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Bhaduri, A., & Robinson, J. (1980). Accumulation and Exploitation an Analysis in the Tradition of Marx, Sraffa and Kalecki. Cambridge Journal of Economics
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Cambridge Journal of Economics 1980, 4, 103-115 Accumulation and exploitation: an analysis in the tradition of Marx, Srafla and Kalecki Amit Bhaduri and Joan Robinson* Piero Sraffa was completely successful in his aim of providing a basis for the critique of neoclassical theory but the model in Production of Commodities by Means of Commodities (1960) provides a very narrow basis for constructive analysis. The model presents a strictly one-technique economy. In the system of equations, each input used up in one period is replaced in kind as production goes on. This entails that the same technique is going to be used in the next period. In itself, this is a merit of the construction, but it needs to be emphasised; Sraffa himself blurs the point by introducing changes into his self-repeating story.f The characterisation of a technique has two elements—the engineering specification of the physical input-output equations and the pattern of applications of labour through time. In Sraffa's story, in Part I, the reproduction of the system takes place in a single period; the turnover of each commodity takes the same time. Thus, in the production of each commodity, the stock in existence at a moment of time, in the pipelines of pro- duction, is the same multiple of its flow of output. The rate of profit is expressed as a percentage per period. % (When fixed capital is introduced in Part II, time patterns are more varied. § Here both types are treated together.) There is no discussion of the realisation of surplus as profit. It is merely taken for granted that whatever is produced is disposed of at such prices as to result in a uniform rate of profits in all lines of production. Finally, the determination of the distribution of net output between wages and net profit is left completely open (apart from the inexplicable suggestion that the rate of profit on capital might be governed by the rate of interest). In this sense, Sraffa presents a scheme more fruitful than Ricardo's. Since it does not specify the real wage, it presents a challenge to attempt to diagnose what forces do determine the distribution of income between profits arid wages. Ian 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 to have ful] information in physical terms (including the real wage), there is no advantage in intro- ducing value as a unit of measurement. But in his own argument, he follows Ricardo in making the real wage a given basket of specified wage goods, which are therefore basics in the system. This entails the determination of distribution from the technical data, • Centre for Economic Studies, Jawaharial Nehru University, New Delhi, and University of Cambridge. t See for example Srafla (1960), p. 86. * See Nott A of the Appendix. § See Mote B of the Appendix. 03O9-166X/80/020103 + 1 3 $02.00/0 © 1980 Academic Press Inc. (London) Limited
Transcript

Cambridge Journal of Economics 1980, 4, 103-115

Accumulation and exploitation: an analysisin the tradition of Marx, Srafla and Kalecki

Amit Bhaduri and Joan Robinson*

Piero Sraffa was completely successful in his aim of providing a basis for the critique ofneoclassical theory but the model in Production of Commodities by Means of Commodities(1960) provides a very narrow basis for constructive analysis.

The model presents a strictly one-technique economy. In the system of equations,each input used up in one period is replaced in kind as production goes on. This entailsthat the same technique is going to be used in the next period. In itself, this is a merit ofthe construction, but it needs to be emphasised; Sraffa himself blurs the point byintroducing changes into his self-repeating story.f

The characterisation of a technique has two elements—the engineering specification ofthe physical input-output equations and the pattern of applications of labour throughtime. In Sraffa's story, in Part I, the reproduction of the system takes place in a singleperiod; the turnover of each commodity takes the same time. Thus, in the production ofeach commodity, the stock in existence at a moment of time, in the pipelines of pro-duction, is the same multiple of its flow of output. The rate of profit is expressed as apercentage per period.% (When fixed capital is introduced in Part II, time patterns aremore varied. § Here both types are treated together.)

There is no discussion of the realisation of surplus as profit. It is merely taken forgranted that whatever is produced is disposed of at such prices as to result in a uniformrate of profits in all lines of production.

Finally, the determination of the distribution of net output between wages and netprofit is left completely open (apart from the inexplicable suggestion that the rate ofprofit 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 arid wages.

Ian 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 to have ful]information in physical terms (including the real wage), there is no advantage in intro-ducing value as a unit of measurement. But in his own argument, he follows Ricardo inmaking the real wage a given basket of specified wage goods, which are therefore basicsin the system. This entails the determination of distribution from the technical data,

• Centre for Economic Studies, Jawaharial Nehru University, New Delhi, and University of Cambridge.t See for example Srafla (1960), p. 86.* See Nott A of the Appendix.§ See Mote B of the Appendix.

