enke econ dev't and unlimited labor supply

7/29/2019 Enke Econ Dev't and Unlimited Labor Supply

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Economic Development with Unlimited and Limited Supplies of LabourAuthor(s): S. EnkeSource: Oxford Economic Papers, New Series, Vol. 14, No. 2 (Jun., 1962), pp. 158-172Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2661958 .

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ECONOMIC DEVELOPMENT WITH UNLIMITEDAND LIMITED SUPPLIES OF LABOURBy S. ENKE

AMONG the most importantarticles on economic developmentto haveappeared during the past decade must be included those by ProfessorArthur Lewis on the significance f capitalistic growth with 'unlimited'supplies of abour.' Few people are able to combine economictheory ndrealistic detail so remarkably. And yet attemptsto restate his 'system' ngeometryor algebra suggest a number of inconsistencies. Some of theseare sufficientlyundamental o indicateamendments o his theory. And anovel policy implication s revealed on how to 'capitalize' an economy.The Lewis Model

The parts ofthe Lewis model of concernhereare the following. here isa country that includes initially a large 'subsistence' sector and a small'capitalistic' sector. The essence of early economic development is thetransfer f labour from the former o the latter during a so-called firststage. The marginal product of labour in the subsistence ector s negli-gible, zero, or negative. The subsistence output is supposedly constant,however.During the first tage there is an 'unlimited' supply of labour to thecapitalistic sector-i.e. the labour supply is infinitely lastic for all prac-tical purposes-at a wage based on the productperworker n the subsis-tence sector.2 During this period, extra capital fromwhateversource isused in the modern sector forcapital 'widening'ratherthan 'deepening',the capital to labour ratio remaining constant. Hence the number ofworkersemployedin the capitalistic sector is a functionof total capitalaccumulation, nd more nvestmentmeans more abour drawnproportion-atelyfrom he subsistence ector. During this first tage it is theproductper worker n the traditional sector that determineswage rates in thecapitalist ector,which nturndetermines apital tolabour ratiosemployedthere. Output per worker n the capitalistsector s higher han wages perworker, for labour is joined with capital, and so entrepreneurs njoy asurplusfromwhichtheycan save and invest. Any technological mprove-ments accrue to the capitalistsbecause wage rates cannot rise so long asthere is 'unlimited' labour supply. Lewis also holds that the ratio of

1 W. A. Lewis, 'Economic Development with Unlimited Supplies of Labour', TheManchesterSchool of Economic and Social Studies, May 1954; also 'Unlimited Labour:FurtherNotes', ibid., June 1958.2 Whichmay include implicit rent fpeasant cultivators own theirown land.

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S. ENKE 159profits o national income must rise and therefore hat the percentageofannual income that is investedmustrisealso. In all essentialrespects thefirst tage is a 'classical' model ofgrowth.The peculiaritiesof the second stage, whichdistinguish t from he firststage, are various and not entirelyunambiguous. On the one hand, thesecond stage is characterizedbyhigherwage rates, higherratios ofcapitalto labour employed n themoderneconomy, nd a total capital stock thataccumulates faster than the hired labour forceso long as the capitalistsectorgrows. On the other hand, the second stage is describedas beingCneo-classical',which presumablymeans that profit nd wage rates aredeterminedbythe relativemarginalproductivities f the aggregate stockof capital and labour in the modernsector,and not conversely. Capitalcatches up with the labour supply. The wage of labour to capitalists isno longerdeterminedby workers' alternatives n the subsistencesector.This last seemsto imply a finalabsorptionofthe subsistence ector and azerowage elasticityoflabour supply.The diagrambelow, not offered y Lewis however, llustrateshis thesisperhaps.' The production soquants refer o the capitalistic sectoronly,the output of the subsistence sector not being shown. OL is the totallabour force n the country,OL, indicates the modern sector's employ-ment,and population is assumed constant forsimplicity's ake. There isOK1 capital in thenation,all in the capitalisticeconomy, nd as capital issaved fromprofits here s a movement duringthe first tage away from0. The capital to labour ratio remainsunchangedduringthis first eriod.The parallel tangentsdrawn to the outputisoquants, assumingwage ratesunchanged, confirm hatprofit ates of return n investedcapital are con-stant also. At A the countrymustmove from he first tage into anotherstage, ifnot before. The argument s notreallyaffectedf a givenresidualquantity of subsistencelabour refuses ever to migrateforsome reason.The capitalist sector, f not the whole economy, expands output, in thelast of all stages by reason of capital accumulation and not extra labour.The marginalproductivity f abour must ncreaseas the capital to labourratio must increase. Real wage rates rise and the profit ate on investedcapital falls. Investmentmay cease ifa pointis reached where those whosave would rather nvestabroad. Duringthe first tagetheworkers o notbenefit directlyfromdevelopment, but they do during the second, thefirst tage beingnecessary to attain the second.2I i.e. Fig. 2; this has been the subject of correspondencebetween Lewis and the author.

