1DynamicsofCapitalandOutput
Kt+1
N−Kt
N sYtN
δ Kt
N
ξ Investmentperworker,thefirsttermontheright.Thelevelofcapitalperworkerthisyeardeterminesoutputperworkerthisyear.Giventhesavingrate,outputperworkerdeterminestheamountofsavingperworkerandthistheinvestmentperworkerthisyear.
ξ Depreciationperworker,thesecondtermontheright.Thecapitalstockperworkerdeterminestheamountofdepreciationperworker.
ξ Observations:
o Ifinvestmentperworker>depreciationperworker,thechangeincapitalperworkerispositive:Capitalperworkerincreases.
o Ifinvestmentperworker<depreciationperworker,thechangeincapitalperworkerisnegative:Capitalperworkerdecreases.
Changeincapitalfrom
yearttoyeart+1
Investmentduring
yeart
Depreciation
duringyeart= ‐
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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Graphicallyillustrated:
ξ Thecurverepresentingoutputperworker,f(Kt/N),asafunctionofcapitalperworker.
ξ Outputperworkerincreaseswithcapitalperworker,but–becauseofdecreasingreturnstocapital–theeffectissmallerthehigherthelevelofcapitalperworker.
ξ Observations:
o Therelationrepresentinginvestmentperworker, sf (Kt / N ) ,hasthesameshapeastheproductionfunction,exceptthatitislowerbyafactorofs(savingrate)
o IfthelevelofcapitalperworkerisequaltoK0 / N .OutputperworkerisgivenbythedistanceAB,andinvestmentperworkerisgivenbyverticaldistanceAC=s*AB
o TherelationrepresentingdepreciationperworkerδKt / N isrepresentedbyastraightline.Atlevelofcapitalperworker,K0 / N ,depreciationperworkerisgivenbytheverticaldistanceAD.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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o Thechangeincapitalperworkerisgivenbythedifferencebetweeninvestmentperworkeranddepreciationperworker.
CD = AC − AD ,socapitalperworkerincreases
8. SteadyStateCapitalandoutput
ξ CapitalperworkereventuallyreachesK*/N,thelevelatwhichinvestmentisequaltodepreciation.OncetheeconomyhasreachedthelevelofcapitalperworkerK*/N,outputperworkerandcapitalperworkerremainconstantatY*/NandK*/N,theirlongrunequilibrium.
o ThereasonforimagineifacountryhascapitalperworkerlowerthanK*/N–thiswouldmeanhighersavingscanleadtoincreasesinoutputandcapitalaccumulationsincetheincreaseincapitalismuchlargerattheinitialstages–decreasingreturnsofcapitaltheory
o However,inacountrywithcapitalperworkerhigherthanK*/N,thesavingratecannotsustainthecapitalaccumulationandthedepreciationiscapitalwouldbegreaterthantheincreaseincapitalresultingincapitalperworkertoreducecloserorequaltoK*/N.
ξ Therefore,thesteadystatevalueofcapitalperworkercanbegivenas:
sf (K*
N) = δ K
*
N
ξ Thesteadystatevalueofcapitalperworkerissuchthattheamountofsavingperworkerisjustsufficienttocoverdepreciationofthecapitalstockperworker
YN
= f (K*
N)
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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ξ Observations:
1. Thesavingratehasnoeffectonthelongrungrowthrateofoutputperworker,whichisequaltozero.
o Inotherwords,inthelongrun,thegrowthrateofoutputisequaltozero,nomatterwhatthesavingrate.
2. Nonetheless,thesavingratedeterminesthelevelofoutputperworkerinthelongrun.Otherthingsequal,countrieswithahighersavingratewillachievehigheroutputperworkerinthelongrun.
o Again,itisnotedthatcountrieswithahighersavingratewillachievehigheroutputperworkerinthelongrun.
3. Anincreaseinthesavingratewillleadtohighergrowthofoutputperworkerforsometime,butnotforever.Thesavingratedoesnotaffectthelong‐rungrowthrateofoutputperworker.Afterahighersavingrate,growthwillendoncetheeconomyreachesitsnewsteadystate.
o Weknowthatanincreaseinthesavingdoesnotaffectthelongrungrowthrateofoutputperworker,whichremainsequaltozero.Furthermore,theincreaseinsavingrate(stos1)doesleadtoanincreaseinthelevelofoutputperworker(fromYo/NtoY1/N).
o Itfollowsthat,asoutputperworkerincreasestoitsnewhigherlevel,theeconomywillgothroughaperiodofpositivegrowthbutthiscomestoanendwhentheeconomyreachessteadystate.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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9. With/WithoutTechnologicalProgress:SavingRateandOutput
ξ Aneconomyinwhichthereistechnologicalprogresshasapositivegrowthrateofoutputperworker,eveninthelongrunascomparedtoonewithouttechnologicalprogress.
ξ Thislong‐rungrowthrateisindependentofthesavingrateiftechnologicalprogressisconsidered.
