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
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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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.