2 One mightask whyK, capital is not combinedwith L labour at D, thereby preadingthe capital more uniformly nd thinlythroughoutthe economy, and attaining a higherisoquant at D. But thiswould involve a realwage rate, given nterest ates,belowoutput perworker n the subsistence sector. Either these workerswould have to labour fora lowerwage or capitalist employerswould have to pay a wage above labour's marginal productwhen combined withcapital in modern processes.



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160 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURFrom this description t is evidentthat most really poor and backwardcountries re still in Lewis's first tage. The theorem sserts that almostanything hat increasesa country's tock of capital, and so causes a trans-

fer ofworkers o more productive employment n the capitalist sector, sindirectly r directly eneficial o labour. Anything hat increasesthe costof labour to capitalistswill reduce profits nd so slow capital accumula-tion.The following nalysis will suggest a number of amendments to theLewis model, however. Using the same basic assumptions,three distinctstages can be distinguished,which will be designated 1, 2, and 3, and beexplained below. It can be shown that during stage 2, while capital tolabour ratios n themoderncapitalistsector are still determined n part bythe productivity f subsistenceworkers, here will be some capital widen-ing and deepening, and that profitswill be decliningrelativeto nationalincome. This might rrestthe developmentprocess. It dependsratheronthe savings function hat is assumed forcapitalists. More mportant rob-ably, as an incentiveto continued nvestment han theratio of aggregateprofits o national income,are the profit eturnon invested capital andwealth per capitalist. Another complication s that the importanceandduration of stage 2, relative to that of stage 1, depends upon whetheraccumulations are used to subtractworkersfrom the subsistencesector(whichis the way Lewis oftenreads) or to add capital to the labour andland already employedin agriculture thereby deferring wage rate in-crease untilstage 3).Definition f Sectors

The validityofthe model dependspartly upon the conceptof capital-ist' and 'subsistence' sectors, partlyupon assumptionsregarding abourproductivity nd familysharing of output within the traditionalsector,and partly upon the savings function f capitalists. These matters helpto determinewhether he first tage terminateswhenthe supply price oflabour to capitalistemployersrises-a large subsistencesector remaining-or whenthe wage in the capitalistsector ceases to be based on subsist-ence alternatives and is determinedby marginal productivities n thecapitalsector bove. We shall first onsider he definitionfthe two sectors.

Lewis does not make the commonerror, ometimesascribed to him bypopularizers, fsupposingthat a capitalistic sector s exclusively n indus-trial one. Mention is made of capitalistic plantation agricultureforin-stance. He realizes, too, that 'if the capitalistsectorproducesno food, tsexpansion increases the demand forfood,raises theprice of food in termsofcapitalist products, nd so reducesprofits'.' He is perfectlyware thatOp. cit.,1954,p. 173.



