1. : UNIT 3 THE SOCOW MODEL
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; Structure
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3.0 Objectives
3.1 Introduction
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3.2 Featuresof the Solownilode1
3.2.1 Supply of Goods
3.2.2 Demand for Good5
3.3 The SteadyState
3 3.1 GrowthofGapital and Steady State
3.3.7 Populatio~~Gromth and Steady State
-5.5.3 Ttctl;lological Progress and Steady State
3 4 7'heC;oldenRule
3.5 hasition totheGoldenRule SteadyState
3.6 Let Us Sum Up
3.7 Key Wot'ds-
3.8 Son~eUseful Hooks
3.9 Answers/k-lintstoCheckYour Progress Exercisec
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3 0 OBJECTIVESr .
After goingthroughthis unit you shouldbe in aposition to
explainthebasic premisesonwhichthe neoclassicalSolowi~lodelisbased:
describcthepropertiesofneoclassicalproduction function;
identifytheimplicationsofSolowmodel;and
explainthe steadystategrowthofaneconomy.
.3.1 1NTROI)UCTION
Tn the previous block we ohsewed that when saving istranslate(!illto investments,
accumulation ol"capita1stock takesplace. Suchaccumulatiorn incapital stockimplies
an increasein the levelof capitalitlput.A basic featureof capital input isthatit does
not get exhausted in a single use, that is, it is durable in nature. However, capital
input undergoeswear and tear, generally termed depreciation, duringthe course of
produc~ion.Thus when we deduct depreciation from gross investment we obtain
net investment,which tantamountto additionto capitalstock.
As you know,capitaland labourare two primary inputsused iri productionprocess
and withtheaid oftechnology trans^; rin intermediateinputsintooutput.If we assume
no shortageof intermediateinput? 'le productioncapacity of aneconomy depends
upon the quantity,qualityand util 'tation of theprimary inputs. We shouldnote that
most of thc growth models arebuilt upon thepremise of.'assuredavailabilityof raw
materials.
2. EconomicGrowth The classical economistsin generaldidnot pay much attentiontothe long-runim act
of investment. In the classical framework the economy passed through the s me
cycleofproductionperiod afterperiod. Thepost-Keynesianeconomists,padc arly '
Harrod and Domar, emphasizedthe increasein capital stock dueto investment see
Block 1 of the course MEC-004: Economics of Growth and Development). ater
on neoclassical economist R. M. Solowpresented a model of economic gro1in
1956which continuesto remainasalardmark in growththeory. Subsequent grdwth
models have brought in refinements and innovations into the Solowmodel.s he
Solowmodel explains the effect of saving, population growth and mchnological
'
progress on the economy's output growth.We discuss below the basic featured and
implicationsofthe Solowmodel. I
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3.2 FEATURESOFTHESOLOWMODEL
The Solowmodel considers an aggregateproduction function for the economJ/as a
whole such that a composite good is produced through a common tcchnolo y by
utilizing homogenous inputs, labour and capital. The first step to understan the
model is to study what determines the supply of and demand for goods i the
economy.
11i
3.2.1 Supply of Goods I
The supply ofgoods in the Solowmodel is determined by the production fundtion.
Theproduction function has.threeinputs (K,L,A) and one output (Y)variablebancl
takes the form I
Y=output I
K =capital
L =labour
A =technologyofpjroduction
The variable, in equation(3.1)denotes time that does not enter the model di
It implies that ovelitime change in Ywill takeplace onlydue to change in
L andA,
It is worthwhile to note that change inA occurs asa consequenceof technol gical
progress. Labour and effectiveness of labour are introduced in the ode1Cmultiplicatively suchthatAL means effeclive labour. It meails that technol gical
progressislabour-augmenting,i.e., it increasestheproductivitj orefliciencyof1 bour.
Thuseven ifquantityofLremains unchanged,technological progressincreafesthe
quantityof effective labour (AL)in the economy.
