Marx Sraffa Kalecki_CJE 1980

7/29/2019 Marx Sraffa Kalecki_CJE 1980

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C ambridge J ournal of EconomicsPatrons:Richard Goodwin, Nicholas Kaldor, Luigi Pasinetti, J oan Robinson, Piero SrafiaEdtors:Sarah Bourne (Managing Editor), Ken Coutts, Francis Cripps, J ohn Eatwell,Alan Hughes, Tony Lawson, Suzy Paine, Jill Rubery, Ajit Singh,Sheila Smith, Roger Tarling, Terry Ward, J ohn Wells, Frank Wilkinson

AssociateEdtors:Mahmoud Abdel-Fadil (Middle East)Geoffrey Harcourt (Australia)Amiya Bagchi (India)Mario Nuti, Ron Smith, Ian Steedman (UK)Diane Flaherty, David Gordon, Anwar Shaikh (USA)Michael Ellman (The Netherlands)

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CambridgeJ ournal of Economics 1980,4, 103-115

Accumulation and exploitation: an analysisimthe tradition ofMarx,Sraffa and KaleckiAn'iit Bhaduri and Joan Robinson*

Pie:ro SrafFa was completely successful in his aim of providing abasisfor the critique ofneoclassical theory but themodel inProduction ofCommodities by M eans ofCommodities(I960) provides avery narrow basis forconstructive analysis.he model presents a strictly one-technique economy. I nthe system ofequations,each input used up in one period isreplaced in kind as production goes on. This entailsthat the same technique is going to be used in the next period. In itself, this isamerit ofthe construction, but it needs to beemphasised; Sraffa himself blurs thepoint byintroducing changes into his self-repeating story.f

T he characterisation ofa technique has two elementsthe engneering specification ofthe physical input-output equations and the pattern of applications of labour throughtime. In Sraffas story, inPart I , the reproduction of the system takes place in a singeperiod; the turnover of each commodity takes the same time. Thus, in the production ofeach commodity, the stock inexistence at amoment of time, in the pipelines of pro-duction, isthe same multiple of its flowofoutput. The rate ofprofit isexpressed as apercentage per period.% (When fixed capital isintroduced in Part I I , time patterns aremorevaried. Here both types are treated together.)

There isno discussion of the realisation ofsurplus asprofit. I t ismerely takenforgranted that whatever is produced is disposed of at such prices as to result in auniformrate of profits in all lines of production.

Finally, the determination of the distribution ofnet output between wages and netprofit isleft completely open (apart from the inexplicable suggestion that the rateofprofit on capital might be governed by the rate of interest). In this sense, Sraffa presentsa scheme more fruitful than Ricardo's. Since it does not specify the real wage, it presentsa challenge to attempt to diagnose what forces do determine the distribution of incomebetween profits and wages.

I an Steedman, in Marx after Sraffa (1977), refutes the various objections that dogmat-ists have raised against this analysis and shows that, if we are supposed tohave fullinformation in physical terms (including the real wage), thereisno advantage in intro-ducingvalueas aunit of measurement. But in his own argument, hefollows Ricardo inmaking the real wageagven basket of specified wagegoods, which are therefore basicsin the system. This entails the determination ofdistribution from the technical data,


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10 4 A. Bhaduri and J. Robinsonleaving no room for class conflict, and it does not touch on the question of realiPresumably, to complete this story, we must suppose that a capitalist uses parprofit for consumption and invests the rest, each in his own business. Here wa pre-K eynesian sett ing where savings govern accum ulation and there is nodiscuwhat form investment takes, or how it could result in a feasible rate of growthsystem, unless in a one-commodity economy.

To avoid these objections, we present a 'Sraffaesque' model, or ra ther a famodels, including distribution according to Ma r x and realisation according to KOur me thod is to elaborate Sraffa's model, first dealing with one problem aand then recombining them. Like his, our models depict a two-class society in capitalist economy, without foreign trade or taxation. For the most part , the aris conducted in terms of a one-technique system with lon g-run norm al pricesit is a set of highly abstract intellectual experiments. It is intended, however, toclogical ground for a discussion of real issues involved in the analysis of caccumulat ion.