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S. ENKE 161industrializationdepends upon agricultural mprovement. Accordingly,his capitalist sector s simplydefined s one that uses reproducible apital,and pays capitalists forthe use thereof'.'The concept of a subsistence sector s equally clear. Lewis defines t asthe non-capitalist ector,not using reproducible capital, and not payingcapitalists for ts use.2 So it includes artisan manufacturers-inthe ori-ginal sense of the word-as well as traditional griculture.The subsistencesector snot limited o agriculturalists ho consumeonly their wnoutput.Each sectormay produce both food and non-food nd both may includeagriculture. Nevertheless, t least initially, t is evident that most oftheagricultural and is in the subsistenceeconomy. And all industrialoutputis from he capitalist sector.Lewis states at one point that the subsistence output is constant3which would imply a zero marginal product of labour in one sense-whereas at other places he states that subsistence abour has a negligible,zero, or even negative marginalproduct.4 This apparent nconsistency anbe reconciled sometimes by assuming that hours worked annually peradult in the subsistence ector vary inverselywith the subsistence abourforce. Thus the marginalproduct ofan hourof workmightbe positivebutthe marginalproduct of a subsistence sector workermight be zero for thetimebeing. But it is obvious that, ong before he subsistenceeconomy sabsorbed, its output must decline. The last subsistence workers, withplenty of land to use, must have a distinctlypositive marginal product.Lewis seems to feel that the average product of subsistence abour isvery 'low' because it has not been fructified ith capital. However, aslabour migratesto the modern capitalistic sector,the relativeattractive-ness of the subsistence sector to workersmay increase. The reason thatLewis gives is that there will be fewerpeople remaining o share its foodand otheroutput.5 Actually, as we shall see, the real reason s likelyto beanother one. And by stressing apitalization of agriculture, atherthanindustry, t can be postponed by an open economy.Labour Supply to Capitalists of Subsistence FamiliesThe location f the boundary etween tages1 and 2 is very ensitiveto assumptions made regarding conomic incentives and output sharingwithin extended families of the subsistence economy. Lewis usuallyassumes that the supply price of subsistence labour to the capitalist

I Op. cit., 1954, p. 146. 2 Ibid., p. 147. 3 Ibid., p. 157.4 Ibid., pp. 142, 189.5 '... if capital accumulation . . . is reducingabsolutely the number of people in thesubsistence sector, the average product per man in that sector rises automatically, notbecause production lters, but because thereare fewermouths to share the product.' Ibid.,p. 172.



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162 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURsector s subsistenceoutput per subsistenceworker. But this s not entirelylogical.1From the outset it is necessary within the subsistence sectorto distin-guish between 1) a worker's verage product, 2) consumptionper head,(3) a worker'smarginal product, (4) hours worked per labourerannually,and (5) an hour's marginalproduct.2It is obvious that most adult male villagers are workingnot only forthemselves but for many dependants. The ratio of dependants to adultworkingmales may typically be about 3 to 1. Thus a worker's averageproduct s about threetimes,say, his consumption er head. Lewis seemsto assume that the marginal product of a worker s zero-for subsistenceoutput during tage 1 is supposedly unchangedwhenworkers migrate-the remaining abourerspossiblyworking littlemore each to compensate.Under these circumstances he supply price of subsistence abour to theothersector-temporarily neglecting pecial livingcoststhere-should beconsumption er head and not productper worker. Moreover,as workers"mouths are notthe only ones that have to be fed n the subsistencefamily,an emigration f workers hould have a relatively mall effect nper capita.availability of food and othergoods. And in fact, once it is admittedthatworkers ave a positive though low marginal product, the departureofadult males from he subsistencefamilymight eave consumption er heada little ower orhigherbut practically onstant. Here, perhaps, s the trueexplanationof unlimited' labour supply during Lewis's stage 1.But rural adult males must be assessed as producers as well as con-sumers. The product of an extra hour's labour is verylow in many poor,and overpopulatedcountries: presumably t is barely sufficiento provide;the extrafoodcalories required for extra energyused and to compensateforthe dis-utilityof work. The marginal product of a worker relativeto his average product may be very low, even lower than the ratio ofalabour hour's marginal to average product, because ofan inverserelationbetweennumberofworkers nd hoursworkedbyeach labourer. However,.as more subsistence sector workers emigrate, it becomes increasinglyimpossibleforremainingworkers o labour more hours each. Moreover,.the ratio of land resources to subsistence workers s increasing,so that.the marginal product of a worker must increasealso.

1 Lewis states (op. cit., 1954, pp. 148-9): '. . in economies wherethemajority of peopleare peasant farmers,workingon their own land, we have a far more objective index, fortheminimum t which abour can be had is now set by the average product ofthefarmer; menwill not leave the familyfarm o seek employment f the wage is worth ess than they wouldbe able to consume if they remained at home.' But outputper worker s not the same as.consumption er head. There are otherdependent people in thefamily..The quoted sentencecontradicts tself.2 In what follows, t is supposed that family consumptionequals familyoutput in value,.there being no saving.