03O9-166X/80/020103 + 1 3 $02.00/0 © 1980 Academic Press Inc. (London) Limited

104 A, Bhadarl and J. Robinson

leaving no room for class conflict, and it does not touch on the question of realisation.fPresumably, to complete this story, we must suppose that a capitalist uses part of netprofit for consumption and invests the rest, each in his own business. Here we are ina pre-Keynesian setting where savings govern accumulation and there is no discussion ofwhat form investment takes, or how it could result in a feasible rate of growth of thesystem, unless in a one-commodity economy.

To avoid these objections, we present a 'Sraffaesque' model, or rather a family ofmodels, including distribution according to Marx and realisation according to Kalecki.

Our method is to elaborate Sraffa's model, first dealing with one problem at a timeand then recombining them. Like his, our models depict a two-class society in a 'pure'capitalist economy, without foreign trade or taxation. For the most part, the argumentis conducted in terms of a one-technique system with long-run normal prices — thusit is a set of highly abstract intellectual experiments. It is intended, however, to clear thelogical ground for a discussion of real issues involved in the analysis of capitalistaccumulation.

A stationary state

Sraffa did not need to ask whether his system was growing or not. Net output may ormay not include some physical items to be added to stock, and the workers receive ashare in the value of net output, not a supply of specific wage goods. Here our systemis a modification of his. We make a physical distinction between means of production,which are basics in Sraffa's sense, each entering directly or indirectly into the output ofall commodities, and consumption goods, which are non-basic.

We first consider simple reproduction (a stationary state). This means that there is aconstant labour force, working standard hours per day and per year and a stock ofmeans of production which is being kept intact by continual replacements of items asthey are used up, while the whole flow of net output is being consumed. The notion of acapitalist economy dwelling contentedly in a self-perpetuating stationary state isevidently artificial. The assumption of stationariness is here introduced provisionally inorder to separate out for analysis the time-pattern aspect of the stock of means ofproduction required for a given technique.

The quantity of each item in the stock depends on the amount of it required in thegeneral flow of production and on its turnover period. + For a type of machine that, say,takes one year to build and has ten years of life at full efficiency (a one-hoss shay), anannual output of a single machine maintains a stock of 10 machines of ages zero to ten.Each year one falls out of use. The production of one machine per year keeps the stockof balanced age composition in being. Along with each item of long-lived equipmentthere is a stock of working capital corresponding to the short-period throughput ofproduction with that equipment.

t Was Marx a neo-Ricardian ? Marx argued that labour power is sold as a commodity and that allcommoditia exchange at their values. The value of labour power is a real wage sufficient to maintain thecustomary standard of life. If the value of labour power remains constant through time, then distributionis determined by technology as Ricardo believed. But if real-wage rates can rise or fall under the influenceof changes in productivity and the balance of power in society, as Marx clearly contemplated that theywould, then the value of labour power is an unnecessary and misleading concept. Sraffa is certainly not aneo-Ricardian in this sense, but he has never gone into the question of the realisation of physical surplus asprofits, leaving his logical scheme open-ended with one degree of freedom in the system of equations.

t For a formal statement of the following argument tee Mote A of the Appendix.

Accumulation and exploitation 105

The length of the period of turnover of the self-reproducing state is the least commonmultiple of the turnover period of all the items. The stock of each item is then repre-sented by the amount of labour time directly and indirectly required to produce it andthe time pattern in which the labour was applied. In the stationary state, the wholelabour force maintains the whole basic stock (and also produces a flow of non-basics forconsumption) but, by the method of sub-systems, the labour embodied in each particularitem can be distinguished from the rest.f

It is to be observed that stocks of animal and vegetable products can have been builtup in this way, but minerals (including coal and oil) are not replaced but taken fromthe earth's crust and dissipated into the air or crumbled into the ground. In contrast,there are installations, such as hydro-electric stations, which required a large invest-ment 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 production already in existence in the correctproportions, because the same technique is assumed to have been in use ever since timebegan.

