![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.](https://image.slidesharecdn.com/unit-3-180219080519/85/Unit-3-14-320.jpg)
Unit 3
- 1. : UNIT 3 THE SOCOW MODEL i ; Structure I 3.0 Objectives 3.1 Introduction i 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 - 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 - 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 I 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 I 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? ........................................................................................................................... ........................................................................................................................... TheSolowModel
- 6. EconomtcGrowth 2) What isthebasicequilibriumconditiondepicted by theSolowmodel? I ........................................................................................................................... .......................................................................................................................i... I 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. ~ 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. v 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) I I I I I I I I I I I I I I I I I I I I 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. I I ~ 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.