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S. ENKE 163Continual emigrationmust eventually result in a worker'smarginalproduct exceeding consumption er head. A subsistenceworker, y stay-ing with his family, s thenadding more output than he is subtracting sconsumption. It would disadvantage the familyfor him to leave for the

capitalist sector unless the net wage there, after deducting special livingcosts away fromhome, equals or exceedshis marginal ubsistenceproductas a worker. Some ofthe excess he can remithomeinmoney form. Thusthe supply priceof subsistence abour to the capitalist sector, s migrationcontinues, s based upon the subsistenceworker's marginal product asstage 2 begins.The relations involved are represented n the following able and inFig. 1. Thereis a village family of 8 dependants plus from1 to 5 adultmale workers. As thenumber ofworkersvaries (col. 1), there s a changein total output (col. 2), a change in number of familymembers col. 3), achange n consumption er familymember col. 4), and a change nworkermarginalproduct (col. 5). This allows forthe possibility hat each workermay labourmorehoursa yearifthereare fewer fthem. The pointofthetable is that consumptionper head varies hardly at all over the rangeof7 to 3 workers. When these relations are charted the segmentof the out-put per head markedST is perhaps Lewis's 'unlimited' supply of abour.But, as labour is withdrawn o that 3 or fewermen remain, the capitalistemployersnthe modern ectormustpay a wage based on the SR segmentof the workers'marginalproduct curve.'It remains to explain the discontinuity nvolvedinhaving consumptionper head establish the supply price of labour, when it exceeds workermarginalproduct, and yet have marginalproduct be determiningwhenitexceeds consumption per head. In the abstract, a subsistenceworkershould always migrate wheneverhe capitalist sector can pay him morethanhismarginalproductat home, even thoughthis s less thandomesticconsumptionper head. But there s a practical problem. Domestic con-sumption per head may approximate some minimumof existence. And

1 In thediagramthe horizontalaxis repre- R APsents the number of adult males more orless gainfully ccupied in a family enterprise. Pt,The vertical axis representseither physicaloutput or its money equivalent. The APcurve is the output per worker.The MP is therelated marginal product curve of a worker.The AC curve is average consumption,being AC \output divided by all resident familymem-bers including8 dependants. The MP' curveshowswhat the marginal product of workers FIG. 1wouldbe ifeach laboured say a standard 2,000hoursannually. It is assumed-vide MP as comparedwith MP'-that workers abour morehourswhen thereare fewerof them.



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164 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURConsumptionnd Marginal Productof Workers

(5)(3) (4) Workers(1) (2) Family Output marginalWorkers Output size perhead product1 80 9 8*9 702 150 10 15-0 553 205 11 18 7 354 240 ,12 20-0 205 260 13 20-0 106 270 14 19-4 57 275 15 18-3

even ifthe capitalists' wage offers sufficiento live on,the workerhimselfmay not want to accept less forpaid work than he consumes at home,despite family oyalties. But most important, t is usually difficult rimpossibleforruralfamiliesto send food or other supportto relatives inthe capitalist sector, althoughurban relatives can always remitmoneyhome. It is this last asymmetry hat logically explains the discontinuityin labour supply schedulesto themoderneconomyofsubsistencefamilies.Special livingcosts in the capitalist sectorhave the effect fextendingthe portionof the over-all labour supply schedule that is based on con-sumptionper head and curtailing hat based onworkermarginalproduct.'This is especially so if workerstake dependants to live with them. Thetheoretical onclusion s that the supply priceofsubsistence abour to thecapitalist sector is the higher f (1) domesticconsumptionper head plusspecial livingcosts ifany, or (2) a worker's ubsistencemarginal product.

Stages 1, 2, and 3All this suggests that there are really three distinct stages and notmerelytwo.The peculiarity f stage 1 is that there s an 'unlimited' supply of abourfrom the subsistence sector at a constant supply price approximatingconsumption per head plus any special costs of living in the capitalistsector. Hence labour to capital ratiosare constant. Profits re a constantfraction fthe capital sector's value ofoutput assumingno technologicalchange. The expansion path is shown by OB in Figure 2. Growthdoesnot benefit he workersbut only capitalists if population is stationary.This is clearly Lewis's first tage.The peculiarityof stage 2 is that, although a considerable subsistencesector remains to be absorbed,the price of labour to the capital sector srising. It is now based on marginal abour product in both sectors. The

