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Domar1946

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Domar1946

  1. 1. Capital Expansion, Rate of Growth, and Employment Author(s): Evsey D. Domar Source: Econometrica, Vol. 14, No. 2 (Apr., 1946), pp. 137-147 Published by: The Econometric Society Stable URL: http://www.jstor.org/stable/1905364 Accessed: 26/10/2010 15:27 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=econosoc. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica. http://www.jstor.org
  2. 2. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT' By EVSEY D. DOMAR I. INTRODUCTION Thispaperdealswitha problemthatisbotholdandnew-therela- tionbetweencapitalaccumulationandemployment.Ineconomiclitera- tureithasbeendiscusseda numberoftimes,themostnotablecontribu- tionbelongingtoMarx.Morerecently,itwasbroughtforthbyKeynes andhisfollowers. A thoroughanalysisofeconomicaspectsofcapitalaccumulationis a tremendousjob.Theonlywayinwhichtheproblemcanbeexamined at all ina shortpaperlikethisis byisolatingitfromthegeneraleco- nomicstructureandintroducinga numberofsimplifyingassumptions. Someofthemare notentirelynecessaryand,as theargumentpro- gresses,thereaderwillseehowtheycanbe modifiedorremoved. The followingassumptionsand definitionsshouldbe notedat the outset:(a) thereis a constantgeneralpricelevel;(b) nolagsarepres- ent;(c) savingsandinvestmentrefertotheincomeofthesameperiod; (d) botharenet,i.e.,overandabovedepreciation;(e) depreciationis measurednotinrespecttohistoricalcosts,buttothecostofreplace- mentofthedepreciatedassetby anotherone ofthesameproductive capacity;2(f)productivecapacityofan assetorofthewholeeconomy is a measurableconcept. Thelastassumption,onwhich(e) alsodepends,isnotentirelysafe. Whethera certainpieceofcapitalequipmentorthewholeeconomyis considered,theirproductivecapacitiesdependnotonlyonphysicaland technicalfactors,butonthewholeinterplayofeconomicandinstitu- tionalforces,suchas distributionofincome,consumers'preferences, 1 This is a summaryofa paperpresentedbeforea jointsessionoftheEcono- metricSocietyandtheAmericanStatisticalAssociationin ClevelandonJanuary 24, 1946. It containsthe logicalessenceof the argumentwithrelativelylittle economicdetail.I hopeto developthelatterin a separatepaperto be published in one oftheothereconomicjournals. Many thanksforhelp and criticismgo to myfellowmembersofthe "Little Seminar":Paul Baran,SvendLaursen,LloydA. Metzler,RichardA. Musgrave, MaryS. Painter,MelvinW. Reder,Tiborde Scitovszky,AlfredSherrard,Mary WiseSmelker,MerlinSmelker,and mostofall to JamesS. Duesenberry. 2 If theoriginalmachineworth$1,000and producing100unitsis replacedby anotherone worthalso $1,000,but producing120 units,only$833.33 will be regardedas replacement,and theremaining$166.67as newinvestment.A simi- lar correctionis madewhenthenewmachinecostsmoreorlessthantheoriginal one. The treatmentof depreciation,particularlywhenaccompaniedby sharp technologicaland pricechanges,presentsan extremelydifficultproblem.It is quite possiblethat our approach,whileconvenientforpresentpurposes,may giveriseto seriousdifficultiesin thefuture. 137
  3. 3. 138 EVSEY D. DOMAR wagerates,relativeprices,structureofindustry,andso on,manyof whicharein turnaffectedby thebehaviorofthevariablesanalyzed here.We shallneverthelessassumeall theseconditionsas givenand shallmeanbytheproductivecapacityofan economy(oran asset)its totaloutputwhenallproductivefactorsarefullyemployedunderthese conditions.3 The economywillbe saidto be inequilibriumwhenitsproductive capacityP equalsitsnationalincomeY. Ourfirsttaskis to discover theconditionsunderwhichthisequilibriumcanbemaintained,ormore precisely,therateofgrowthatwhichtheeconomymustexpandinorder toremainina continuousstateoffullemployment. II. THE PROBLEM OF GROWTH The idea thatthepreservationoffullemploymentin a capitalist economyrequiresa growingincomegoesback(inoneformoranother) at leastto Marx.It has beenfullyrecognizedin numerousstudies (recentlymadein Washingtonand elsewhere)ofthe magnitudeof grossnationalproductneededto maintainfullemployment.But thoughthevariousauthorscometodifferentnumericalresults,they all