The question was raised by Keynes on an early draft of the book as to whether 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 is appropriate to one flowof work being performed with one technique. A differently 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 stationary 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 manner in which a new stock is built 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 profits

Sraffa set out to provide the basis for a critique of the economic theory that was prevalentwhen he began work in the 1920s, before the first rumbles of the Keynesian revolutionhad been heard. The dominant theory of distribution was that of Alfred Marshallvulgarised by J. B. Clark (1891):

What a social class gets is, under natural law, what it contributes to the general output of industry.

f This point is drastically simplified in Robinson (1978). The simplification was made in order to meetthe Marxian argument on its own terms.

X For his treatment of fixed capital, see Note B of the Appendix.

106 A. Bhadnri and J. Robinson

Sraffa opposed to this the argument that, with a given flow of production defined inphysical terms, the share of real wages in physical net output may, in principle, beanything between unity and zero with the corresponding rates of profit between zeroand the physically possible maximum.

Given the physical specification of the model, a particular rate of profit, uniformthroughout the economy, entails a particular pattern of prices for all the items in theflow of production (including non-basics) and for the stocks of inputs, and a pattern ofthe ratios of gross profit to wages in each industry.

Sraffa's argument was largely concerned with the construction of a numeraire inphysical terms—the standard commodity. It seems equally satisfactory to use as numer-aire ihe labour time performed by a representative worker, say over a week. We canpostulate an arbitrary money-wage rate per man-week, say $10, and specify all therelationships within the system in terms of dollars. We then have a wage bill, say perannum, as a flow of dollars, independent of the rate of profit. Corresponding to anygiven rate of profit (with its appropriate pattern of prices and gross margins) there is aparticular flow of net profits in dollars received by capitalists.

Comparing a higher with a lower rate of profit, the pattern of prices may be widelydifferent but the overall level of prices must be higher and the real-wage rate lower.

It seems appropriate to express the ratio of the flow of net profits to the wage bill asthe rate of exploitation. (Marx defined this in terms of labour values; here we aretranslating into a system of prices of production.)

The rate, or better the ratio, of exploitation is not determined by the technicalspecification of the system. It is an independent element in the situation which may beexplained by the fortunes of the class war. This freedom of the distribution parameterenabled Sraffa to break out of the 'iron-law of real wages'. He was himself somewhatreluctant to make such a departure from classical traditions but for us it is this liberationthat enables us to integrate the problem of realisation into our analysis.

In the formal model there is no causality. The rate of profit entails and is entailed bythe ratio of exploitation whatever it may be. But when we want to step down from themodel into an interpretation of reality we have to consider which determines which.It is certainly easier to do the sums if we start from a given rate of profits, but Marx'sinstinct was correct; the causal factor is the share of profit from which the uniform ratecan be derived only as a postulate of the long-run normal configuration of prices.

A variety of non-basics

To concentrate upon the main argument, we have so far said nothing about the physicalnature of the output of non-basics. We now introduce into the model the fact thatrentiers and workers consume different physical baskets of non-basics—luxuries andwage goods. (There may be some items in common but in different quantities; thus theluxury basket contains less bread than the wage-good basket, and more whisky.) Thevalue of the flow of luxuries in dollars is equal to the flow of rentier income, and thevalue of wage goods is equal to the wage bill. This requires a somewhat different basicstock of means of production for each ratio of exploitation; the main bulk of the stock isnot affected but there must be appropriate productive capacity for the flow of output ofthe physically different non-basics.

Now we come to a puzzle. The ratio of exploitation is logically prior to the flows ofluxuries and wage goods, yet the stocks to produce them must already be in place.

Accumulation and exploitation 107

The Marxists have long recognised this problem as the 'crisis of proportionality'—toeach given real wage rate must correspond a certain division of productive capacitybetween the investment sector and the consumption-goods sector. To a different real wagerate, entailing a different ratio of exploitation, must correspond a different proportionbetween sectors, while a sudden change in the real wage rate would throw the propor-tions in the stock out of line with the flows of production.

The answer is that, when the stocks are in balance with outputs, it must be supposedthat the investment in the two stocks was made in the light of correct expectations of thereturns to be enjoyed on each.

A uniform rate of profit can be imposed upon a set of prices by an economist describinghis 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.