I ITheproductionfunctiond.escribed at (3.1)presents constantreturnsto scale( ~ R s )
Thisassumptiongreatlysimplifiesthe analysisand is often considered'Fealist' .Tkic
presence of CRS implies ,thatif we double all the inputs output will be dou led.
F(aK aAL)=aF(K, AL)
t
...(3.2
3. whereacanbe my non-negativeconstant. TheSolow Model
,The CRSassumptioncanbe utilizedto ccllvertthe productionfunctionspecifiedin
1
e$yition (3.1) to per effectivelabourterms. If o=-we canrepresent (3.1)as '
AL
I
Thisformoftheproduction functiongiven at (3.3) isknownasthe intensiveform.It
allowsustoanalyseallvariablesinthe-economyrelativetothe sizeofeffectivelabour
force.
K
Thus --- iscapitalexpressedrelativetoeffectivelabour,i.e,.,itiscapitalpauniteffective
AL
Y
labour. Moreover, F(% = -which is output unit effective labour. We
AL -
K Y
designatethese in Iowercaseletters suchas -= k and -= Y andflk) =F(k, 1)- AL AL
sothatthe productionhction in(3.3)canbe writtenas
Y =f@) ...(3.4)
Fig.3.1 illustratestheaboveproductionfunction
Fig. 3.1:Neoclassical Production Function
I In Fig. 3.1 we measurek onthex-axlsandy onthey-axis. Sincekrepresentscapital
/ labourratio,aswemovealongx-axistheamountofcapital availableperunit of labour
I increases.Abasicfeatureof (3.1)isthatwhileCRSprevails,thereisdiminishingreturns
i tocapitalinput.ItimpliesthatwhenbothK andL areincreasedproportionatelythereis
4. EconomicGrowlh CRS.On the other hand. if there isan increase inKwhile keeping AI, constant,we
obtaindiminishingreturnstoK. -
Theslopeoftheproducthn function givesthemarginalproductivityofcapital (MPK)- ~K
that showsthe extraoutputper effecthe labourproduced when -isincreasedby 1
AL
unit.MPKcan bemathematicallywritten as .
MPK -.flk+l) -8k) ...(3.5)
Theintensiveform ofproductionh c ,iongiven at(3.4)anddepictedthrough Fig.3.1
isassumedto satisfjithe following con&tions:
1) a) at k = 0, f(k) = f(0) = 0
b) MPK ispositive,that is, f '(k) >0
c) MPK declines as k rises,that is. f "(k) 4
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2) Theintensiveforminadditionisalsoassumedto satisfLingthe lnuu'uconditions.
(a) yz.f'(k) = ,which impliesthatwhen capitalstockistoo smallthe MPK
isverylarge.
(b) k - + y ~lim -f'(k) =O, which impliesthatMPK is very smallwhenthe capital stock
istoo large.
Theseconditionsaremuch strongerthanareneeded to derivethe resultsof the model
* and have been introduced to ensure that the growth path of the economy docs not
diverge.
Tt isevidentfromFig. 3.1 thatatangent drawnat anypoint on the curcehas a positive
slope,but the slopeof tangents is declining as we go towards the right (as krises).
HenceMPK ispositive but declining.Moreoveratk=0the tangent totheproduction
functionis a vertical line (which impliesthat MPK =a).As krises the production
function becomes flatterand when k--+ we have MPK=0. It is importantto note
herethat Solowmodel assumesotherinputsbeside K, LandA not tobe importantand
hencearenot includedintheproduction function.
3.2.2 Demand for Goods
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Ina Soloweconomygoodsaredemandedfitr consumptionandinvestmentpurposes.
n1us
1
Tfwe express(3.6) inper effectivelabourterms(thatis,divideby -)weobtain ~AL
We omit government expenditureand net exports in (3.6) which are present in the
nationalincomeaccountiidentity(seeUnit 1). Whilegovernmentexpenditureisignored
5. forsimplificationinpresentation,netexports(thatis,exportsminusimports)is excluded
becausethe economyis assumedtobe closed.
