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October 02 , 2010

The Accumulation of Capital


Academic economists have recently returned from the elaboration of static equilibrium to the classical search for a dynamic model of a developing economy. Rosa Luxemburg, neglected by Marxist and academic economists alike, offers a theory of the dynamic development of capitalism which is of the greatest interest. The book is one of considerable difficulty (apart from the vivid historical chapters), and to those accustomed only to academic analysis the difficulty is rendered well-nigh insurmountable by the Marxist terminology in which it is expressed. The purpose of this preface is to provide a glossary of terms, and to search for the main thread of the argument (leaving the historical illustrations to speak for themselves) and set it out in simpler language.

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The result is no doubt too simple. The reader must sample for himself the rich confusion in which the central core of analysis is imbedded, and must judge for himself whether the core has been mishandled in the process of digging it out.[1]

Our author takes her departure from the numerical examples for simple reproduction (production with a constant stock of capital) and expanded reproduction (production with capital accumulating) set out in volume ii of Marx’s Capital. As she points out,[2] Marx completed the model for simple reproduction, but the models for accumulation were left at his death in a chaos of notes, and they are not really fit to bear all the weight she puts on them (Heaven help us if posterity is to pore over all the backs of old envelopes on which economists have jotted down numerical examples in working out a piece of analysis). To follow her line of thought, however, it is necessary to examine her version of Marx’s models closely, to see on what assumptions they are based (explicitly or unconsciously) and to search the assumptions for clues to the succeeding analysis.

To begin at the beginning—gross national income (for a closed economy) for, say, a year, is written c + v + s; that is, constant [Pg 14]capital, variable capital and surplus. Variable capital, v, is the annual wages bill. Surplus, s, is annual rent, interest, and net profit, so that v + s represents net national income. (In this introduction surplus is used interchangeably with rent, interest and net profit.) Constant capital, c, represents at the same time the contribution which materials and capital equipment make to annual output, and the cost of maintaining the stock of physical capital in existence at the beginning of the year. When all commodities are selling at normal prices, these two quantities are equal (normal prices are tacitly assumed always to rule,[3] an assumption which is useful for long-period problems, though treacherous when we have to deal with slumps and crises). Gross receipts equal to c + v + s pass through the hands of the capitalists during the year, of which they use an amount, c, to replace physical capital used up during the year, so that c represents costs of raw materials and wear and tear and amortisation of plant. An amount, v, is paid to workers and is consumed by them (saving by workers is regarded as negligible[4] ). The surplus, s, remains to the capitalists for their own consumption and for net saving. The professional classes (civil servants, priests, prostitutes, etc.) are treated as hangers-on of the capitalists, and their incomes do not appear, as they are not regarded as producing value.[5] Expenditure upon them tends to lessen the saving of capitalists, and their own expenditure and saving are treated as expenditure and saving out of surplus.

In the model set out in chapter vi there is no technical progress (this is a drastic simplification made deliberately[6] ) and the ratio of capital to labour is constant (as the stock of capital increases employment increases in proportion). Thus real output per worker employed is constant (hours of work per year do not vary) and real wages per man are constant. It follows that real surplus per man is also constant. So long as these assumptions are retained Marxian value presents no problem. Value is the product of labour-time. Value created per man-year is constant because hours of work are constant. Real product per man year being constant, on the above assumptions, the value of a unit of product is constant. For convenience we may assume money wages per man constant. Then, on these assumptions, [Pg 15]both the money price of a unit of output and the value of a unit of money are constant. This of course merely plasters over all the problems of measurement connected with the use of index numbers, but provided that the technique of production is unchanging, and normal prices are ruling, those problems are not serious, and we can conduct the analysis in terms of money values.[7] (Rosa Luxemburg regards it as a matter of indifference whether we calculate in money or in value.[8] )