It is sometimes objected that expectations introduce an illegitimate subjective elementinto analysis, but the subjective expectations held in the past are manifest in theobjective stocks in existence today. Not to recognise stocks explicitly is then tantamountto ignoring the importance of expectations—correctly or falsely held—as an essentialcharacteristic of time in the analysis.

The same consideration applies to the formation of prices. When a uniform rate ofprofit rules, gross profit margins (the excess of proceeds over prime costs) for baskets ofnon-basics are determined. A product which requires a higher capital to output ratiohas correspondingly higher gross margins at any given level of the rate of profit. Eachtype of product in the flow of output requires a certain rate of gross investment to keepits stock intact and a certain allowance of net profit to yield the given rate of profit on thevalue of its stock of long-lived and short-lived basics, which we may now describe as itscapital. 'Capital' is thus seen as a two-edged concept, in the tradition of Marx, involvingboth the physical aspect of means of production and property rights which give rise toprofit as the source of capitalists' income.

Now, in industry, prices have to be set in advance of sales. The level of unit costs, withlong-lived equipment, depends on its level of utilisation. Gross margins in each line arefixed in such a way as to cover costs and yield a 'subjective-normal' rate of net profitat a standard level of utilisation of capacity. The ex-post rate of profits for each will benormal when the standard rate of output is realised. If actual output were higher thanstandard, profits would be more than normal, and vice versa.

Our earlier puzzle—the proportionality crisis revisited in the form of the question ofhow stocks can be exactly right to fit with whatever may be the distribution of income—is 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 to guess whatthey 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 are left in theair.

108 A. Bhaduri and J. Robinson

Changing exploitation

In a steady state, with confident expectations, the ratio of exploitation is, so to say,built into the stock of basics. A change from one ratio of exploitation to another wouldrequire an appropriate adaptation in the stock.

A rise in the exploitation ratio might come about from an increase in monopolypower and weakening of trade union resistance, causing a rise in profit margins and anincrease in distribution to rentiers. This generates a rise in expenditure on luxuries,which may run them up to full capacity and raise their profitability all the more. A fallin the consumption of wage goods checks and may even reverse the increase in the flowof profits in that sector.

Suppose that there has been a once and for all change and that the new situation lasts,and is expected to last, indefinitely so that there is now a new state of long-termexpectations. We can trace a traverse with gross investment below replacement in thewage-good industries and above it in luxury industries until the rate of profit has beenequalised between the sectors, at a new higher level, and the composition of the stock ofbasics has been readjusted accordingly.

A fall in the exploitation ratio might be caused by a growth of trade union strengthcombined with more intense competition among capitalists that prevents them frompassing raised money-wage costs fully into prices. Now the flow of profits has beenreduced in both sectors.

Technical conditions do not exclude a traverse to a lower rate of profit, the mirrorimage of the above, for as Keynes (1936, p. 374) observed, there is no reason why thegame should not be played for lower stakes once the players are used to them. Butthe experience of a fall in net proceeds from one quarter to the next may have giventhe capitalists a shock. They jib at maintaining the former rate of gross investment. Anincrease in capacity for wage goods fails to balance a decline in that for luxuries so thatthe total stock of basics is allowed to shrink, and the full-capacity level of employment isreduced. Thus the neoclassical dictum that high wages reduce employment may turnout to be true for quite un-neoclassical reasons: the capitalists' reaction, in terms of thevolume and composition of investment, to a lower ratio of exploitation may lead thecourse of the traverse to a new stock configuration appropriate to a permanently lowerlevel of output and employment.

Accumulation without rentier consumptionWe now introduce a model in which there is no consumption out of profits, but netinvestment is going on. There is a growth rate which is given by the overall ratio of thevalue of the flow of net investment to the value of the stock. In this case, since we are ina one-technique economy, employment must be growing in step with the growth rate.The analysis is familiar (von Neumann, 1945). We need only remark that the growthrate must have been built into the system from the first; a single technique is beingreproduced on an ever-widening base. Thus economies of scale are here ruled out.