approachtheirproblemfromthepointofviewofthesizeofthe laborforce.Thelaborforce(man-hoursworked)anditsproductivity aresupposedto increaseaccordingto oneformulaoranother,and if fullemploymentis to be maintained,nationalincomemustgrowat thecombinedrate.Forpracticalrelativelyshort-runpurposesthisisa goodmethod,butitsanalyticalmeritsarenothigh,becauseitpresents a theoreticallyincompletesystem:sincean increasein laborforceor in its productivityonlyraisesproductivecapacityand doesnotby itselfgenerateincome(similarto thatproducedby investment),the demandsideoftheequationis missing.Noris thedifficultydisposed ofbyMr.Kalecki'smethodaccordingtowhichcapitalshouldincrease proportionallyto theincreaseinlaborforceanditsproductivity.4As Mrs.Robinsonwellremarked,"Therateofincreaseinproductivityof laborisnotsomethinggivenbyNature."6Laborproductivityisnota functionoftechnologicalprogressin theabstract,but technological progressembodiedincapitalgoods,andtheamountofcapitalgoodsin 3 It shouldundoubtedlybe possibleto workout a moreprecisedefinitionof productivecapacity,but I preferto leave thematteropen,because a morepre- cise definitionis not entirelynecessaryin thispaperand can be workedout as andwhenneeded. 4 See his essay,"Three Waysto Full Employment"in TheEconomicsofFull Employment,Oxford,1944,p. 47,andalso his"Full EmploymentbyStimulating PrivateInvestment?"in OxfordEconomicPapers,March,1945,pp. 83-92. 5 See herreviewofTheEconomicsofFull Employment,EconomicJournal,Vol. 55, April,1945,p. 79.
  4. 4. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 139 general.Evenwithouttechnologicalprogress,capitalaccumulationin- creaseslaborproductivity,at leastto a certainpoint,bothbecause morecapitalis usedperworkmanineachindustryandbecausethere is a shiftoflabortoindustriesthatusemorecapitalandcanaffordto paya higherwage.Soiflaborproductivityisaffectedbycapitalaccum- ulation,theformulathatthelattershouldproceedat thesamerateas theformer(andas theincreaseinlaborforce)isnotas helpfulas itap- pears. ThestandardKeynesiansystemdoesnotprovideus withanytools forderivingtheequilibriumrateofgrowth.Theproblemofgrowthis entirelyabsentfromitbecauseoftheexplicitassumptionthatemploy- mentisa functionofnationalincome.Thisassumptioncanbejustified onlyovershortperiodsoftime;it willresultin seriouserrorsovera periodofa fewyears.Clearly,a full-employmentlevelofincomeof fiveyearsagowouldcreateconsiderableunemploymenttoday.Weshall assumeinsteadthatemploymentis a functionoftheratioofnationalin- cometoproductivecapacity.Whilethisapproachseemsto me to be superiorto thatofKeynes,it shouldbe lookeduponas a secondap- proximationratherthana finalsolution:itdoesnotallowustoseparate unusedcapacityintoidle machinesand idle men;dependingupon variouscircumstances,thesameratioofincometocapacitymayyield differentfractionsoflaborforceemployed. BecauseinvestmentintheKeynesiansystemis merelyan instru- mentforgeneratingincome,thesystemdoesnottakeintoaccount theextremelyessential,elementary,andwell-knownfactthatinvest- mentalso increasesproductivecapacity.6Thisdual characterofthe investmentprocessmakesthe approachto the equilibriumrate of growthfromtheinvestment(capital)pointofviewmorepromising:if investmentbothincreasesproductivecapacityandgeneratesincome, itprovidesuswithbothsidesoftheequationthesolutionofwhichmay yieldtherequiredrateofgrowth. Let investmentproceedat therateI peryear,andlettheratioof thepotentialnetvalueadded(afterdepreciation),i.e.,oftheproduc- tivecapacityofthenewprojectsto capitalinvestedin them,i.e.,to I, beindicatedbys.?Thenetannualpotentialoutputoftheseprojects willthenbeequaltoIs. Buttheproductivecapacityofthewholeecon- 6 Whethereverydollarinvestedincreasesproductivecapaoityis essentiallya matterofdefinition.It can safelybe said thatinvestmenttakenas a wholecer- tainlydoes. To makethisstatementholdin regardto residentialhousing,im- putedrentshouldbe includedin thenationalincome.See also note 19. 7 The use oftheword"project"doesnotimplythatinvestmentis donebythe government,orthatitis alwaysmadeinnewundertakings.I am using"project" (intheabsenceofa betterterm)becauseinvestmentcan meantheact ofinvest- ingand theresultoftheact.