The assumption of constant real wages presents a difficulty which we may notice in passing. The operation of the capitalist system is presumed to depress the level of wages down to the limit set by the minimum subsistence of the worker and his family. But how large a family? It would be an extraordinary fluke if the average size of family supported by the given wage of a worker were such as to provide for a rate of growth of population exactly adjusted to the rate of accumulation of capital, and she certainly does not hold that this is the case.[9] There is a reserve army of labour standing by, ready to take employment when the capitalists offer it. While they are unemployed the workers have no source of income, but are kept alive by sharing in the consumption of the wages of friends and relations who are in work.[10] When an increase in the stock of capital takes place, more workers begin to earn wages, those formerly employed are relieved of the burden of supporting some unemployed relations, and their own consumption rises. Thus either they were living below the subsistence minimum before, or they are above it now. We may cut this knot by simply postulating that real wages per man are constant,[11] without asking why. The important point for the analysis which we are examining is that when employment increases the total consumption of the workers as a whole increases by the amount of the wages received by the additional workers.[12]

We may now set out the model for simple reproduction—that is, annual national income for an economy in which the stock of capital is kept intact but not increased. All output is [Pg 16]divided into two departments: I, producing capital equipment and raw materials, (producers’ goods), and II, producing consumption goods. Then we have

I: c1 + v1 + s1 = c1 + c2
II: c2 + v2 + s2 = v1 + v2 + s1 + s2


c2 = v1 + s1

This means that the net output of the producers’ goods department is equal to the replacement of capital in the consumers’ goods department. The whole surplus, as well as the whole of wages, is currently consumed.

Before proceeding to the model for accumulation there is a difficulty which must be discussed. In the above model the stock of capital exists, so to speak, off stage. Rosa Luxemburg is perfectly well aware of the relationship between annual wear and tear of capital, which is part of c, and the stock of fixed capital,[13] but as soon as she (following Marx) discusses accumulation she equates the addition to the stock of capital made by saving out of surplus in one year to the wear and tear of capital in the next year. To make sense of this we must assume that all capital is consumed and made good once a year. She seems to slip into this assumption inadvertently at first, though later it is made explicit.[14] She also consciously postulates that v represents the amount of capital which is paid out in wages in advance of receipts from sales of the commodities produced. (This, as she says, is the natural assumption to make for agricultural production, where workers this year are paid from the proceeds of last year’s harvest.)[15] Thus v represents at the same time the annual wages bill and the amount of capital locked up in the wages fund, while c represents both the annual amortisation of capital and the total stock of capital (other than the wages fund). This is a simplification which is tiresome rather than helpful (it arises from Marx’s ill-judged habit of writing s⁄(c + v) for the rate of profit on capital), but it is no more than a simplification and does not invalidate the rest of the analysis.

Another awkward assumption, which causes serious trouble [Pg 17]later, is implicit in the argument. Savings out of the surplus accruing in each department (producers’ and consumers’ goods) are always invested in capital in the same department. There is no reason to imagine that one capitalist is linked to others in his own department more than to those in the other department, so the conception seems to be that each capitalist invests his savings in his own business. There is no lending by one capitalist to another and no capitalist ever shifts his sphere of operations from one department to another. This is a severe assumption to make even about the era before limited liability was introduced, and becomes absurd afterwards. Moreover it is incompatible with the postulate that the rate of profit on capital tends to equality throughout the economy,[16] for the mechanism which equalises profits is the flow of new investment, and the transfer of capital as amortisation funds are re-invested, into more profitable lines of production and away from less profitable lines.[17]

The assumption that there is no lending by one capitalist to another puts limitation upon the model. Not only must the total rate of investment be equal to the total of planned saving, but investment in each department must be equal to saving in that department, and not only must the rate of increase of capital lead to an increase of total output compatible with total demand, but the increase in output of each department, dictated by the increase in capital in that department, must be divided between consumers’ and producers’ goods in proportions compatible with the demand for each, dictated by the consumption and the investment plans in each department.