Each year people save a fractions of their income. Thus s is the savingrate and it
assumesavaluebetween 0and 1.Therelationshipbetweenoutputandsavingisdepicted.
inFig.3.2.
V . Output f(k)
Fig.3.2:OutputandSaving
Savingper effectivelabour= sy
Therefore, consumption c =(1 -s)y
..a s y = i .(3.9)
L
Equation(3.9)showsthatsaving equalinvestment,a condition necessary for equilibrium
intheeconomy.
CheckYourProgress 1
1) Whatarethebasicassumptionsonwhichthe Solowmodelisbased?
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TheSolowModel
6. EconomtcGrowth
2) What isthebasicequilibriumconditiondepicted by theSolowmodel? I
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3.3 THESTEADYSTATE
Asseeninequation(3.9)investmentperunit ofeffectivelabour equalssavingperunitlof
effectivelabotir:
i = sy
Sincey =f(k) wecanwrite equation(3.9)as
The aboveshowstherelationshipbetweenexistingcapital stock (k)andaccumulatibn
of newcapital(i)expressedin'pereffectivelabour'tenn.
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Asyouknow,increaseincapitalstockisduetoinvestment.Thusthediffaencebetw&n
capitalstockintwo successiveyears isequaltoinvestmentthathastakenplaceduribg
theyear.Inotherwords,therateofgrowthcapitalstockisequaltotherateofinvestmebtt.
Inper effectivelabourterm,we can express(3.10)as
..k = sf (k) .(3.11)
where k refers to the growth rate in k (In general we put a dot over a variableto
represent itsgrowthrate). I
Theaboveequilibriumconditionistrueforaneconomywherethereisno depreciatibn
tocapitalstock,thereisnopopulationgrowthandtechnologicalprogressdoesnot&e
place.Letusassumeforthetimebeingthatthereisnopopulationgrowthandtechnologi
progressintheeconomy.Wewillrelaxtheseunrealisticassumptionslateron. I
3.3.1 Growth of Capital and Steady State
I
TheSolowmodelassumesthatexistingcapitaldepreciatesattherate S.Thuseachy
SKamountofcapitalisdepreciated.
hivestmentanddepreciationactinoppositedirectionsandthegrowthin
netofthetwoquantities.
k(t) =i(t)-Sk(t) I
since i = sf(k(t)) i
7. Fig. 3.3:DepreciationRate
From (3.12)we inferthat capital stockrises when sf k(t)) > &(t); fallswhensf(k(t))
< &(t) and remains constantwhen sf(k(t)) = &(t).
Fig. 3.4 depictsequation(3.12)graphically.
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1 Fig. 3.4:SteadyStateof anEconomy
TheSolowModel
8. EcoriomicGrowth Thetwo curves,savinganddepreciation curves,intersect at point X, where capital
stockisk*anddepreciationequalsinvestment.Atthispoint thereisnogrowthin capital.
stockhence outputalsoremainssteady. k* isthereforeknown asthe steadystatelevel
ofcapital.Therearetwouniquefeaturesofthe steadystate:(i) economyinsteadysate
will remaintheretillthereischangeinanyothervariable,and(ii) economywill always
movetowardsthesteadystate.Forexample,iftheeconomy startsat k,levelofcapital,
where k,<k* (seeFig. 3.4),investmentexceedsdepreciation.As aresult, capital st&k
k,alongwithoutputf(k)risestill kreachesk*.Ontheotherhand,ifthe economysWs
at k2level of capital, which is greaterthan k*, investmentis lessthan depreciatibn.
Consequentlythere isadeclinein capitalstockandoutputintheeconomyuntilstekdy
statecapital,that is,k* isreached.