1 Diagrammatically,this is shownby the dotted curve, terminating t S'.



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S. ENKE 165alteringratios in which labour is combined with capital in the modernsector, and hence the relative marginal products of these two factors, spartly determinedby workers'marginal alternatives in the subsistencesector. Extra sector output is partly contributedby extra employedlabour. The expansion path is BCE in the diagram.The peculiarity of stage 3 is that no subsistencesector remains. Therelativemarginalproductivities f abour and capital inthe modern ectordepend upon its productionfunction nd the relativequantities of abourand capital in the economy. The direction f causationhas been reversed.Only extra capital-or improved technology-can augment output. Theexpansionpath is vertical n the diagram.Both stages 2 and 3, as definedhere, seem on occasion to fit Lewis'sdescriptions of his second stage. In both cases wage rates are rising,capital to labour combinations re increasing, nd the profit ate of returnon invested capital is declining. This squeeze on profitsmay terminatecapital accumulation and growth.It is exactly this danger that makes the distinctionbetween stages 2and 3 so important. Growthduring tate 3 inevitablymeans higherwageratesthat slow capital accumulation. There is no more abour to be had.1But during tage 2 there s more subsistence abour available. The crucialquestion is how much higherwages have to be paid to obtain it for usewithextra capital. Certainly his is the case if abour is subtractedfromsubsistence griculture nd employed n capitalistic ndustry.Fortunately,an alternative exists as we shall see (in the sectionafternext), and thatis to add capital to rural abour and land to establish a modern griculturalsector. For an open economy,there s hence an opportunity o convertapotentialstage 2 into an actual stage 1, therebypostponing n increase nwages. But stage 3 can never be transformed nto stage 1 because thesubsistenceeconomy has been absorbed.Capitalists' Savings and ProfitLevels

Continual output expansion of the modern sectorrequires continuingaccumulations ofcapital whateverthe stage ofgrowth. The capitalistsdopractically ll the saving by theeconomyfrom heirprofits. n fact,Lewisalmost seems to assume that aggregate annual savings and profits reidentical. Consumption of capitalists is apparently zero or constant.Accordingly, e is confident faccelerating nvestment uring tate 1. Butprofitsmay be 'squeezed' during tage 2, and a fortiori uring tage 3, sothat growthmay be slowed or arrested. It will be useful to explorehisreasoningon profit evels and capitalists' savings.

1 International mmigration nd 'labour-saving' innovationsare ignored.4520.2 M



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166 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURStage 1 Profits

Capital accumulates supposedly at an acceleratingpace because profitsare increasing. As Lewis writes:So long as unlimited abour is available at a fixedreal wage, the share ofprofitsin the national ncome will ncrease. There are two reasonsfor his. First,theshareofprofitsn the capitalist sector may increase. And secondlythe capitalistsectorwill expand relatively o the national income.1

But there are several difficulties.First, if it is profits er se that matter why bother about the relationbetween capital sector output and national income, the latter includingas it does the subsistenceector's output?

AK2-

0 L1 L2 b L CFIG. 2

Second, should one consider the ratio of profits o the capital sector'soutput relevant, his s not ncreasingduring hefirst tage ifone abstractsfrom nnovations. If the country s an open economyas regards capitalmovements,nterest atesmaybe an exogenousdetermination y the out-side world,and so theratio of nterest or profits) o wages is presumablyconstant too. If the economy is closed, and the capital sector has ahomogenousfirst egreefunction fproduction, constant real wage willresult in a constant residual profit eturn on investment. Fig. 2 is con-structedon the assumption that, in expandingfrom0 to B, there willbeconstantratios amongtotal capitalists' profits, otal labour payroll,total

1 op. cit., 1958, . 8.