[Pg18]There is no difficulty, however, in choosing numbers which satisfy the requirements of the model. The numerical examples derived from Marx’s jottings are cumbersome and confusing, but a clear and simple model can be constructed on the basis of the assumptions set out in chapter vii. In each department, constant capital is four times variable capital.[18](Constant capital is the stock of raw materials which is turned over once a year; variable capital is the wages bill, which is equal to the capital represented by the wages fund.) Surplus is equal to variable capital (net income is divided equally between wages and surplus) and half of surplus is saved.[19] Savings are allotted between constant and variable capital in such a way as to preserve the 4 to 1 ratio. Thus four-fifths of savings represents a demand for producers’ goods, and is added to constant capital each year, and one-fifth represents a demand for consumers’ goods, and is added to the wages fund (variable capital). These ratios dictate the relationship between Department I (producers’ goods) and Department II (consumers’ goods).[20] It can easily be seen that the basic assumptions require that the output of Department I must stand in the ratio of 11 to 4 to the output of Department II.[21] We can now construct a much simpler model than those provided in the text.

c v s Gross Output
Department I 44 11 11 66
Department II 16 4 4 24
Total 90

In Department I, 5·5 units are saved (half of s) of which 4·4 are invested in constant capital and 1·1 in variable capital. In Department II 2 units are saved, 1·6 being added to constant and 0·4 to variable capital. The 66 units of producers’ goods provide 44 + 4·4 constant capital for Department I and 16 + 1·6 [Pg 19]constant capital for Department II and the 24 units of consumers’ goods provide 11 + 4 wages of labour already employed, 5·5 + 2 for consumption out of surplus, and 1·1 + 0·4 addition to variable capital, which provide for an addition to employment.

After the investment has been made, and the labour force increased in proportion to the wages bill, we have

c v s Gross Output
Department I 48·4 12·1 12·1 72·6
Department II 17·6 4·4 4·4 26·4
Total 99  

The two departments are now equipped to carry out another round of investment at the prescribed rate, and the process of accumulation continues. The ratios happen to have been chosen so that the total labour force, and total gross output, increase by 10 per cent per annum.[22]

But all this, as Rosa Luxemburg remarks, is just arithmetic.[23] The only point of substance which she deduces from Marx’s numerical examples is that it is always Department I which takes the initiative. She maintains that the capitalists in Department I decide how much producers’ goods to produce, and that Department II has to arrange its affairs so as to absorb an amount of producers’ goods which will fit in with their plans.[24] On the face of it, this is obviously absurd. The arithmetic is perfectly neutral between the two departments, and, as she herself shows, will serve equally well for the imagined case of a socialist society where investment is planned with a view to consumption.[25]

But behind all this rigmarole lies the real problem which she is trying to formulate. Where does the demand come from which keeps accumulation going?

She is not concerned with the problem, nowadays so familiar, of the balance between saving and investment. Marx himself was aware of that problem, as is seen in his analysis of disequilibrium under conditions of simple reproduction (zero net investment).[26] When new fixed capital comes into existence, part [Pg 20]of gross receipts are set aside in amortisation funds without any actual outlay being made on renewals. Then total demand falls short of equilibrium output, and the system runs into a slump. Contrariwise, when a burst of renewals falls due, in excess of the current rate of amortisation, a boom sets in. For equilibrium it is necessary for the age composition of the stock of capital to be such that current renewals just absorb current amortisation funds. Similarly, when accumulation is taking place, current investment must absorb current net saving.[27]

It is in connection with the problem of effective demand, in this sense, that Marx brings gold-mining into the analysis. When real output expands at constant money prices, the increasing total of money value of output requires an increase in the stock of money in circulation (unless the velocity of circulation rises appropriately). The capitalists therefore have to devote part of their savings to increasing their holdings of cash (for there is no borrowing). This causes a deficiency of effective demand. But the increase in the quantity of money in circulation comes from newly mined gold, and the expenditure of the gold mining industry upon the other departments just makes up the deficiency in demand.[28]

Rosa Luxemburg garbles this argument considerably, and brushes it away as beside the point. And it is beside the point that she is concerned with. She does not admit the savings and investment problem, for she takes it for granted that each individual act of saving out of surplus is accompanied by a corresponding amount of real investment, and that every piece of investment is financed by saving out of surplus of the same capitalist who makes it.[29] What she appears to be concerned with is rather the inducement to invest. What motive have the capitalists for enlarging their stock of real capital?[30] How do they know that there will be demand for the increased output of goods which the new capital will produce, so that they can ‘capitalise’ their surplus in a profitable form? (On the purely [Pg 21]analytical plane her affinity seems to be with Hobson rather than Keynes.)