Once the economy attains the steady state there is no pressure on k to increasd or
decreasehence the economy stays there. Thus the Solow model does not explhin
sustainedeconomicgrowth.Aneconomywithahighsavingratewillhavehigherlev4of
outputandcapital ascomparedto acountry with lowrate ofsaving.Thus savingdate
isanimportantdeterminantofaneconomy's outputandcapital.Thisto some extbnt
explainsthedisparityinoutput acrosscountries.Savingratemayvaryacrosscounth
duetoplethora ofreasons ';kedevelopmentoffinancialmarkets. tax policy. cultdral
differences,retirementpolicies,politicalstabilityandpolitical institutions.Empidcal
evidencegivenbyMankiwcomparingincomeperpersonwithinvestmentaspercentage
ofoutputof 84countriesconfirmstheassociationbetweenhigh savinglinvestmentdate
andhighlevelofincomeperperson. ow ever1.ecitesthecaseof~ e x i c oandZimbdwe
that have similarinvestmentratesbut incomeper person in Mexicoisthriceofthait in
Zimbabwe.Thisleadsusto thequestionthat besidessavingand investmenttherehre
otherpotentialfactorsthatdeterminelivingstandards.We studytwoofthembelow,diz..
population growthandtechnicalchange.
3.3.2 Population Growth and Steady State
ToanalysetheeffectofpopulationgrowthweexpandtheSolowmodel.wenowconsiber
the casewherepopulationandthe labourforcegrowata constantrate n.When labur
force grows,additionalcapitalisrequiredto maintain the samelevelof k. Hencetthe
economyshouldhaveadequateinvestmentstotakecareofdepreciation (6k)aswell as
population growth (nk). In orderto introducenwe modifjrequation(3.12)as
I '
i ( t ) =sf (k(t))-(n +6)k(t) ...(3.13) ~
For steadystatethe amountof investmentrequiredmust not only coverdepreciadon
(a)but alsoprovidenewworkerswithcapital(nk).Break-eveninvestmentnowwo(u1d
be (n+S)k.The steadysateisachievedatthepoint of intersectionof investment b d
(n+S)kcurves.The line 2% in Fig. 3.4 accordinglyis adjustedto represent (J+n)k.
The steadystateisreached ina similarmannerasdiscussedin earliersection.Ifk, k*
investmentisgreaterthanbreak eveninvestmentsokandyrise.Ontheotherhan if
k,>k*, kdeclinestill it reachesk*.
d'I
Populationgrowthsucceedsinexplainingsustainedeconomicgradinaneconom .In
thisframework,however,outputper effectivelabourremainsunchanged.Remen! ber
that atthe steadystatewewitnessconstantkandy Butcapitalstock(K)andoutput)(v
keeps on growingat the rate n to keep kandy constant. Sucha featureexplainsthe
cross-countrydisparityinincomes.LetusassumethatcountryI haspopulationgrab
ofn, andcountryI1has n2suchthatn,>n2.Savingrate inboth countriesisassume1to
9. k,' -k,'
TheSolowModel
Steady state
capital declines
Fig.3.5:Steady.-- Statein TwoCountries
bethe same.Accordingly,in Fig. 3.5 we drawa line(&n,)k witha slopegreaterthan
that of (&n,)k.
We can easily comprehend from Fig. 3.5 that the country with high growthrate of
populationn, haslowerlevelofk* (thesteadystatelevelofk)andthuslowery.Empirical
evidencecitedby Mankiwsupportstheabovemodel. Thusit isoftenemphasizedby
policymakersinIndiatoconmlpopulationgrowthinordertoattainhigherlivingstandads.
3.3.3 Technological Progress and Steady State
Toexplaingrowthin outputper effectivelabour,we need to introducetechnological
progressinthe Solowmodel.As statedearliertechnologicalprogressisassumedtobe
(n + +6 )k
*
sf (k)
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k' k
Fig.3.6:SteadyState
10. EconomicGrowth labow-augmenting.Thustechnologicalprogressincreasesthequantityofeffectivela+
(AL). Letus assumethat therateoftechnologicalprogressisg.