When the growth rate is given, the corresponding ratio of exploitation is determined,but it is not true that the exploitation ratio, by itself, determines the rate of growth. Theratio determines the potential surplus of the system, but investment decisions by activecapitalists are needed to turn the surplus into profit. Professor von Weizsacker (1973)has argued that there can be no exploitation in such a case because the entire profit isneeded to finance accumulation. But he failed to observe that realisation of surplus as

Accumulation and exploitation 109

profits is possible only through accumulation, which capitalists arbitrarily decide uponin their own interests, without consulting workers. Thus the workers' share in netoutput is still governed by the ratio of exploitation, while accumulation (without the aidof capitalists' consumption) turns the potential share of the capitalists, set by the ratioof exploitation, into the corresponding rate of profit by creating enough effectivedemand to realise it. It is to be observed that we are here comparing different growthrates with a single technology. When actual capitalist economies are compared, it oftenhappens that the one with a higher growth rate uses superior techniques and has ahigher rate of innovation so that faster growth is associated with higher rather thanlower real wages in a particular phase of development.

The general model

When we combine growth with rentier consumption, net output consists of net additionsto the stock of basics plus the flow of non-basics. The flow of output contains threephysical elements, the complex of basics (replacement and additions) and the baskets ofluxuries and of wage goods.

The flow of realised net profits is now 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 by working class resistance.

In the former model, the rentiers simply spent whatever profits they received. If theyalso have a propensity to save, then: C = a + (l —s) D, where C is the flow of rentierconsumption and D distributed profits. The savings of the rentiers are lent to thecapitalists to finance investment. Now, if each capitalist financed the whole of hisgross investment out of gross profits, he would automatically be financing net invest-ment out of net profit. There could not then be any savings by rentiers. If rentiersfail to spend part of the distributed profits that they receive, profits are realised on areduced scale and distributions are correspondingly lower. Rentier income then couldnot rise above the constant, a in the above equation, which is all consumed.

When investment exceeds retentions, rentiers' income exceeds expenditure forconsumption and their savings are exactly what is required to finance the excess ofinvestment over retained profits.

The Anglo-Italian formula, n = glsp (the rate of profits, on a steady growth path, isequal to the rate of growth divided by saving out of profits) is formally correct whenthere is no saving except out of profits, but it obscures the mechanism of the financialsystem by failing to distinguish between saving out of profits in the form of retentions andsaving out of rentier income.

The foregoing argument shows that to postulate a given physical real wage in advancewould require the rest of the model to be draped around it so that technical conditions,the ratio of exploitation, the realisation of the potential surplus and the rate of profits areall consistent with it. Starting from the other end, we find that the level of real wages in aparticular economy depends, first of all, on technical conditions and the stocks of meansof production in existence, which determine the net output that the system can yield in

•f Saving out of earned income may be treated as saving to spend later. Workers may lend and borrowamong themselves without providing any finance to the capitalists through the banking system.

110 A. Bhmdori and J. Robinson

a self-reproducing state. Secondly, it depends upon the share of profits in net output,which is governed by the rate of accumulation and of non-wage consumption, subjectto the limit on the ratio of exploitation permitted by social conditions.

On this view, capitalists, in the various sectors of industry, set their selling prices inrelation to costs, according to various profit-seeking strategies. The interaction amongthem establishes the 'degree of monopoly', that is, the overall mark-up on the total wagebill. But until flows of output of commodities are sold at those prices in the market, themark-up over the wage bill remains only a. potential surplus. Investment and consumptionexpenditure by the capitalists determines how much of this potential surplus is realisedas actual profits.

This is as far as a one-technique model will take us. A one-technique economy is notto be found in the history of capitalism, for accumulation is always accompanied byinnovations and at any moment the stock of means of production in existence is mainlycomposed of fossils from earlier phases of technical development while current grossinvestment is installing the latest types of equipment. To set the model in historicaltime, we must take account of change.

Out of the strait-jacketIn a steady state all events are predetermined. Anything that happens 'today' is fullydetermined by the past, including expectations about 'today' that were held in the past.It is precisely those expectations, confidently held, which are now reflected in the variousstocks in existence in the appropriate configuration 'today'.

To discuss the effects of change in any element in our story, we must break this linkbetween the past and the future and treat 'today' as a gap between the two in whichunpredetermined events may occur. This is necessary to set the analysis in historical, notlogical, time.

There is one point on which all schools of thought can agree—that the actual processof capitalist accumulation goes on through historical time. In spite of this contemporaryeconomic methodology applied to the analysis of the process of accumulation does notusually make a distinction between past and future time. A case in point is the neoclassical'production function' with its treatment of'malleable capital' made of putty as a factorof production.