  5. 5. 140 EVSEY D. DOMAR omymayincreasebya smalleramount,becausetheoperationofthese newprojectsmayinvolvea transferoflabor(andotherfactors)from otherplants,whoseproductivecapacityisthereforereduced.8Weshall definea-,the potentialsocial averageinvestmentproductivityas dP dt (1) Thefollowingcharacteristicsofo-shouldbe noted: 1. Itsusedoesnotimplythatotherfactorsofproductionandtech- nologyremainconstant.On thecontrary,itsmagnitudedependsto a verygreatextentontechnologicalprogress.It wouldbe morecorrect tosaythato-referstoanincreaseincapacitywhichaccompaniesrather thanonewhichis causedbyinvestment. 2. o-referstotheincreaseinpotentialcapacity.Whetherornotthis potentialincreaseresultsin a largerincomedependson thebehavior ofmoneyexpenditures. 3. o-is concernedwiththeincreasein productivecapacityofthe wholesociety,andnotwiththerateofreturnderivedorexpectedfrom investment.Thereforeo-isnotaffecteddirectlybychangesindistribu- tionofincome. 4. s isthemaximumthata-canattain.Thedifferencebetweenthem willdependon themagnitudeoftherateofinvestmenton theone hand,andthegrowthofotherfactors,suchas labor,naturalresources, andtechnologicalprogressontheother.A misdirectionofinvestment willalsoproducea differencebetweens ando-. Weshallmaketheheroicassumptionthats anda areconstant. From(1) itfollowsthat (2) dP I. dt - It is importantto notethat,witha giveno-,dP/dtis a functionof I, and notofdI/dt.WhetherdI/dtis positiveornegative,dP/dtis alwayspositivesolongas a andI arepositive. Expression(2) showingtheincreaseinproductivecapacityis essen- tiallythesupplysideofoursystem.Onthedemandsidewehavethe multipliertheory,too familiarto needanycomment,exceptforan emphasisontheobviousbutoftenforgottenfactthatwithanygiven marginalpropensityto save, dY/dtis a functionnotofI, butofdI/dt. Indicatingthemarginalpropensitytosavebya, andassumingittobe constant,9wehavethesimplerelationshipthat 8 I am disregardingthe externaleconomiesand diseconomiesof the older plantsdue to theoperationofthenewprojects. ' Overtheperiod1879-1941theaveragepropensitytosave (ratioofnetcapital
  6. 6. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 141 dY dI 1 (3)=__ dt dt a Let theeconomybeinan equilibriumpositionso that10 (4) Po = Yo. To retaintheequilibriumposition,wemusthave dP dY dt dt Substituting(2) and (3) into(5) weobtainourfundamentalequation dl 1 (X6) I - -, dt a thesolutionofwhichgives (7) I = Ioeaat. ao-istheequilibriumrateofgrowth.So longas it remainsconstant, themaintenanceoffull employmentrequiresinvestmenttogrowat a con- stantcompound-interestrate. If,as a crudeestimate,a is takenat 12percentand a-at some30 percent,theequilibriumrateofgrowthwillbe some3.6 percentper year.lOa The readerwillnowseethattheassumptionofconstanta andafis notentirelynecessary,andthatthewholeproblemcanbe workedout withvariablea and a. formationto nationalincome)was fairlyconstantand approximatelyequal to some 12 per cent. See Simon Kuznets,National ProductSince 1869, National BureauofEconomicResearch(mimeographed,1945) p. II-89 and theSurveyof CurrentBusiness,Vol. 22, May, 1942,and Vol. 24, April,1944.In a problemof cyclicalcharacter,an assumptionofa constantpropensityto save wouldbe very bad. Sinceweareinterestedherein a secularproblemofcontinuousfullemploy- ment,thisassumptionis nottoo dangerous. 