A stationary stateSraffa did not need to ask whether his system was growing or not. Net outputm ay not include some physical items to be added to stock, and the workers rshare in the value of net output, not a supply of specific wage goods. Here ouis a modification of his. Wemake a physical distinction between means of prowhich are basics in Sraffa's sense, each entering directly or indirectly into the oall commodities, and consumption goods, which are non-basic.We first consider simple reproduction (a stationary state). This means that thconstant labour force, working standard hours per day and per year and ameans of production which is being kept intact by continual replacements ofthey areused up, while the whole flow of net output isbeing consumed. The nocapitalist economy dwelling contentedly in a self-perpetuating stationary evidently artificial. The assumption of stationariness is here introduced provisioorder to separate out for analysis the t ime-pattern aspect of the stock of mproduction required for a given technique.The quant i ty of each item in the stock depends on the a moun t of it requiregeneral flow of production and on its turnover period. +For a type of machine ttakes oneyear to build and has ten years of life at full efficiency (a one-hoss sannual output of a single machine maintains a stock of 10 machines of ages zerEach year one falls out of use. The production of one machine per year keeps tof balanced age composition in being. Along with each item of long-lived eqthere is a stock of working capital corresponding to the short-period througproduction with that equipment.

t Was Marx a neo-Ricardian? Marx argued that l abour power is sold as a commodi ty ancommodities exchange at their values. The value of l abour power is a real wage sufficient to mcustomary s tandard of life. If the value of l abour power remains constant through t ime, then diis determined by technology asRicardo believed. But if realwage rates can rise or fall under theof changes in product ivi ty and the balance of power in society, as Marx clearly contemplated would, then the value of l abour power is an unnecessary and misleading concept. SrafTa is certneo-Ricardian in this sense, but he hasnever gone into thequestion of the realisat ion ofphysicalprofits, leaving his logical scheme open-ended with onedegree of freedom in the system of equa


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Accum ulation and exploitation 105The length of the period of turnover of the self-reproducing state is the least common^multiple of the turnover period of al l the items. The stock of each item is then repre-se n t e d by the amount of labour time directly and indirectly required to produce it and*.he time pattern in which the labour was applied. In the stationary state, the whole

11 abour force maintains the whole basic stock (and also produces a flow of non-basics forcronsumption) but, by the method of sub-systems, the labour embodied in each particularifiem can be distinguished from the rest.f| It is to be observed that stocks of animal andvegetable products canhave been builtuj)) in this way, but minerals (including coal and oil) are not replaced but taken fromth-i earth's crust and dissipated into the air or crumbled into the ground. In contrast,tWpre are installations, such as hydro-electric stations, which required a large invest-m e n t in the past and are kept permanently in being by a relatively low rate of expendi-ture on maintenance thereafter.(When these two types of investments are excluded, the existence of the whole self-reproducing stock can be traced back through logical time in the manner which SrafFaapplies to working capital. J This is not a process in historical time. It never reaches amoment when the stock was first completed (at the end of a supposed initial gestationperiod) but continues indefinitely into the past. At any stage in the process, however farback it is taken, there is a stock of means of prod uction alread y in existence in the correctproportions, because the same technique is assumed to have been in use ever since timebegan.T'he question was raised byKeynes on an early draft of the book as to wheth er Sraffa'ssystem allows for variable returns to scale (Sraffa, 1960, p. vi). The question seems to beirrelevant to a one-technique model. One total stock of basics isappropria te to one flowof work being performed with one technique. Adifferently employed labour force wouldrequire a correspondingly different stock. If there were differences in returns to scalebetween the two cases, the items in the two stocks would not be in the same proportionsand they would represent two different techniques. Thus, once the existence of stocksin a station ary state is explicitly recognised, the question of changing the scale of outputdoes not arise. As we shall see, the one-technique model can be adapted to deal withsteady growth, but growth with changing proportions of inputs requires an historicalanalysis of the m ann er in which a new stock is bu ilt up to support the changed techniqueof production.

