Ushan Premaratne BSP2001: Macroeconomics – Long Term Growth · 05.11.2008 · BSP2001:...
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Ushan Premaratne BSP2001: Macroeconomics – Long Term Growth 1 Chapter 10 1. Facts of Growth ξ The emphasis is on output per capita rather than the numbers for total output. The evolution of a country’s standard of living is given by the evolution of its output per capita, not the evolution of its total output. ξ Output per capita equals GDP divided by population. g t = Y t − Y t −1 Y t ξ Long term growth is a composition of short or medium term business cycles of an economy and usually illustrated through real GDP. ξ So far, in constructing output numbers for countries other than the United States, the straightforward method of taking that country’s GDP expressed in that country’s currency, and then using the current exchange rate to express it in terms of dollars would cause complications such as: o Exchange rate can vary a lot o The prices of basic goods differ from country to country. So does the average consumption of an individual. In general, lower a country’s output per capita, the lower the prices of food and basic services in that country. ξ Hence, to compare GDP across countries, we use a common set of prices for all countries. Adjusted real GDP numbers are measures of purchasing power across countries, also called purchasing power parity (PPP) numbers. ξ Historical observations: o The picture for OECD countries is much the same as all start in high levels of output per capita and then there is a clear convergence. o Convergence is also visible for most Asian Countries. Japan leading the pack with the four tigers (Korea, Singapore, Hong Kong and Taiwan close behind) o The picture is very different for African countries
Transcript of Ushan Premaratne BSP2001: Macroeconomics – Long Term Growth · 05.11.2008 · BSP2001:...
UshanPremaratne
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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
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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.
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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
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ξ Thecurveisdrawnsothatincreasesincapitalleadtosmallerandsmallerincreasesinoutput.Thisfollowsfromthepropertythattherearedecreasingreturnstocapital.
ξ AtpointA,wherecapitalperworkerislow,anincreaseincapitalperworker,representedbythehorizontaldistanceAB,leadstoanincreaseinoutputperworkerequaltotheverticaldistanceA’B’.
ξ AtpointC,wherecapitalperworkerislarger,thesameincreaseincapitalperworker,presentedbythehorizontaldistanceCDleadstoamuchsmallerincreaseinoutputperworker,onlyC’D’.
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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
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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
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thisassumption,outputperworker,outputpercapitaandoutputitself,allmoveproportionately.
Thereisnotechnologicalprogress,sothefunctionfdoesnotchangeovertime.
ξ Rewritetheaboveequation:
YtN
= f (Kt
N) ≡ F( Kt
N ,1)
Note:highercapitalperworkerleadstohigheroutputperworker.
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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.
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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).
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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= ‐
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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.
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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)
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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.
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9. With/WithoutTechnologicalProgress:SavingRateandOutput
ξ Aneconomyinwhichthereistechnologicalprogresshasapositivegrowthrateofoutputperworker,eveninthelongrunascomparedtoonewithouttechnologicalprogress.
ξ Thislong‐rungrowthrateisindependentofthesavingrateiftechnologicalprogressisconsidered.
ξ Anincreaseinthesavingrateleadstogrowthgreaterthanthesteady‐stategrowthrateforsometime,untiltheeconomyreachesitsnewhigherpath
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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.
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ξ Forslargerthan sG ,increasesinthesavingratestillleadtohighervaluesofcapitalperworkerandoutputperworker;buttheynowleadtolowervaluesofconsumptionperworker.
o Thisoccursbecausetheincreaseinoutputismorethanoffsetbytheincreaseindepreciationduetothelargecapitalstock.
o Note:increaseinsavingrateleadstolowerconsumptionforsometimebuthigherconsumptionlater.
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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.
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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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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
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o Postsecondaryeducation,theopportunitycostofapersons’educationishisorherforgonewageswhileacquiringtheeducation
o Formaleducationisonlypartofeducation.Muchofwhatwelearncomesfromonthejobtrainingformalorinformal.
o Skillsdeterioratetoojustlikecapital(maybeataslowerrate)
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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)
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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
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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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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.