10 The problemcan be also workedout forthecase whenPO> YO. lOa Afterthispaperwas sentto the printer,I founda veryinterestingarticle by E. H. Stern,"Capital Requirementsin ProgressiveEconomies,"Economica, Vol. 12, August,1945,pp. 163-171,in whichtherelationbetweencapital and outputintheU. S. during1879-1929isexpressed(inbillionsofdollars)as capital =3.274 income-3.55. My estimatesgave roughlysimilarresults.This would place s around30 percent,thoughthisfigureshouldbe raisedto accountforthe underutilizationofcapitalduringa partofthatperiod.It is also notclearhow thejunkingprocess(see p. 144) wasreflectedinthesefigures. The averagerateofgrowthofrealnationalincomeovertheperiod1879-1941 was some3.3 percent.See Table V, p. 818,and AppendixB, pp. 826-827,in my paper,"The 'Burden'oftheDebt andtheNationalIncome,"AmericanEconomic Review,Vol. 34, December,1944.
  7. 7. 142 EVSEY D. DOMAR III. THE EFFECTS OF GROWTH Ournextproblemis toexplorewhathappenswheninvestmentdoes growat someconstantpercentagerater,which,however,isnotneces- sarilyequaltotheequilibriumrateac-.It willbenecessarytointroduce two additionalconcepts:averagepropensityto save IIY and the averageratioofproductivecapacityto capitalP/K. To simplifythe problem,weshallassumethat 1. IIY= a, so thataveragepropensityto saveisequaltomarginal. 2. P/K=s, i.e.,theratioofproductivecapacityto capitalforthe wholeeconomyis equalto thatofthenewinvestmentprojects. We shall considerfirstthe special simple case a-=s, and then the moregeneralcase when -<8s.11 Case 1: a-=s. SinceI = oert,capital,beingthesumofall netinvest- ments,equals rt 10 (8) K =Ko + IoJ ertdt= Ko +- (ert-1). O ~~~~r As tbecomeslarge,K willapproachtheexpression (9) - ert, r so thatcapitalwillalsogrowat a rateapproachingr. As Y= (l/a)Ioert,theratioofincometocapitalis 1 - Ioert Y a (10) . Ko +-(ert-1) r and y r C lim- = - t(11 goo K a Thusso longas r and a remainconstant(or changein thesame proportion)no "deepening"of capital takes place. This, roughly speaking,wasthesituationintheUnitedStatesoverthelastseventy yearsorso priortothiswar. 11It is also possiblethat,owingto capital-savinginventionsinexistingplants, a>s. Formallythis case can be excludedby fallingback on the definitionof depreciationgivenin note2. This,however,is not a veryhappysolution,but theapproachusedin thispaperwillhardlyoffera betterone. I think,however, thata inoursocietyis sufficientlyhighto makeof>s ina continuousstateoffull employmentmorean exceptionthana rule.