At the same time, when joint production is excluded, the pattern of prices, with anyone technique, is independent of the proportions in which commodities are produced.This was misleadingly called by Samuelson 'non-substitution' (see Pasinetti, 1977) andby Pigou (1932) 'constant supply price' for individual commodities.The ratio of exploitation and rate of profitsSraffa set ou t to pro vide the basis for a critique of the economic theory that was prevalentwhen he began work in the 1920s, before the first rumb les of the Keynesian revolutionhad been heard. The dominant theory of distribution was that of Alfred Marshallvulgarised by J. B. Clark (1891):


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' f 106 A.BhaduriandJ.RobnsonSraffa opposed tothis the argument that, with agiven flowofproduction d

physical terms, theshare of real wages inphysical netoutput may, inprinanything between unity andzero with thecorresponding rates ofprofit betwand the physically possible maximum.

G iven thephysical specification ofthe model, apart icular rate ofprofit, throughout theeconomy, entails aparticular pattern ofpric.es for al the iteflowof production (including non-basics) and forthe stocks ofinputs, andapthe ratios ofgrossprofit towages ineach industry.Sraffa's argument waslargely concerned with theconstruction of anumphysical termsthe standard commodity. Itseems equally satisfactory to useaaire the labour time performed by arepresentative worker, sayover aweekpostulate anarbitrary money-wage rate perman-week, say $10, andspecifrelationships within the system interms ofdollars. Wethen have awage billannum, as aflowofdollars, independent of the rate ofprofit. Correspondingven rateofprofit (with itsappropriate patternofprices and grossmargins) particular flowofnet profits indollars received bycapitalists.

Comparingahigher with alower rate ofprofit, the pattern ofprices may bdifferent but the overall level ofprices mustbehigher and the real-wage rate

/ Itseems appropriate toexpress the ratio oftheflowofnet profits tothewathe rate of exploitation. (Marx defined this in terms of labour values; hertranslating into asystem ofpricesofproduction.)

T he rate, or better theratio, of exploitation is notdetermined by thespecification ofthe system. It is anindependent element inthe situation whichexplained bythe fortunes oftheclasswar. This freedom ofthe distribution penabled Sraffa tobreak out ofthe 'iron-law ofreal wages'. He washimself sreluctant to make suchadeparture from classical traditions but forusit isthis that enables usto integrate the problem of realisation into our analysis.

I n the formal model there isno causality. The rateofprofit entails and isenthe ratio ofexploitation whatever itmay be. But when wewant tostep downmodel into aninterpretation ofreality wehave toconsider which determinI t iscertainly easier to dothe sums ifwe start from agiven rate ofprofits, binstinct wascorrect: the causal factor istheshare ofprofit from which the ucan bederived only as apostulateofthe long-run normal configuration ofpr

A variety of non-basicsT o concentrate upon the main argument, wehave sofarsaid nothing about thnature of the output of non-basics. We nowintroduce into themodel therentiers andworkers consume different physical baskets ofnon-basicsluxwagegoods. (There may be some items incommon but indifferent quantitiesluxury basket contains lessbread than the wage-good basket, and more whivalue ofthe flowof luxuries indollars isequal to theflowofrentier incomevalue ofwagegoods isequal tothewage bill. This requiresasomewhat diffestock ofmeansofproduction foreach ratio ofexploitation; the main bulk ofthnot affected but there must be appropriate productive capacity fortheflowofthe physically different non-basics.

Now wecometo apuzzle. The ratio ofexploitation islogically prior tothluxuries andwaee eoods. vet thestocks toproduce them must already be


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Accumulationandexpoitation 107T he Marxists have long recognised this problem as the 'crisis of proportionality'toeach gven real wage rate must correspond a certain division of productive capacitybetween the investment sector and the consumption-goods sector. To adifferentreal wagerate, entailing a different ratio of exploitation, must correspond a different proportion

between sectors, while a sudden change in the real wagerate would throw the propor-tions in the stock out of line with theflowsof production.