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S. ENKE 167sectoroutput, total workers mployed,and total capital stock. Thus theratio oftotal profits o total sector output is presumably constant.Third, annual total investment might be determined by the rate ofreturn on investment, nd at times one infersLewis assumes that evenwithout technologicalimprovements his will increase during stage 1.1However, ifthereare constant returns o scale in the capitalist sector, heprofit eturnon investedcapital will be constant.2Stage 2 Profits

How will aggregateprofits e affected y capital accumulation n stage2 ? Assuming ome savings, such as an increase n total capital stockfromsay K1 to K2 in Fig. 2, rival capitalists will seek to add labour drawnfromthe subsistenceeconomy. For reasons given, to all workers heywillhaveto pay a higherwage perworker, nd they willadd labour until its margi-nal value product s equal to its increased average cost. Perhaps the newequilibrium s at C on Q2with L2 labour employed n the modernsector.Wages per worker n the capitalist economywereOL1/Ob fQ1 nd theyare now OL2/Oc of Q2. If there are constantreturns o scale in themodernsector,3 he residual profits f capitalists will equal the marginalproductofcapital times total capital employed,and thereward per unit of abour

I Videthediagramon p. 152 ofthe 1954 article; and in the 1958 article p. 26) describingentry nto stage 2, he writes: . . . and the profitmargin now) does not necessarily ncreaseall the time'.2 Lewis seems to have been led astray,and into assumingan increasingratio of profits ocapital sector output, by his two-dimensionaldiagram as reproduced here (op. cit., 1954,p. 152). The horizontal axis represents uantity of abour employed n the capitalist sectorand the verticalmeasures nmoneythewage and marginalvalue product of abour in the capital sector. The wage isW and constant. As capitalists make more investments,the marginal value product of any given ordered unit oflabour increases. The area above the wage line but belowlabour's marginal product curve can be integrated to wrepresent otal profits. Suppose V1 s the marginal valueproduct curve of labourwith $x of capital. If the capitalstock is doubled, and assuming constant returns o scale soas to exhaust the product according to neoclassical dis-Ltributionprinciples,the marginal product that was pre-viously the Ith labourer's will now be that of the 21th FIG. 3labourer. Thus V' (dotted) results. But Lewis assumeda curve such as V2. Hence he supposed the total area under the marginal product curve

increases proportionatelymore than therectangularpayroll area as capital and labour areincreased by the same percentage. But using continuous curves, and assuming constantreturns o scale, the point is that the second workerwith double capital is the equivalent ofthe firstworkerbefore, he second quarterworker fterwardshas the same product as thefirstquarterworkerbefore, nd so on, the two marginal product curves (e.g. V1and VD)properlyhaving the same vertical axis intercept.3 Fig. 2 is drawn on the assumption that a doubling of K and L will result in doubleoutput, so that, ifQ2 s twice the Q1 output, any ray fromthe originwill intersectQ2 attwice the distance as Q1from0.



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168 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURwill be higher nd that ofcapital will be lower than before. Profits ecomea smaller fraction f sector output.Why Capitalists SaveIn any event, not very much s known about what makes reallywealthycapitalists save, in contrast, ay, to what makes professional alary earnerssave. It is a very middle-classview, suitable perhaps for advanced coun-tries, that people consumeand so save as a function f their ncome. Inundeveloped countries, he vast majority of the population eithercannotor willnot save, and it is thewealthy who do most of the saving withoutmuch difficulty.2

One peculiarity f wealthyfamilies s probably that they consumewhatconstitutes regressive raction f owned asset values. They do not altertheir way of living fromyear to year as incomes fluctuate. Given theirposition,both financially nd socially, they have a more or less customaryexpenditurepattern. An extra dollar on consumption dds little satisfac-tion and decreasing utilityreturns. But an extra dollar saved may giveincreasing eturns s regardsfamily tatus and power. The numberofrivalfamilies diminishes very rapidly in a small country as family wealthaccumulates.One could very reasonably assert that the savings ofwealthy capitalistfamilies re the residual that remains after sset determined onsumptionhas been deducted. For example, an individual capitalist's savings mayfollowthe rule: AK* K~r- C.whereK* s his wealth inmillionsof dollars, r the annual rate ofreturn nassets, C is the dollars spent on consumptionper million dollars' worthofcapital assets, and the oz xponent s less than unity.3The above formulationmeans that capitalists collectively onsume essif a given national asset stock is owned by a few capitalists ratherthanmany. But the distribution f produced wealth does not alter capitalists'profit ncome. Hence, aggregate annual savings vary inverselywith the

1 It is fortunatefor society that capitalists do not operate as a monopolisticconspiracy,basing theirsavings decisions on the relation of changes n profits o changes n total capitalstock. A slight ncrement n capital, used to transferworkers at a slightlyhigherwage,increasesthetotal sectorpayroll by a greaterpercentage than thewage increase. The extrapayroll is offsetby reduced total profits. Hence the rate of returnon the last dollar ofinvestmentmay be negative. However, most investorssee onlythe ratio of total profits ototal capital, and this average rate of return being positive) may provide enough ncentiveto continue them saving.