  8. 8. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 143 SubstitutingK = P/s into(11) weobtain Y r (12) lim-= t-*O P aS Sinceinthepresentcaseo=s, Y r (13) lim-=-* t- o P ao Theexpression r (14) 0 =- maybe calledthecoefficientofutilization.Whentheeconomygrows at theequilibriumrate,sothatr= ao-,0= 100percentandproductive capacityisfullyutilized.Butas rfallsbelowao-,a fractionofcapacity (1-0) isgraduallyleftunused.12Thusthefailureoftheeconomytogrow attherequiredratecreatesunusedcapacityandunemployment. Case2: o-<s. As investmentproceedsat therateI, newprojects witha productivecapacityofIs arebuilt.Sincetheproductivecapac- ityofthewholeeconomyincreasesonlybyIo, it followsthatsome- wherein theeconomy(notexcludingthenewprojects)productive capacityis reducedby I(s - o). Thereforeeveryyearan amountof capitalequal to I(s - o-)/sbecomesuseless. Theproblemcannowbe approachedfromtwopointsofview.The amountsI(s-o)/s, can be lookeduponas capitallosses,whichare nottakenintoaccountincalculatingincomeandinvestment.13In this case,I stillindicatestherateofnetinvestment,andallothersymbols retaintheiroldmeaning,exceptthatcapitalhastoberedefinedas the integralof investmentminuscapitallosses:everyyear chunksof capital(overandabovedepreciation)arewrittenoffandjunked.The annualadditionto capitalwillthenbe dK I(s-) Of (15) ~ ~ =I- - = I-, dt s s and (16) K = Ko + Io-f ertdt= Ko + Io -(e't - 1). s sr 1 It shouldbe notedthatifr,a, and o areconstant,0is also a constant.Even thoughthe economyfailsto growat the requiredrate,the relativedisparity betweenits capacity and incomedoes not become wider,because its capital also growsnotat theao but at ther rate. 18 These lossesare notnecessarilylossesin theaccountingsense.See note 14.
  9. 9. 144 EVSEY D. DOMAR Also, Y r s (17) lim- = -.-, )K a a and Y r (18) lim-=-, t c P ao whichis exactlythesameresultwehadin (13). ThesecondapproachconsistsintreatingtheamountsI(s - o)/s not as capitallossesbutas a specialallowanceforobsolescence.Netinvest- mentwouldthenhavetobe definednotas I, butas IoIs. Othersym- bolswouldhaveto be redefinedaccordingly,and thewholeproblem couldthenbe reworkedoutinthesamewayas onpp. 142-143. In a sensethe choicebetweenthesetwomethodsis a matterof bookkeeping;dependinguponthecharacteroftheproblemin hand, oneortheothercanbeused,thoughI suspectthatthesecondmethod can easilybecomemisleading.The natureoftheprocesswillbe the samewhichevermethodisused.Thefactisthat,owingtoa difference betweens and o-,theconstructionofnewinvestmentprojectsmakes certainassets(notexcludingthenewprojectsthemselves)useless,be- causeunderthenewconditionsbroughtaboutbychangesindemand, ora riseinthewagerates,orboth,theproductsoftheseassetscannot be sold.'4Asstatedonp. 140thedifferencebetweens and o-is created eitherbymisdirectionofinvestmentorbythelackofbalancebetween thepropensityto saveontheonehand,andthegrowthoflabor,dis- coveryofnaturalresources,and technologicalprogresson theother. So longas mistakesaremadeorthislackofbalanceexists,thejunking processisinevitable. Froma socialpointofview,thejunkingprocessis notnecessarily undesirable.In thiscountry,wheresavinginvolveslittlehardship,it maybe perfectlyjustified.But it maypresenta seriousobstacleto theachievementoffullemployment,becausethe ownersof capital assetsheadedforthejunkpilewilltrytoavoidthelosses.So longas theyconfinethemselvesto changesin theiraccountingpractices,no specialconsequenceswillfollow.But it is morelikelythattheywill tryto accumulatelargerreserveseitherby reducingtheirowncon- 14 To be strictlytrue,the statementin the text would requireconsiderable divisibilityofcapital assets. In the absenceofsuch divisibility,the expression "junking"shouldnotbe takentoo literally. The factthattheseassetsmaystillbe operatedto someextentor thattheir productsare sold at lowerpricesor that boththeseconditionsexist,does not invalidateourargument,becauseo, beingexpressedin realterms,willbe higher thanit wouldbe iftheassetswereleftcompletelyunused.