T he answer is that, when the stocks are in balance with outputs, it must be supposed! that the investment in the two stocks was made in the light of correct expectations of thei returns to be enjoyed on each.) A uniform rate of profit can be imposed upon a set of prices by an economist describing; his model, but in terms of the behaviour of the inhabitants of the system, the equalisa-tion of the rate of profit takes place through investment decisions influenced by expecta-

tions of future profitability. Only when expectations have turned out exactly correctis there a perfectly uniform ex-post rate of profits in the system.i I t is sometimes objected that expectations introduce an illegtimate subjective elementinto analysis, but the subjective expectations held in the past are manifest in theI objective stocks in existence today. Not to recognise stocks explicitly is then tantamount

I to ignoring the importance of expectationscorrectly or falsely heldas an essential; characteristic of time in the analysis.I The same consideration applies to the formation of prices. When a uniform rate ofprofit rules, grossprofit margns (theexcessof proceeds over prime costs) for baskets ofnon-basics are determined. A product which requires a higher capital to output ratio

: has correspondingy higher grossmargins at any given level of the rate of profit. Eachi type of product in theflowof output requires a certain rate of grossinvestment to keepj its stock intact and a certain allowance ofnet profit toyieldthegvenrate of profit on thej value of its stock of long-lived and short-lived basics, which we may now describe as itsI capital. 'Capital' is thus seen as a two-edged concept, in the tradition of Marx, involving! both the physical aspect of means of production and property rights which gveriseto; profit as the source of capitalists' income.

Now, in industry, prices have to be set in advance of sales. Thelevel ofunit costs, withlong-lived equipment, depends on its level of utilisation. Gross margns in each line arcfixed in such a way as to cover costs and yield a 'subjective-normal' rate of net profit; at a standard level of utilisation of capacity. The ex-post rate of profits for eachwill benormal when the standard rate of output is realised. If actual output were higher thanstandard, profits would be more than normal, andvice versa.Our earlier puzzlethe proportionality crisisrevisited in the form of the question ofhow stocks can be exactly right to fit with whatever may be the distribution of incomeis precisely the outcome of an assumption that expectations in the past have beenexactly correct. On the composition of the basket at least of luxuries, there must be someinfluence of consumers' tastes. But consumers are not choosing between 'n' ready-madecommodities, as in so-called general equilibrium. Rather, producers have toguesswhat* they will be able to entice consumers to buy.

These considerations show that it is unreasonable, except in a pure thought experi-ment, to postulate that an absolutely uniform rate of profit is ever realised even in fairlytranquil conditions, for expectations can never be exactly correct. In the type of modelin which the rate of profit is technically determined, it may be postulated to be uniform,but then the conditions for the realisation of the physical surplus as profit areleft in the


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108 A BhaduriandJ.Robinson

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Changng exploitationI n a steady state, with confident expectations, the ratio ofexploitation is, so tbuilt into the stock of basics. A change from one ratio ofexploitation to another require an appropriate adaptation in the stock.

A rise in theexploitation ratio might come about from an increase in monpower and weakening of trade union resistance, causingarise in profit margns aincrease in distribution torentiers. This generates a rise in expenditure on luwhich may run them up to full capacity and raise their profitability all the more.in the consumption ofwagegoods checks and may even reverse the increase in thof profits inthat sector.

Suppose that there has been aonce and for all change and that the new situationand isexpected to last, indefinitely so that there is now a newstate- of lonexpectations. Wecan tracea traverse with gross investment below replacementwage-good industries and above it in luxury industries until the rate of profit haequalised between the sectors, at anew higher level, and the composition of the sbasics has been readjusted accordingy.

A fall in the exploitation ratio might becaused by agrowth oftrade union stcombined with more intense competition among capitalists that prevents thempassing raised money-wage costs fully into prices. Now theflowof profits hareduced in both sectors.Technical conditions do not exclude a traverse to a lower rate ofprofit, the image ofthe above, for asKeynes (1936, p.374) observed, there isno reason wgame should not beplayed for lower stakes once the players are used to thethe experience of afall innet proceeds from one quarter tothe next may havethe capitalistsashock. They jib atmaintaining the former rate ofgrossinvestmeincrease in capacity for wagegoods fails to balanceadecline in that for luxuries the total stock of basics is allowed to shrink, and the full-capacity level of employmreduced. Thus the neoclassical dictum that high wages reduce employment maout to be true for quite un-neoclassical reasons: the capitalists' reaction, in termsvolume and composition of investment, to a lower ratio ofexploitation may lecourse of the traverse to anew stock configuration appropriate to apermanentlylevel of output and employment.