2 The importance of the middle class for economic development ies not in theirsavings-which in the aggregate are small relative to those of thewealthy-but to theirservicesasmanagers, engineers,biologists,doctors, teachers,&c.3 As r is a variable (see below), the above equation is not tantamount to defining on-sumptionin terms of income; in addition, even capitalists may have some earned income,but ifso the incentive to workis not usually the salary.



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S. ENKE 169numberof capitalists, otherthings equal. If all real capital assets wereowned by tenfamilies, he rate ofsaving fromprofitswould presumablybe greaterthan ifequal value assets wereowned by a millionfamilies, otbecause the ten families' ndividual incomeswould be larger but just be-cause they would have morewealth n an average. All this suggeststhataggregatesavings of an economydepend only in part on total nationalprofits nd not at all on the ratio of profits o national income.If savings are partlydeterminedby wealth per capitalist, it becomesimportant to consider the rate at which capital as contrasted withcapitalistsis increasing nnually-something that is hardly mentioned neconomicdevelopment iterature. f capitalists are increasing t the samerate as mostundeveloped countries'populations, which s about 2 to 2-5per cent.a year,theyaredoubling heirnumbers very hirty-fiveo thirtyyearsapproximately.Thismeansthat their ggregate onsumptionmaybedoublingeverythirty-odd ears. Ceteris aribus, fannual investment ercapitalistfamily s to be maintained, otal capital stocksmustbe doublingevery thirty-oddyears also. If capital stocks double sooner, the morerapid increase in individual familyassets will in turn increase annualsavings, and thisrecursiveelement or 'feedback') may be an importantgrowthfactor.The question remains as to whether capital accumulation may bebroughtto a halt duringstage 2. As explained already, an increment fcapital 'seeking' an immigrantworkerwill probably raise wages, whichhigherwagesmust be paid to all capitalistsectorworkers. Hence therateof return n capital (r)willfall. The danger s that an increment fcapitalmay decreaserproportionately ymorethanK increasesproportionately.The reducedprofits, urther ffset y increased consumption,must thenoccasion smaller annual total savings. Additions to the stock of capitalmighteven cease. Hence it is important o considerways in whichextracapital mightotherwise e employedwithoutundulyraisingwages duringthe second stage.Capitalizing AgricultureNecessaryThe reason that wages rise during tage 2 is that the subsistencemarginalproducts ofremainingruralworkers ncrease as otherstransferto the capitalistsector. This is inevitable, fmanywere but are no longerengagedin agriculture, nd usable land is a scarcegood. The ratioof andto labour willthenbe increasedbyworkers' migration nd anyremaininglabourerbecomes a substitute t themarginformoreacres.This would not occur,however, fextra capital could be employed n amannerthat would not alterthe labour to land ratio in subsistenceagri-culture. In otherwords,wagesmightnot riserelativeto profits f and and



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170 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURlabour could be transferrednto the capitalistsector at 'equal' rates.1 Asland is immobilephysically, this means that capital must come to it,ratherthan labour migrating o capital.

As indicated before, he subsistencesector is not entirely gricultural,noris the capitalistsectorentirelyndustrial. Rural labour does nothaveto leave therural and in orderto workwithexpensive producedmeans ofproduction. Capital does not have to be combinedwith labour to theexclusion of and. So oneway to ensurean 'unlimited' supply of abour ata fixedreal wage during the early stage would be, not only to subtractsubsistence labour for capitalist sector employment, but also to addcapital to the labour and land of the subsistence sector. Obviouslythislattercapital addition wouldenforce revolution n agriculturalpractices.Modernization nd capitalization ofagriculturewould have to go hand inhand.2There are other potent reasons why there will have to be a certainamount ofcapitalizingofagriculture nyway. When labourmigratesfromthe subsistence ector, here s a tendencyforthose whoremain behind toeat much of the previous share of the departed relatives,so that theremustbe an increasedfoodavailability nthenation whenpopulationshiftsto urban industry.3Moreover, f the capitalist sector is almost entirelyindustrial nd theeconomy s closed, thedesire ofcapitalist sectorworkersto eat will increase the real income per head within the subsistenceeconomy and shiftthe terms of trade against the industrial capitalistsector.4A finalquestion is whether tage 2 can be eliminatedentirely,withthewhole early stage being like stage one, as Lewis describes t. This seemspossible if the land and labour resourcesremaining n the subsistencesector are maintained in the same proportions. This would require nocombination of capital with labour that was not accompanied by itstraditional amount of land.Practically, hismeans ess stressonindustrialization,nd concentratinginstead onmodernizing nd capitalizing griculture. The higher ercapitaincomesthat result will naturallyoccasion a demand for ndustrial pro-ducts that may be imported n exchange for gricultural xports. A very