  10. 10. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 145 sumptionorby charginghigherprices(orpayinglowerwages).As a result,thetotalpropensityto savemayrise.Thiswillbe exactlythe oppositemeasurefromwhatis neededto avoidthejunkingprocess, andwillofcourseleadtogreatertrouble,thoughI amnotpreparedto say to whatextentcapitalownerswillsucceedin passingon these losses. In so faras theyareable to controlnewinvestment,theywilltry toavoidlossesbypostponingit.Consequently,therateofgrowthmay wellbe depressedbelowtherequiredao-,andunusedcapacitywillde- velop.Ourpresentmodeldoesnotallowustoseparateunusedcapacity intoidlecapitalandidlemen,thoughmostlikelybothwillbepresent.'" Becauseofhumanitarianconsiderations,wearemoreconcernedwith unemployedmen.But unemployedcapitalis extremelyimportant,because its presenceinhibitsnewinvestment.'6It presentsa gravedangerto a full-employmentequilibriumina capitalistsociety. IV. GUARANTEED GROWTH OF INCOME In theprecedingsectionsitwasshownthata stateoffullemploy- mentcanbe maintainedifinvestmentandincomegrowat an annual rateao. The questionnowarisesas towhatextenttheargumentcan bereversed:supposeincomeisguaranteedtogrowat theao rate;will thatcallforthsufficientinvestmenttogeneratetheneededincome? We areconcernedherewitha situationwherespontaneousinvest- ment(i.e.,investmentmadeinresponsetochangesintechnique,shifts inconsumers'preferences,discoveryofnewresources,etc.)isnotsuffi- cient,andthereforea certainamountofinducedinvestment(madein responseto a riseinincome)is alsorequired."To simplifytheargu- ment,letus assumethatspontaneousinvestmentisabsentaltogether. It shouldalsobe madeclearthattheproblemis treatedfroma theo- reticalpointofview,withoutconsideringthenumerouspracticalques- tionsthattheincomeguaranteewouldraise. Ifan economystartsfroman equilibriumposition,an expectedrise inincomeofYao willrequireaninvestmentequalto Yao/s.Asbefore, twocaseshavetobe considered. 15 The presenceofunemployedmenmaybe obscuredby inefficientutilization oflabor,as in agriculture. 16 It istruethata givencapitalownermayoftenhave a hardtimedistinguish- ing betweencapital idlebecauseofa<s, and capital idle becauseofr< aa. The firstkindofidleness,however,is relativelypermanent,and cannotbe corrected by greaterexpenditures,whilethe secondis temporary(it is hoped) and is due to poorfiscaland monetarypolicies. 17 Cf. AlvinH. Hansen, Fiscal Policyand BusinessCycles,New York, 1944, Part Three,and particularlyp. 297.