Accumulation wthout rentier consumptionWe now introduceamodel inwhich there is noconsumption out ofprofits, binvestment isgoingon. Thereis agrowth rate which isgven bythe overall ratiovalue of theflowof net investment to the value of the stock. In this case, since wea one-technique economy, employment must begrowing in step with the growt: The analysis isfamiliar (von Neumann, 1945). Weneed only remark that the rate must have been built into the system from the first; asinge technique ireproduced on an ever-widening base. Thus economies of scale are here ruled o

When the growth rate isgven, the corresponding ratio of exploitation isdeterbut it is not true that the exploitation ratio, by itself, determines the rate of growtratio determines the potential surplus ofthe system, but investment decisions bycapitalists are needed toturn the surplus into profit. Professor von Weizsacker has argued that there can be no exploitation in suchacase because the entire pneeded to finance accumulation. But he failed to observe that realisation of sur


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Accumulationandexpoitation 109profits ispossible only through accumulation, which capitalists arbitrarily decide uponin their owninterests, without consulting workers. Thus theworkers' share in netoutput isstill governed bythe ratio ofexploitation, while accumulation (without the aidof capitalists' consumption) turns the potential share ofthe capitalists, set bythe ratioof exploitation, into thecorresponding rate of profit by creating enough effectivedemand to realise it. I t isto beobserved that we are here comparing different growthrates with asingetechnology. When actual capitalist economies are compared, itoftenhappens that the one with a higher growth rate uses superior techniques and hasahigher rate of innovation so that faster growth isassociated with higher rather thanlower real wages inaparticular phase of development.The general modelWhen we combine growth with rentierconsumption, net output consists ofnet additionsto the stock of basics plus the flow ofnon-basics. The flow ofoutput contains threephysical elements, the complex of basics (replacement and additions) and the baskets ofluxuries and of wagegoods.

T he flowof realised net profits isnow composed of two elements, net investment andrentier consumption. This accords with Kalecki's famous epigram: the workers spendwhat they get and the capitalists get what they spend.f

We may suppose that the rate of growth has emerged from the decisions of the activecapitalists (entrepreneurs) who manage business and that they also decide upon theamount of profit to be distributed to rentiers, subject to the limitation upon the overallshare of profit set byworking class resistance.

I n the former model, the rentiers simply spent whatever profits they received. If theyalso have apropensity tosave, then:C = + ( 1 s D, where C istheflowof rentierconsumption and D distributed profits. The savings of the rentiers arelent to thecapitalists to finance investment. Now, if each capitalist financed thewhole of hisgross investment out ofgross profits, he would automatically be financing net invest-ment out of net profit. There could not then be any savings by rentiers. I f rentiersfail tospend part of the distributed profits that they receive, profits are realised onareduced scale and distributions are correspondingy lower. Rentier income then couldnot riseabove the constant, a in the above equation, which isall consumed.

When investment exceeds retentions, rentiers' income exceeds expenditure forconsumption and their savings are exactly what isrequired to finance the excessofinvestment over retained profits.T he Ango-Italian formula, = g!sp (the rateofprofits, onasteady growth path, isequal tothe rate ofgrowth divided bysavingout ofprofits) isformally correct whenthere isnosavingexcept out ofprofits, but it. obscures the mechanismofthe financialsystem by failingto distinguish betweensavingout of profits in the form ofretentions andsavingout of rentier income.T he foregoing argument showsthat to postulateagvenphysical real wagein advancewould require the rest of the model to be draped around itso that technical conditions,the ratio ofexploitation, the realisation of the potential surplus and the rate of profits areall consistent with it. Starting from the other end, we find that thelevel of real wagesinaparticular economy depends, firstof all, on technical conditions and the stocks of means


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110 A. Bhaduri and J. Rob insona self-reproducing state. Secondly, it depends upon the share of profits in netwhich is governed by the ra te of accumulat ion and of non-wage consumption,to the l imit on the ratio of exploitation permitted by social conditions.