I
Thechangeinkovertimeisnowmodifiedas
~
k(t) =sf (k(t))-(n+g +S)k(t) ...(3.14)
In fact, equation(3.14) is the key equation of the Solowmodel of growth. Fig. 31.6
explainstheequationthroughadiagram.
Asisevident,theanalysisofsZeadystatedoesnotchangewiththeinclusionoftechnologiM
progress. But the break-even investmentnow is (n+g+S)dc.Out of total investrndnt
sf(k), isneeded to coverdepreciationandnktomaintaincapitalper effectivelabdur
constant.However,asaresultoftechnologicalprogressygrowsatarateofg.~ l t h o u b
n, gand Sarenot individuallyrestricted,thesumisassumedtobepositive inthemodiel,
i.e.,n +g +S>0.As mentioned earlier, inthe steadystatecapitalper effectivelabdur
and outputper effectivelabourremainsunchanged. There is a growth in outputder
effective labour at a rate g and total output grows at the rate (n+g).We see that
introductionoftechnologicalprogressenablesustoaccountforincreasein output+r
worker.
Weconcludethat accordingto Solowmodelpersistentlyrisinglivingstandards(~h)
can be explained onlythroughtechnologicalprogress.
3.4 THEGOLDENRULE
Let us see the impact of variationin savingrate on steady state.Let us assume that
savingrateriseswhile n, g, andSremainunchanged (seeFig. 3.7).Sincei =sf@)
idbehigherinvestmentwhichinturnwillleadtocapitalaccumulationandoutputgm
andthe economywill eventually reach to anew steadystatewithhigher capital
output.
Fig.3.7: Impactof SavingRate
11. Whensavingrate risesfroms,tos,the investmentcurveshiftsup fioms,f(k)tos,f@). TheSolowModel
Thusthe ecoriomyreaches a new steadystatek,' after goingthroughthe process of
capitalaccumulationasdescribedabove.
Itmayleadus to'thinkthat ahigh rateof savingisalwaysdesirablesincehigher saving
resultsinhigher capitalstockandoutput.Youmaythinkthat ifsaving is 100%therewill
belargestpossibleoutputandcapitalstockintheeconomy.Atvariouslevelsofsdifferent
steadystateareachievedwithdifferentlevelsofcapitalaccumulation.However,thereis
anoptimumlevelofcapitalaccumulationwhichi2calledthegoldenrulelevelofcapital.
Atthegoldenrulelevel ofcapitalthelevelofsissuch@at theconsumption per effective
labour is maximum at the steady state. Why is consumption per effect~belabour
maximized?Thisisbecause individuals,whomakeup theeconomy,arenotconcerned
aboutthecapitalstockortotal outputoftheeconomy.Forthemwhat isimportantisthe
amountofoutputtheyconsume.Amongthe various steadystatesonethatmaximizes
consumptionper effectivelabour isthusthe most desirableoneandhencecalledthe
'goldenrulelevel'.
Youknowthatincome(whichisequaltooutput)isallocatedonconsumptionand savhg
(whichisequalto investment),that is, Y = C+1. .Steazfystateconsumptionisoutput
netofinvestment.Thus
c*= y* - i' -
We can writethe aboveas
Asincreasein steadystatecapitalhascontrastingeffectonsteadystateconsumption-
morecapitalleadsto more outputwhichcontributespositivelyto consumption,but it
alsomeanshigherbreak eveninvestment(n+g+gk.
Fig. 3 . 8 illustratessteadystatey andbreak-eveninvestmentasa functionof steady
statecapital,k*.
(n +g +6)k*
sf [k')
I Fig. 3.8: GoldenRule SteadyState
12. I
EconomicGrowth Steadystateconsumptionisthe gapbetweenthe steadystateoutputand steadystatk
break-eveninvestment,whichism ~ ~ dat kiOwlevelofcapid p r effctive labo*.
Recallthattheslopeoftheproductionfunctionisthemarginalproduct ofcapitalMPd.