1 i.e. the quantity of land transferred,s a percentage of total land in the subsistencesector,must equal the percentageofsubsistence abour transferred.2 If these nnovationsare 'land-saving', raisingthemarginalproductivity f and relativeto labour, so much the better.

3 See Enke, S., 'Food Constraints n IndustrialDevelopment inPoor Countries',SouthernEconomicJournal,Apr. 1961.4 See Gutman,G. O., and Black, J., A Note on Economic DevelopmentwithSubsistenceAgriculture',Oxford conomicPapers, Oct. 1957; Ranis, G., and Fei, J. C. H., 'A TheoryofEconomic Development', AmericanEconomicReview,Sept. 1961; also Enke, S., 'Indus-trializationthroughGreaterProductivity n Agriculture', ReviewofEconomics and Statis-ties,Feb. 1962.



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S. ENKE 171open economy,with extensiveparticipation n foreign rade, then becomesa condition of national economic development. This was the imperialprescription or olonial growth nd thereare many examples of ts moder-ate success. However, rightly r wrongly, uch development policies arepolitically unacceptable in most independentbackward countries.Conclusions

The extraordinarilymportant nalysis and conclusionsof Lewis mightusefullybe amended or supplemented n at least five significant espects.First, there are three distinct stages in the capital sector's outputgrowth,the first nvolving only capital 'widening', the second entailingboth capital 'widening' and 'deepening', and the thirdoccasioningcapital'deepening' only. The boundary between the first nd second stage ismarked by a change froman infinitely lastic to a less than infinitelyelastic labour supply to the capital sector. The boundary between thesecond and third stage is markedby a change froma positive to a zeroelasticityof labour supply.Second, the abour supply by subsistencefamilies o the capitalistsectoris not a continuousfunction. The supply price, assuming extended familysharingoffood and otheroutput, s the higherof consumptionper heador workermarginal product. The asymmetrys caused by the abilityofurbanized workers to remit funds to rural relatives and the inabilityof subsistence families to support relatives employed in the capitalsector.Third, although nothing conclusive can be asserted, it seems possiblethat aggregate annual saving by capitalists depends upon their totalprofit ncome and individual capitalists' wealth. There seems no specialreason for assuming that annual accumulations are determined by theratio ofprofits o national income. Unequally owned assets may contributesomething o growth.Fourth, the raising of wages in the capitalist sector might be lessened(increasing ccumulation and sectorgrowth), f ncrements f capital werecombinedwith rural land and labour in modernagriculture. The alter-native of transferringabour from subsistence agriculture o capitalizedindustry, aisingthe ratio of land to labour in the subsistence economy,must raise the marginal product of a subsistence worker. This is ofspecial significancewhere limited land resourcesoccasion markedlyin-creasing returns o workers n subsistence griculturewhenother workersemigrate.Fifth, developmentplan that stresses capitalistic' agriculture s prob-ably impossible n a closedeconomy. The resultant unbalance' ofoutputwould swing the termsof trade against a capital sector that was almost



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172 ECONOMIC DEVELOPMENT AND SUPPLIES OF LABOURentirely gricultural. The policy choice is betweenaccepting higherrealwagesduring tage 2 orpostponing tage 2 indefinitelyut acceptingopentrade withtheworld economy.'DukeUniversity,.S.A.

1 The authoracknowledgeshis indebtednessto his graduatestudentsat Duke University,and to Professor . P. F. Horwood oftheUniversity fNatal, whosequestionsand commentsinstigatedthispaper.

enke econ dev't and unlimited labor supply

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