On this view, capitalists, in the various sectors of industry, set their selling prelation to costs, according to various profit-seeking strategies. The interactionthem establishes the 'degree of monopoly', that is, the overall mark-up on the tobill. But until flows ofoutput ofcommodities are sold at those prices in the marmark -up over the wage bill remains only a potential surplus. Investment and conexpenditure by the capitalists determines how much of this potential surplus isas actual profits.This is as far as a one-technique model will take us. A one-technique economto be found in the history of capitalism, for accumulation is always accompainnovations and at any mome nt the stock of means of product ion in existence icomposed of fossils from earlier phases of technical development while curreinvestment is installing the latest types of equipment . To set the model in htime, wemust take account of change.

C v

Out of the strait-jacketIn a steady state all events are predetermined. Anything that happens ' todaydetermined by the past, including expectations about ' today' that were held in It is precisely those expectation s, confidently held, w hich a re now reflected in thestocks in existence in the appropriate configuration ' today' .To discuss the effects of change in any element in our story, wemust break between the past and the future and treat ' today' as a gap between the two iunp redeterm ined events may occur. This is necessary to set the analysis in histological, time.There isone point on which all schools of thought can agreethat the actuaof capitalist accumulation goes on through historical time. In spite of this conteeconomic methodology applied to the analysis of the process of accumulation usually mak e a distinction b etween past and future tim e. A case inpoint is the neo'production function' with its treatm ent o f 'malleab le c apita l ' ma de of putty aof production.The 'pseudo-production function' , which emerged in the course of the still-controversy over capital theory, purported to exhibit a numbe r of steady slogical time, with different techno logies. By the very con struction, each such stehad to be independent of the rest. For, as our argument has shown, each had toappropriate stock configuration fully determined by its own past. Consequentcould be no way of moving from one steady state to another without undoing thistories. And, since history is not malleable, there can be no question of movone quantitative stock configuration to another; each configuration entailsindividual history of expectations on which its own particular stock wasThus , the concept of switching techniques with changes in the ra te of profit hunfortunate aberration.Prelude to a critiqueStudents broug ht up on contemporary textbooks may have some difficulty in shearinp- of Sraffa's 'critiaue of economic theory'. Current neoclassical teaching


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Accumulationandexpoitation 111in general equilibrium and'scarce means with alternative uses'. No heavy gunsareneeded to bring that structure down. As Kornai has shown, it fallsapart of its own accordas soon as it is set in historical time (Kornai, 1971 ; also Robinson, 1979). Sraffa'scritique was aimedat adifferent targetthe amorphous moralising Marshallian theoryof'factors ofproduction' receiving "rewards' consonant with their respective productiv-ities. Thisstill underlies much neoclassical doctrine, although nowadays it isnot openlyspelled out.Sraffa shows that theinfluence upon distribution in capitalist industry must bedivided into two separate elements. On the oneside are thetechnical factorstheproductivity of labour and the stock ofmeans ofproduction required to implementit.I n reality, thiswill notbe in apure formas inhis model. I twill generally bea 'job lot',brought into existence bythe evolution oftechnology and accumulation over the moreor lessrecent past. At any moment, the requirements fordepreciation liepartly inthefuture, sothat the relation ofgross tonet output isnot exact. However, byand large,potential productivity is governed by technical factors while thecurrent level ofutilisation depends upon the state ofeffective demand.f

Against this, the share ofwages in netoutput (and therefore thepotential ratioofprofit oncapital) depends upon commercial, social andpolitical influences and thefortunes oftheclass war.

I n principle, agven technical situation iscompatible with any proportion of relativeshares. This rules out the notion of earnings determinedbyproductivity. Now the timegvesitproof, for we can see more or lessthe same technology being used in 'developingas in 'developed' industry with asmall fraction ofthereal-wagerate.

There isno difficulty in releasing thesecond set of influences into historical time;indeed, indescribing the model it washard tohold them back. Weknow somethingabout how the shareofwages inthe value ofnet output isaffected bymonopoly powerand the pricing policy ofcorporations, byparticular scarcities, byeffective demand,bybargaining power and the social and political climate inwhich it operates; and aboutthe 'inflation barrier' which drives moneywagesirresistibly upward when real wagesarepushed too low.