The 'pseudo-production function', which emerged in the course of the still-unsettledcontroversy over capital theory, purported to exhibit a number of steady states, inlogical time, with different technologies. By the very construction, each such steady statehad to be independent of the rest. For, as our argument has shown, each had to have itsappropriate stock configuration fully determined by its own past. Consequently, therecould be no way of moving from one steady state to another without undoing their pasthistories. And, since history is not malleable, there can be no question of moving fromone quantitative stock configuration to another; each configuration entails its ownindividual history of expectations on which its own particular stock was built up.Thus, the concept of sxvitching techniques with changes in the rate of profit has been anunfortunate aberration.

Prelude to a critiqueStudents brought up on contemporary textbooks may have some difficulty in seeing thebearing of Sraffa's 'critique of economic theory'. Current neoclassical teaching is rooted

Accumulation and exploitation 111

in general equilibrium and 'scarce means with alternative uses'. No heavy guns areneeded to bring that structure down. As Kornai has shown, it falls apart of its own accordas soon as it is set in historical time (Kornai, 1971; also Robinson, 1979). Sraffa'scritique was aimed at a different target—the amorphous moralising Marshallian theoryof 'factors of production' receiving 'rewards' consonant with their respective productiv-ities. This still underlies much neoclassical doctrine, although nowadays it is not openlyspelled out.

Sraffa shows that the influence upon distribution in capitalist industry must bedivided into two separate elements. On the one side are the technical factors—theproductivity of labour and the stock of means of production required to implement it.In reality, this will not be in a pure form as in his model. It will generally be a 'job lot',brought into existence by the evolution of technology and accumulation over the moreor less recent past. At any moment, the requirements for depreciation lie partly in thefuture, so that the relation of gross to net output is not exact. However, by and large,potential productivity is governed by technical factors while the current level ofutilisation depends upon the state of effective demand.f

Against this, the share of wages in net output (and therefore the potential ratio ofprofit on capital) depends upon commercial, social and political influences and thefortunes of the class war.

In principle, a given technical situation is compatible with any proportion of relativeshares. This rules out the notion of earnings determined by productivity. Now the timegives it proof, for we can see more or less the same technology being used in 'developing'as in 'developed' industry with a small fraction of the real-wage rate.

There is no difficulty in releasing the second set of influences into historical time;indeed, in describing the model it was hard to hold them back. We know somethingabout how the share of wages in the value of net output is affected by monopoly powerand the pricing policy of corporations, by particular scarcities, by effective demand, bybargaining power and the social and political climate in which it operates; and aboutthe 'inflation barrier' which drives money wages irresistibly upward when real wages arepushed too low.

The first half of the story—the influence of changes in technology on demand forlabour, on accumulation and on effective demand—has been very little discussed. Thisis a serious defect in our theoretical apparatus, for the evolution of technology is themost important of all aspects of capitalist development. A start on the subject was madein the 1950s (Robinson, 1956), but it was smothered with neoclassical putty, while theanti-neoclassicals were distracting themselves with reswitching. Now it is time to takeup the challenge afresh.

Appendix: notes on capital

Note A: stocks and flowsThe problem of stocks and flows can be sharply visualised by assuming exchange to take place atregular time intervals of, say, T periods, while production and consumption go on continuouslythrough time. Due to continuous production and consumption there is a certain requirement Niof each commodity i during every time period in the stationary state. In familiar notation:

N, = Z X,j+r, (1)

t See Nott C of the Appendix.

112 A. Bhaduri and J. Robinson

where XtJ = requirement of commodity i per period in the production of specified amounts ofcommodities jf (j = 1, . . . , n) per period, and T, = final demand of commodity i per period.

Therefore, at the end of each exchange until the next one, a stock of commodity i, S(, mustbe held in the system, so that

S, = TN,. (2)

But since production, like consumption, is continuous through time, the flow of production duringeach period may be assumed to match exactly requirement of the commodity j in a self-replacingstate; i.e. for a commodity i (i = 1, . . . . n) we have:

JV« = X, (3)

where X, is the flow of production of commodity i during a period.Under these assumptions, from (1), (2) and (3), the ratio of stock S, to flow of output Xt in

physical terms for each commodity i can be seen to be uniform; i.e.:

= T(i=l, ,n) (4)

where T is defined as the uniform turnover period of the system.Without any loss of generality, we may now choose a convention of reckoning with time by

setting T = 1. Consequently, the uniform rate of profit r is defined as a pure number per unit ofrime T = 1, in accordance with the convention of the model.