WenoticeinFig. 3.8 that at cioMlevelofconsumption(goldenrule level)the slopedf
productionfunctionequalstheslopeofbreak-eveninvestment,that is,
MPK= ( n + g + S )
Or
(MPK-S)= (iz + & ...(3.16)
At thegoldenrule leveloicapital,the MPK net ofdepreciationisequaltotheratebf
growthoftotal output (n +g).
Thegoldenrulesteadystateisnotachievedautomatically.Itrequiresaparticularratedf
saving sgo,asshowninFig. 3.9.
Fig.3.9: Golden RuleSaving
To achievethe goldenrule steady state level of capital kioida savingrate of s,, 1s
required suchthat,consumptionismaximizedatciold.
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~ f s> sgold(equivalently,k*>ki0, )theeconomyissaidtobedynamicallyinefficiedt.
Inthiscaseafallinsavingfiomsto sgOldwillincreaseconsumption.Ontheotherh U ,
ifs < sgOld(equivalently,k*<ki0, )arisein savingwill decreaseconsumptionintne
shortrunbutwilleventuallyleadtohigherconsumptioninthelongrun. Howthetransitidn
togoldenrulesteadysatecanbe achievedbychangingthesavingratefiomsto sgOld/is
dealtwithinthenext Section.
13. 3.5 TRANSITIONTOTHEGOLDENRULESTEADY
TheSolow Model
STATE
Let us discuss the impact of change in savingrate to achieve golden rule level of
consump60n,investmentandcapital. therecanbetwo situations:(i)when s > sgoldor
steadystatecapitalper effectivelabourismorethanrequiredforgoldenrule level,and
(ii)whens < sgoldorsteadystatecapitalpereffectivelabourislessthanthegoldenrule
level of k;,, .
Case 1:when s > sgdd
In this caseto achieve the goldenrule level the savingrate needs to be decreased to
sg0,.When savingratefallsconsumptionper effectivelabourimmediatelyrisesand
investmentdeclines.Theeconomyisnolongerinasteadystateasinvestmentislessthan
break-even investmentof (n +g +s) k*. Thisleadsto a declinein capital stockper
effectivelabour.Outputpereffectivelabourisafunctionofksothat Y/AL alsodeclines.
Sincec=y- iwe observethat consumptionpereffectivelabouralsodeclines. These
variablesJ c and ifalltilltheeconomyreaches anew steadystatewhich isthe golden
rule steadystate.
At this level consumptionishigherthanthe earliersteadystatealthoughthe levelsof
outputandinvestmentarelower.Consumptionpereffectivelabourishigherintheentire
period oftransitiontothe goldenrulesteadystatefromtheearlierlevel.
Case 2:when s <sgo,
When at a steady state s < sw we have kt < ki,,d. In this case s needs to be
increasedtoachievethegoldenrulesteadystate.Whensrisesthereisariseininvestment
whichnowexceedsbreak-even investment(n +g +6)andthe economyisinastateof
transition.Thereisaccumulationofcapitalleadingtorise inoutputper effectivelabour
(Y/AL). So when saving is increased consumption per effective labour declines
immediatelybutwithriseinoutputpereffectivelabouritrisestoalevelhigherthanthe
levelwhichinitiallyprevailed.
I
Thedilemmaofwhethertotrytoreachthe goldenrulesteadystateornotisaquestion
of choicebetween currentand futureconsumers.It isatradeoffbetweenpresent and
i firturelevelsofconsumption.Wewilldiscussmoreabouttheinta-tempomlconsumption
I decisionsinBlock4.
i CheckYourProgress2
I 1) What doyoumeanby steadyState?