ξ Anincreaseinthesavingrateleadstogrowthgreaterthanthesteady‐stategrowthrateforsometime,untiltheeconomyreachesitsnewhigherpath
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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10. SavingrateandConsumption
ξ Governmentscanaffectthesavingrateinvariousways.Firstly,theycanvarypublicsaving,Givenprivatesaving,positivepublicsaving–abudgetsurplus,inotherwords–leadstohigheroverallsaving.
ξ Savingrate=0
o Aneconomyinwhichthesavingrateiszeroisaneconomyinwhichcapitalisequaltozero.Inthiscase,outputisalsoequaltozero,andsoisconsumption
ξ SavingRate=1
o Peoplesavealltheirincome,thelevelofcapitalandoutputwillbeveryhigh.Simplymaintainingthatlevelofoutputrequiresthatalloutputbedevotedtoreplacingdepreciation.Asavingrateequaltoonealsoimplieszeroconsumptioninthelongrun.
ξ GoldenRulelevelofCapital
o Thelevelofcapitalassociatedwiththevalueofthesavingratethatyieldsthehighestlevelofconsumptioninsteadystateisknownasthegoldenrulelevelofcapital.
ξ Forsbetween0and sG (GforGoldenRule),ahighersavingrateleadstohighercapitalperworker,higheroutputperworker,andhigherconsumptionperworker.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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ξ Forslargerthan sG ,increasesinthesavingratestillleadtohighervaluesofcapitalperworkerandoutputperworker;buttheynowleadtolowervaluesofconsumptionperworker.
o Thisoccursbecausetheincreaseinoutputismorethanoffsetbytheincreaseindepreciationduetothelargecapitalstock.
o Note:increaseinsavingrateleadstolowerconsumptionforsometimebuthigherconsumptionlater.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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11. GettingaSenseofmagnitude
F(K ,N ) = K NDivide ≈ N
YN
=K NN
F(KN) = K
N
Productionfunctioncanbe:
f (Kt
N) = Kt
N
UsingthisisthepreviousProductionfunction:
Kt+1
N−Kt
N= s
YtN
− δ Kt
N
ξ Therefore,outputperworkerequalsthesquarerootofcapitalperworker.Theequationaboveshowstheevolutionofcapitalperworkerovertime.
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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12. SavingRateonSteadStateoutput
1. CapitalperWorker
sK *N
= δ K *N
ξ Squarerootbothsides:
s2K *N
= δ 2 (K *N)2
ξ Rearrangetoget:
K *N
= ( sδ)2
Note:Thesteadystatecapitalperworkerisequaltothesquareoftherationof
savingratetothedepreciationrate.
2. Outputperworker
Therefore,thesteadysateoutputperworkerisgivenby:
Y *
N=
K *N
= ( sδ)2 = s
δ
ξ Observations:
o SteadyStateOutputperworkercanincreaseby:
Ahighersavingrateand
Alowerdepreciationrate
o Asoutputperworkerdoubles,fromonetotwo.Thisdoublingofsavingrateleads,inthelongrun,todoublingtheoutputperworker.Thisisalargeeffect.
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BSP2001:Macroeconomics–LongTermGrowth
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3. Consumptionperworkerwouldbe:
CN
=sδ− δ ( s
δ)2 = s(1− s)
δ
13. ExtendingtheproductionFunction
ξ Whenthelevelofoutputperworkersdependsonboththelevelofphysicalcapitalperworker,K/N,andthelevelofhumancapitalperworker,H/N,theproductionfunctionmaybewrittenas:
YN
= f (KN+
, HN+
)
ξ Note:Anincreaseincapitalperworkerortheaverageskillofworkersleadstoanincreaseinoutputperworker.
ξ Thesetofskillsoftheworkersintheeconomyiscalledhumancapital.
ξ Aneconomywithmanyhighlyskilledworkersislikelytobemuchmoreproductivethananeconomyinwhichmostworkerscannotreadorwrite.
ξ Theconclusionsdrawnaboutphysicalcapitalaccumulationremainvalidaftertheintroductionofhumancapitalintheanalysis.
13.1 HumanCapital,PhysicalCapitalandOutput
ξ Anincreaseinhowmuchsociety“saves”intheformofhumancapital—througheducationandon‐the‐job‐training—increasessteady‐statehumancapitalperworker,whichleadstoanincreaseinoutputperworker.
ξ Inthelongrun,outputperworkerdependsnotonlyonhowmuchsocietysavesbutalsohowmuchitspendsoneducation.
o But:education,especiallyhighereducationispartlyconsumption
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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o Postsecondaryeducation,theopportunitycostofapersons’educationishisorherforgonewageswhileacquiringtheeducation
o Formaleducationisonlypartofeducation.Muchofwhatwelearncomesfromonthejobtrainingformalorinformal.
o Skillsdeterioratetoojustlikecapital(maybeataslowerrate)
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BSP2001:Macroeconomics–LongTermGrowth
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Chapter12
14. TechnologicalprogressandtheProductionfunction
ξ Technologicalprogresshasmanydimensions:
o Itcanleadtolargerquantitiesofoutputforgivenquantitiesofcapitalandlabor
o Itcanleadtobetterproducts
o Itcanleadtonewproducts
o Itcanleadtoalargervarietyofproducts
ξ Wecanthinkofthestateoftechnologyasavariablethattellsushowmuchoutputcanbeproducedfromgivenamountsofcapitalandlaboratanytime.