  11. 11. 146 EVSEY D. DOMAR 1. If a is equal or reasonablycloseto s, theresultingamountof investmentofYa willequalthevolumeofsavingsthatwillbe made at thatlevelofincome,and equilibriumwillbe maintained.18Thusa mereguaranteeofa risein income(iftakenseriouslyby the investors) willactuallygenerateenoughinvestmentandincometomaketheguarantee goodwithoutnecessarilyresortingtoa governmentdeficit. 2. Ifu-is appreciablybelows,investmentwillprobablyfallshortof savingsandequilibriumwillbedestroyed.Thedifficultyarisesbecause a full-employmentrateofinvestmentinthefaceofa u<s makesthe junkingprocess(discussedon pp. 143-145)inevitable,whilea mere guaranteeofa riseinincome,as a generalrule,lackstheinstrument toforcethecapitalownerstodiscardtheirequipment.Theywillsimply investYao-IsinsteadofYa. Onlyifintheeconomyas a wholethere is a considerablenumberofproductsthedemandforwhichis highly elasticwithrespecttoincome,andthereforea goodnumberofothers thedemandforwhichisnegativelyelasticwithrespecttoincome,will a largeramountthanYaorIsbe investedanda correspondingamount ofcapitaljunked.Ofcourse,iftheriseinincomeis accompaniedby shiftsin consumers'preferences,the appearanceof new products, aggressivecompetition,andotherchanges,thejunkingprocesswillbe speededup,butifthesechangesdo takeplacetheymaygiveriseto spontaneousinvestmentoftheirownandtheguaranteedriseinincome willnotbe important.Still,theassuranceofa highandrisingincome is undoubtedlyoneofthebestmethodsforencouraginginvestment. Asexplainedbefore,a substantialdifferencebetweens andufsimply indicatesthatwiththeavailablelaborforceandthecurrentprogress oftechnology,themaintenanceoffullemploymentundera givena requirestheaccumulationofcapitalata fasterratethanitcanbeused. As a ge.neralrule,thisappliesequallywelltobothprivateandpublic investment,thoughtheremaybe specialcases when,owingto the developmentofparticularconsumers'preferences(e.g.,forvacations), orto technologicalreasons(e.g.,needforpower),orto institutional conditions(as in urbanredevelopment),considerableneedforpublic investmentstillexists.'9 18 Thereis a slighterrorin the magnitudesin the textbecause ofthe use of discontinuousfunctions. 19As soonas thegovernmententersthepicturewe findourselvesin a maze of definitionalproblems.Fromthe pointofviewofthispaper,savingand invest- mentshouldbe understoodin referenceto the wholeeconomy,includingthe government,and notto itsprivatesectoronly.But whichgovernmentexpendi- turesshouldbe regardedas investment?The difficultyis presentin theprivate sectoras well,exceptthattherewe can take refugein formaldefinitions,which cannot be well applied to government.I leave the questionopen. Certainly, investmentneednotbe limitedto inventories,steel,and concrete.
  12. 12. CAPITAL EXPANSION, RATE OF GROWTH, AND EMPLOYMENT 147 I am notpreparedto saywhetherwe alreadyare orshallsoonbe facedwitha seriousdifferencebetweens and o-,thoughI doubtthat itwasan importantprobleminthepast,exceptperhapsfortheshort boomyears.Myownguessisthatweshallbemoreconcernedwiththe disparitybetweenao-andr,thatis withthefailureofincometogrow at therequiredrate. If,however,thedifferencebetweena-ands becomesseriousandin- hibitsinvestment,orifthejunkingprocessproceedsat a fasterrate thanis deemedsociallydesirable,thesocietywillhaveat itsdisposal twomethodsnotmutuallyexclusive:(1) thereductionofthepro- pensitytosave,or(2) thespeedingupoftechnologicalprogress.I hope thatthemainemphasiswillbe placedonthelatter. Thispaperattemptedto analyzetherelationbetweeninvestment, rateofgrowth,and employment.The analysiswas carriedout on a veryabstractandsimplifiedlevel-a procedurewhichmaybejustified at thebeginningofan investigation,butwhichmustbe correctedlater on.In general,thereis no sucha thingas an absolutelygoodorbad assumption:whatmaybe safein onekindofa problemcanbecome fatalinanother.Oftheseveralassumptionsmadehere,thatregarding depreciationis likelyto causethegreatestdifficulties,butit is byno meanstheonlyone.I hopeto developthewholesubjectfurtherat a laterdate. The centralthemeofthepaperwas therateofgrowth,a concept whichhas beenlittleused in economictheory,and in whichI put muchfaithas an extremelyusefulinstrumentofeconomicanalysis. Onedoesnothaveto be a Keynesianto believethatemploymentis somehowdependentonnationalincome,andthatnationalincomehas somethingtodowithinvestment.Butas soonas investmentcomesin, growthcannotbe leftout,becauseforan individualfirminvestment maymeanmorecapitalandlesslabor,butfortheeconomyas a whole (as a generalcase)investmentmeansmorecapitalandnotlesslabor.If botharetobeprofitablyemployed,a growthofincomemusttakeplace. Washington,D. C.

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