14. EconomicGrowth 2) Underwhat conditiondoes&I economyrealisesteadystate?
3) What isthegoldenrule steadystateforaneconomy? I
LETUS SUMUP
The Solowmodel explains long-term growth in per capita output experienced b
economiesworldover.Itassumesaconstantreturnsto scaleproductionfunctionwhic4allowsfordiminishingretumsto scaletocapitalinput.Themodeldepictsthattheeconom
has atendencytc;convergeto a steady statewhereavailabilityof capitalper worke1mnainsunchanged.Initssimplestformthesolowmodelisbuiltupontheequality
savingandinvestment. II
Investmentresultsinincreaseincapitalinputwhichisdurableinnatureandundergoe$
depreciationduringthecourseofproduction. In steadystateascapital stockavailabl4
perunitoflabourremainsunchanged,theeconomyshouldhavejust enoughinvestme4
totakecareof, i)depreciation,ii)populationgrowth,andiii)technicalprogress.
TheSolowmodelconcludesthat savinghasonlya 'level effect' andno 'growth effect'.
Itmeansthathigher saving in aneconomyincreasesper capita availabilityofcapi
andoutput,butnosustained outputgrowth. Sustained growth inoutputisexplained4i
themodelneither by higher savingnor bipopulation growth. ath herhighpopulatiob
growthreduces the per capita availability of output and capital.Accordingto thb
Solowmodel sustainedoutputgrowthispossibleonlythroughtechnologicalprogress]
Higher savingrate,althoughit increasesper capitaoutput, isnot alwaysdesirable.Thb
objectiveofanemnomyistomaximizeconsumption,notsaving.Thegoldenlulesugge&
thatcapitalshouldbeatthatlevelwhereMPK net of kpreciation is equalto outp
growth.
15. 3.7 KEYWORDS TheSolow Model
Break-evenInvestment Theamountofinvestmentjustm&to compensate
forthedepreciationtotl% existingcapital stock.
CapitalAcumulation Capitalinputdaesnotgetexhaustedinasingleuse
andremainsinuse fora longperiod oftime. Thus
duetoinvestmentin successiveyears,capitalinput
getsaxmdated.
Depreciation
GoldenRule
Naturalwealandtear undergoneby capitalinputs
(suchasmechineries,buildig,etc.)whenproduction
ofgoodsand servicestakeplace.
Theconditionforobtainingthesteadystatewhich
maximizesconsumption.Itisgiven bytheequality
betwenMPKnetofdepreciation andoutputgrowth
rate, that is, (MPK- 6= n +g).
InadaConditions Twoconditionsrequidfortheproductionfunction
tobewellbehaved,formulatedby Ken-Ichi Inada
in 1961P'
Labour-augmenting Technical change that results in increasing the
TechnicalChange productivityorefficiencyoflabour.
Steady State A conditionwhenthe economydoesnothaveto
changeitscapital-labourratio.
SustainedGrowth Growthinoutputonasustainedh i s , ovaalonger
periodoftime.
3.8 SOMEUSEFULBOOKS
e
,,
Solow, R. M., 1970,Growth Theory,OxfordUniversityPress,Oxford.
Romer, D., 1996, AdvancedMacroeconomics,McGraw Hill Company Ltd., New
York., Chapters 1,2,3.
f Mankiw, N.G, 2003,Macroeconomics(FifthEdition),WorthPublishers,NewYork,
Chapters 7 & 8.
t
3.9 ANSWERSIHINTSTOCHECKYOUR PROGRESS
EXERCISES
CheckYourProgress 1
I ) Thebasicassumptionspertaintopropertiesofthe classicalproductionfunction.
en ti ontheseproperties.Also mentionthatther&delel appliesto aclosedeconomy.
2) Thesupplydemandequilibriumconditionneedsto be mentioned.Point outthat
equilibriumisrealizedwhen saving=investment.
16. EconomicGrowth CheckYourProgress2
1) It refers to a state or conditionwhen the economy does not need to change it6
capitalstockrelativeto itslabourforce.
2) Go through Section 3.3 and explain the condition sf (k) =n +g +6 through
diagram (similartoFig. 3.4).Explaintheprocesshowtheeconon~yrevertsback tb
theaboveequalityincasethereisdeviation.
3) GothroughSection3.4andanswer.