Y = F(K+,N
+,A+)
ξ However,foreaseamorerestrictiveformistaken:
Y = F(K+,AN
+)
ξ Observations:
o Technologicalprogressreducesthenumberofworkersneededtoproduceagivenamountofoutput.DoublingAproducethesamequantityofoutputwithonlyhalftheoriginalnumberofworkers.
o Therefore,ANcanbethoughtastheamountofeffectivelaborinaneconomy.
o Therefore,revisittheoutputperworkerandcapitalperworkerfunctiontoaccountfortheeffectivelabor.Soitbecomesoutputpereffectiveworkerandcapitalpereffectiveworker.
YAN
= F( KAN
,1)
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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o or,ifwedefinethefunctionfsothat:
YAN
= f ( KAN
)
Outputpereffectiveworkerisafunctionofcapitalper
effectiveworker
14.1 ChangestoSavingrateFunction
I = S = sY
ξ Dividebothsidesbythenumberofeffectiveworkers,AN
IAN
= sYAN
ξ andreplace YAN
= f ( KAN
) toget:
IAN
= sf ( KAN
)
ξ Observations:
o Before,theanswertowhatlevelofinvestmentperworkerisneededtomaintainagivenlevelofcapitalpereffectiveworkerwasinvestmentperworker=depreciationofcapitalstock.
o However,theanswerchangeswhendealingwithinvestmentper
effectiveworker.Nowthatweallowfortechnologicalprogress.Thenumberofeffectiveworkers,AN,increasesovertime.
o Thustomaintainingthesameratioofcapitaltoeffectiveworkers,
K/AN,requiresanincreaseinthecapitalstock,Kproportionaltothe
increaseinthenumberofeffectiveworker
ΔK ∝ ΔAN
UshanPremaratne
BSP2001:Macroeconomics–LongTermGrowth
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CloserLook:
ξ Letδ bedepreciationrateofcapital.Lettherateoftechnologicalprogressbeequalto gA .Lettherateofpopulationgrowthbeequalto gN .Ifweassumethattherationofemploymenttothetotalpopulationremainsconstant,thenumberofworkers,N,alsogrowsatannualrate, gN .
ξ Together,theseassumptionsimplythatthegrowthrateofeffectivelabor,AN,equals
o gA + gN
o Therefore,thelevelofinvestmentneededtomaintainagivenlevel
ofcapitalpereffectiveworkeris:
δK + (gA + gN )K
ξ Orrearrange:
(δ + gA + gN )K
ξ Observations:o δK isneededjusttokeepthecapitalstockconstant.Ifthedepreciation
rateis10%,theninvestmentmustbeequalto10%ofthecapitalstockjusttomaintainthesamelevelofcapital.Andanadditionalamount
(gA + gN )K isneededtoensurethatthecapitalstockincreasesatthe
samerateaseffectivelabor.
ξ Theamountofinvestmentpereffectiveworkerneededtomaintaina
constantlevelofcapitalpereffectiveworkerisgivenby:
(δ + gA + gN )KAN
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BSP2001:Macroeconomics–LongTermGrowth
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14.2 DynamicsofCapitalandOutput
ξ Thesteadystateofthiseconomyissuchthatcapitalpereffectiveworkerandoutputpereffectiveworkerareconstantandequalto(K/AN)*and(Y/AN)*,respectively.
ξ Thisimpliesthat,insteadystate,outputY,isgrowingatthesamerateas
effectivelabor,AN.Becauseeffectivelaborgrowsatrate, gA + gN ,output
growthinsteadstatemustbeequalto (gA + gN ) .Thereasoningappliestocapital
pereffectiveworkerisconstantinsteady,capitalisalsogrowingat (gA + gN ) .
NOTE:
ξ Insteadystate,thegrowthrateofoutputequalstherateofpopulationgrowth( gN ),plustherateoftechnologicalprogress( gA ).Byimplication,thegrowthrateofoutputisindependentofsaving
rate.
ξ Sinceallofthemgrowatthesamerate,thisiscalledbalancedgrowthandwecannotethat:
o Capitalpereffectiveworkerandoutputpereffectiveworker
areconstant
o Equivalentlycapitalperworkerandoutputperworkeraregrowingattherareoftechnologicalprogress, gA
o Or,intermsoflabor,capitalandoutput Laborisgrowingattherateofpopulationgrowth, gN Capitalandoutputategrowingatarateequaltothe
sumofpopulationgrowthandrateoftechnologicalprogress. (gA + gN )
ξ Savingratedoesnotaffectthesteadystategrowthratebutonlyaffectsthelevelofoutputpereffectiveworker.
ξ Notetaken:o Outputpereffectiveworkerandcapitalpereffectiveworkerare
constanto Outputperworkerandcapitalperworkergrowattherateof
technologicalprogress
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o Outputandcapitalgrowatthesamerateaseffectivelaborandtherefore,atarateequaltothegrowthrateofthenumberofworkersplustherateoftechnologicalprogress.
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