T he first half of the storythe influence of changes in technology ondemand forlabour, on accumulation and oneffective demandhas been very little discussed. Thisis aserious defect in ourtheoretical apparatus, for theevolution of technology is themost important of all aspects ofcapitalist development. Astart on the subject was madein the 1950s (Robinson, 1956), but it wassmothered with neoclassical putty, while theanti-neoclassicals were distracting themselves with reswitching Now it istime to takeup the challenge afresh.Appendx:notes on capitalNote A : stocksand flowsT he problem ofstocks andflowscan besharply visualised byassuming exchange totake place atregular time intervals of, say, periods, while production andconsumption go oncontinuouslythrough time. D ue tocontinuous production andconsumption there is acertain requirement Ntof each commodity i during every time period inthe stationary state. Infamiliar notation:


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112 A. Bhaduriand J . Robinsonwhere XtJ = requirement of commodity iper period in the production of specified amocommoditiesj(j= 1, . . . ,n) per period, and Tt = final demand of commodity i per T herefore, at the end of each exchange unti l the next one, a stock of commodity i, Sbe held in the system, so thatBut since production, likeconsumption, is continuous through time, the flowof productioneach period may be assumed to match exactly requirement of the commodi ty i in a self- restate; i.e. for a commodity i (i = 1, . . . . n) we have:

JV, = Xlwhere Xt is the flowof production of commodity i during a period.U nder these assumptions, from (1) , (2) and (3), the ratio of stockphysical terms for each commodity ican be seen to be uniform; i.e.: to flow of outpu

SJX, = T(i=1, .,)where is defined as the uniform turnover period of the system.Without any loss of generality, we may now choose a convention of reckoning with tsetting = 1. C onsequently, the uniform rate of profit r is defined as a pure number pertime = 1, in accordance with the convention of the model.I n contrast to physical stock, the value of stock held in the production of commodsustain production for a period (when = 1) is gven by:

V, = XJ tPjJ =lwhile the value of the flowof output during the unit period is gven as:

F, = P , X,.T he postulate of uniform rate of profit entails:

ht[Ft-Vt) h(Fj~V)V, V,

where h, = share of profi t in the value added of sector i, defined by the profit margin sepricing policy of commodity i(i = 1, ).I t is evident from (7) that with uniform profit margins, i.e. ( = hj, the ratio of stocks in value terms is also uniform for all commodities; i.e.:V,

Otherwise, as is impl ied by (7), a commodity which has a higher ratio of stock to flow,terms, must correspondingly also have a higher profit margin to equalise the rate of profitdifferent lines of production.I t should be noted that, in the above discussion, the effectivedemand considerations arignored. I t is simply assumed that profit margins are set so as to equalise the rate of profiwhere. But whether, at those resulting prices, the pattern of effective demand issufficabsorb the flowsof output, remains an open question.Mote : treatmentoffixed captal in a stationary stateC onsider a stock of machines of balanced age composition in a stationary state. Each mhaving constant efficiency over its servicelifeof n, periods in sector j earns a constant flowprofit or quasi- rent Q jper period (a one-hoss shay assumption) . Thus, machines are udistributed from age 0 (i.e. a brand new machine) to age (j 1) ( i.e. a machine in its lasof service) with X0J machines of each age. On reaching the n th period, the oldest group of mdisintegrates to be replaced by another XaJ brand new machines to keep the station


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Accumulationand exploitation 113I n this context repacement is apurely physical notion, but depreciation is avalue notion, where

eachmachine in the stock becomes one period older and consequently earns correspondingy lessquasi-rent over its remainingservice life, discountedatthegven rate of profit r. But the assump-tions of the stationary state are such that the value of replacement bybrand new machines, i.e.Rj =POQXQJ , wherepa0 isthe price of abrand new machine, exactly coincides with the valueofdepreciation D3interms of discounted quasi-rent (see Robinson, 1960, pp. 209-221). In order tosee this, consider first the priceofa -period old machineas:

p _ Q.J , . (Li 0. , mTheprice of a brand new machine is obtainedbysetting = 0in (1) to yield:

D epreciation in the valueofa machine as itbecomes one-period older isgven from (1)as:

( ) =H ence the total value ofdepreciation on the balanced stock ofmachinesis:

nj-iD = XQ) (Pot Po,t+i)

t= owhich, inviewof (3) and (2), becomes:

D =X03Pm =Rj (4)showing the exact equality between replacement and depreciation invalue termsin astationarystate.