In contrast to physical stock, the value of stock held in the production of commodity t tosustain production for a period (when T = 1) is given by:

V, = i XJ,PJ (5)

while the value of the flow of output during the unit period is given as:

Ft = P, X,. (6)

The postulate of uniform rate of profit entails:

h,(F,-Vt) hj(Fj-Vj)

V,(7)

where h, = share of profit in the value added of sector i, defined by the profit margin set in thepricing policy of commodity i {i = 1, n).

It is evident from (7) that with uniform profit margins, i.e. A( = hj, the ratio of stocks to flowsin value terms is also uniform for all commodities; i.e.:

j-r = ^,i£h,=hj. (8)

Otherwise, as is implied by (7), a commodity which has a higher ratio of stock to flow, in valueterms, must correspondingly also have a higher profit margin to equalise the rate of profit amongdifferent lines of production.

It should be noted that, in the above discussion, the effective demand considerations are totallyignored. It is simply assumed that profit margins are set so as to equalise the rate of profit every-where. But whether, at those resulting prices, the pattern of effective demand is sufficient toabsorb the flows of output, remains an open question.

Note B: treatment of fixed capital in a stationary stateConsider a stock of machines of balanced age composition in a stationary state. Each machinehaving constant efficiency over its service life of rij periods in sector_; cams a constant flow of grossprofit or quasi-rent Qjper period (a one-hoss shay assumption). Thus, machines are uniformlydistributed from age 0 (i.e. a brand new machine) to age (itj — 1) (i.e. a machine in its last periodof service) with X^j machines of each age. On reaching the n,th period, the oldest group of machinesdisintegrates to be replaced by another X^t brand new machines to keep the stationary agecomposition intact over time.

Accumulation and fxp1o<tatlon 113

In this context replacement is a purely physical notion, but depredation is a value notion, whereeach machine in the stock becomes one period older and consequently earns correspondingly lessquasi-rent over its remaining service life, discounted at the given rate of profit r. But the assump-tions of the stationary state are such that the value of replacement by brand new machines, i.e.Rj — pmX<,j, where fa is the price of a brand new machine, exactly coincides with the value ofdepreciation Dj in terms of discounted quasi-rent (see Robinson, 1960, pp. 209-221). In order tosee this, consider first the price of a /-period old machine as:

P =

The price of a brand new machine is obtained by setting / = 0 in (1) to yield:

Depreciation in the value of a machine as it becomes one-period older is given from (1) as:

Hence the total value of depreciation on the balanced stock of machines is:

DJ = XV " z 1 (P.t - J>...+i)t - o

which, in view of (3) and (2), becomes:

D} = XojPn = Rj (4)

showing the exact equality between replacement and depreciation in value terms in a stationarystate.

The value of the balanced age composition of machines in sector j with X0J machines of eachage is given as:

»j.i

Cj = E XUPUr-o

which, in view of (1) and (2), boils down to:

n, X,j Q_} = rCj+Xtj Pw (5)

or, using (4) in (5):

"j X°J 0.1 = rCj+Rj = rCj+Dj. (6)

Equation (5) above could also be written as:

Cj 0+ }

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

_ f (1+r)* 1

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

r) £ X.oP.+rC+J^P^ (8)

114 A. Bhadari and J. Robinson

or, dividing throughout by the annual flow of machines X,, in (2) and using (7), we obtain:

Solving for die price of a brand new machine from (9) in terms of other prices Pt{i = 1, . . . . , n),w, r and n, we obtain:

The price of any commodity j (j = 1, . . . , n) is given in accordance with (9) as:

or, using (10) in (11) and simplifying, we obtain:

= w{lj+kjk)+(\+r) i (ou+kja,,) P, (12)i-i

where:

Equation (12) can be rewritten in the matrix notation as:

P = wl+(l+r)A'P

where the elements of vector / and matrix A correspond to (Ij+kji,,) and {att-\-kjatJ) respectivelyfrom which, in principle, reduction to 'dated labour' in die form

P = [ / - (

= [I+(l+r)A'+(l+r)'A"+ . . . .] wl

is possible, provided such a series is convergent, t

NoUC: the short periodTo focus sharply on the short period problem, consider an economy widi two vertically integrateddepartments: department 1 producing investment goods and department 2 producing consump-tion goods. All wages are consumed and a constant fraction s, of profits is saved. Assuming A, andhc to be the profit margins in the two departments respectively, the savings investment equalityyields:

/ = , , (A./+A.C)

o r ( l - i / , ) / = j^cC. (1)

It is worth pausing on equation (1) for a moment: die bracketed term on the left-hand side showsthe demand generated for consumption goods per unit of value added by the investment sectorand consists of (1 — A() as consumption demand out of wages plus (1 — sr) h, as consumption demandout of profits; similarly, the coefficient sjiz on the right-hand side is die surplus available per unitof value added in the consumption sector to meet demand of the investment sector. Therefore,equation (I) balances demand for consumption goods over and above all consumption in thatsector. The theory of effective demand, especially as formulated by KalecM, is essentially basedupon the idea diat given investment / , die degree of capacity utilisation in the consumption sectoris determined by (1) provided sr, h, and Ac are constants.

t The convergence properties are not discussed here, but have been examined in an as yet unpublishednote by Ajit K. Biswas of the Indian Statistical Institute, Calcutta.

Accumulation and exploitation 115

This short-period effective demand problem is also linked with 'the problem of proportionalities'between the two sectors. In order to see it in simple terms, rewrite (1) as:

/ P,X, sjta ( 2 )

L re A.c (I —Sfhi)

where X, and Xc are the physical flows of investment and consumption goods and Pt and Pc arethe respective prices. Given a money wage rate w, we have:

so that (2) becomes, on rearrangement:

If Xc and X, represent 'normal capacity outputs', then Xc = q*Mc and X, = q*M, where <; J andq* are annual outputs at normal capacity per machine in the consumption and in the investmentsectors and MQ and M, are the stocks of machines in those two sectors respectively. Thus:

W_ = [M.\ q*sMl-h,) ...Pe \MtJ qW-sM K '

so that the proportion of machine stocks in the two sectors at normal capacity utilisation are linkedto the real wage rate. Therefore, a different real wage rate must be associated with a differentstock configuration distributed between the sectors at normal capacity utilisation, while anyabrupt change in the real wage rate will throw these proportions out of balance, but may stillsatisfy effective demand considerations in (1) by capacity utilisation above or below the normalrates in the two sectors. This corresponds to a situation of longer term disproportionality in thecapacities of the two sectors in face of a sudden change in short period distribution resulting from achange in the real wage rate.

Bibliography

Clark, J. B. 1891. Distribution as determined by the law of rent, Quarterly Journal of Economics,vol. 5, April

Kahn, R. F. and Champemowne, D. G. 1953-4. The value of invested capital, Review of EconomicStudies

Keynes, J. M. 1936. The General Theory of Employment, Interest and Money, London, MacmillanKomai, J . 1971. Anti-equilibrium: On Economic Systems Theory and the Tasks of Research, Amsterdam,

North-HollandNeumann, J. von, 1945. A model of general equilibrium, Review of Economic Studies, vol. XIIIPasinetti, L. L. 1977. On 'non-substitution' in production models, Cambridge Journal of Economics,

DecemberPigou, A. C. 1932. The Economics of Welfare, 4th edition, London, Macmillan, Chapter XIRobinson, J. V. 1956. The Accumulation of Capital, London, MacmillanRobinson, J. V. 1960. Collected Economic Papers, vol. II, Oxford, Basil BlackwellRobinson, J. V. 1978. The organic composition of capital, Kyklos, vol. 31Robinson, J. V. 1979. History versus equilibrium, in Collected Economic Papers, vol. V, Oxford, Basil

BlackwellSraffa, P. 1960. Production of Commodities by Means of Commodities, Cambridge, CUPSteedman, I. 1877. Marx after Sraffa, London, New Left BooksWeizsacker, C. C. von 1973. Modern capital theory and the concept of exploitation, Kyklos, vol.

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