Thevalue ofthe balanced age composition ofmachinesinsector_; with X0 machinesofeachage isgvenas:n/=lCj = , XojPot = 0

which, inviewof (1) and (2), boils down to:njX0j(Zj =rCj+X0 Pm (5)

or, using (4) in (5):nJXujQj =rCj+Rj=rCj + D. (6)

Equation (5) above could also be writtenas: rPoo rnJ

which inview of (2) boils down to the Kahn-Champernowne formula (Kahn and Champer-nowne, 1953-4, pp. 107-111):

In order to obtain the price equation for the machine sector denoted by subscript 0, we have:


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\t :

114 . BhaduriandJ. Robinsonor, dividing throughout by the annual flowof machinesXo in (2) and using (7), we

Poo=u>


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Accumulationand exploitation 115This short-periodeffectivedemand problem isalsolinked with 'the problem of proportionalities'between the two sectors. In order to see it in simple terms, rewrite (1)as:

7=

P'Xi = s'h' (2)whereXt and Xc are the physical flowsof investment and consumption goodsand P, and /*c arethe respectiveprices. Given amoneywage ratew, we have:

P' =so that (2) becomes, on rearrangement:

If T c andX, represent 'normal capacity outputs', then Xc =q*M^andX% = *M , where yj andq* are annual outputsatnormal capacity per machine inthe consumption and in the investmentsectors andMQ and , are the stocks of machines in those two sectorsrespectively. Thus:

, ' -*'1 -L ^'1 so that the proportion ofmachinestocks in the two sectors at normal capacity utilisation are linked; tothe real wage rate. Therefore, adifferent real wage rate must beassociated with a different1 stock configuration distributed between thesectors at normal capacity utilisation, whileany! abrupt change in the real wage rate will throw these proportions out ofbalance, but may stillsatisfy effective demand considerations in (1) bycapacity utilisation above orbelow the normalrates in the two sectors. This corresponds to asituation of longer term disproportionality in thecapacities of the two sectors infaceof a sudden change in short period distribution resulting fromachange inthe real wage rate.

Bibliography' Clark, J . B. 1891. Distribution asdetermined by the law ofrent, Quarterly JournalofEconomics,> vol. 5, Aprilf Kahn, R. F. and Champernowne, D. G. 1953-4.Thevalueof investedcapital, ReviewofEconomicI StudiesKeynes, J . M. 1936. TheGeneral TheoryofEmpoyment, Interest andMoney, London, MacmillanK ornai, J . 1971. Anti-equilibrium: OnEconomicSystems Theory and the Tasks ofResearch, AmsterdamN orth-H olland,1 N eumann, J . von, 1945. Amodel of general equilibrium, ReviewofEconomic Studies, vol. XI I II Pasinetti, L. L. 1977, On 'non-substitution' inproduction models, Cambridge JournalofEconomics,I DecemberPigou, A. C 1932. TheEconomicsofWelfare, 4th edition, London, Macmillan, ChapterXI

Robinson, J . V. 1956. TheAccumulation ofCaptal, London, MacmillanRobinson, J . V. 1960. ColectedEconomicPapers, vol. I I , Oxford, Basil Blackwellj Robinson, J . V. 1978. The organic composition of capital, Kyklos, vol.31Robinson, J . V. 1979. History versusequilibrium, inColectedEconomicPapers, vol. V, Oxford, BasiBlackwellSraffa, P. 1960. ProductionofCommoditiesby Means ofCommodities, Cambridge, CUPSteedman, I . 1877. Marx after Sraffa, London, New Left BooksWeizsacker, C. C. von 1973. Modern capital theory and the conceptofexploitation, Kyklos, vol.26

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Marx Sraffa Kalecki_CJE 1980