Needless to say, our author does not formulate the problem of the inducement to invest in modern terminology, and the ambiguities and contradictions in her exposition have left ample scope for her critics to represent her theory as irredeemable nonsense.[31] But the most natural way to read it is also the clearest. Investment can take place in an ever-accumulating stock of capital only if the capitalists are assured of an ever-expanding market for the goods which the capital will produce. On this reading, the statement of the problem leads straightforwardly to the solution propounded in the third Section of this book.

Marx has his own answer to the problem of inducement to invest, which she refers to in the first chapter.[32] The pressure of competition forces each individual capitalist to increase his capital in order to take advantage of economies of large-scale production, for if he does not his rivals will, and he will be undersold. Rosa Luxemburg does not discuss whether this mechanism provides an adequate drive to keep accumulation going, but looks for some prospective demand outside the circle of production. Here the numerical examples, as she shows, fail to help. And this is in the nature of the case, for (in modern jargon) the examples deal with ex post quantities, while she is looking for ex ante prospects of increased demand for commodities. If accumulation does take place, demand will absorb output, as the model shows, but what is it that makes accumulation take place?

In Section II our author sets out to find what answers have been given to her problem. The analysis she has in mind is now broader than the strict confines of the arithmetical model. Technical progress is going on, and the output of an hour’s labour rises as time goes by. (The concept of value now becomes treacherous, for the value of commodities is continuously falling.) Real wages tend to be constant in terms of commodities, thus the value of labour power is falling, and the share of surplus in net income is rising (s⁄v, the rate of exploitation, is rising). The amount of saving in real terms is therefore rising (she suggests [Pg 22]later that the proportion of surplus saved rises with surplus, in which case real savings increase all the more[33] ). The problem is thus more formidable than appears in the model, for the equilibrium rate of accumulation of capital, in real terms, is greater than in the model, where the rate of exploitation is constant. At the same time the proportion of constant to variable capital is rising. She regards this not as something which is likely to happen for technical reasons, but as being necessarily bound up with the very nature of technical progress. As productivity increases, the amount of producers’ goods handled per man-hour of labour increases; therefore, she says, the proportion of c to v must increase.[34] This is an error. It arises from thinking of constant capital in terms of goods, and contrasting it with variable capital in terms of value, that is, hours of labour. She forgets Marx’s warning that, as progress takes place, the value of the commodities making up constant capital also falls.[35] It is perfectly possible for productivity to increase without any increase in the value of capital per man employed. This would occur if improvements in the productivity of labour in making producers’ goods kept pace with the productivity of labour in using producers’ goods to make consumers’ goods (capital-saving inventions balance labour-saving inventions, so that technical progress is ‘neutral’). However, we can easily get out of this difficulty by postulating that as a matter of fact technical progress is mainly labour-saving, or, a better term, capital-using, so that capital per man employed is rising through time.

Rosa Luxemburg treats the authors whom she examines in Section II with a good deal of sarcasm, and dismisses them all as useless. To some of the points raised her answers seem scarcely adequate. For instance, Rodbertus sees the source of all the troubles of capitalism in the falling proportion of wages in national income.[36] He can be interpreted to refer to the proportion of wages in gross income. In that case, she is right (on the assumption of capital-using inventions) in arguing that a fall in the proportion of wages is bound up with technical progress, and that the proportion could be held constant only by stopping [Pg 23]progress. He can also be taken to refer to the share of wages in net output, and this is the more natural reading. On this reading she argues that the fall in share of wages (or rise in rate of exploitation) is necessary to prevent a fall in the rate of profit on capital[37] (as capital per man employed rises, profit per man employed must rise if profit per unit of capital is constant). But she does not follow up the argument and inquire what rise in the rate of exploitation is necessary to keep capitalism going (actually, the statisticians tell us, the share of wages in net income has been fairly constant in modern industrial economies[38] ). It is obvious that the less the rate of exploitation rises, the smaller is the rise in the rate of saving which the system has to digest, while the rise in real consumption by workers, which takes place when the rate of exploitation rises more slowly than productivity in the consumption good industries, creates an outlet for investment in productive capacity in those industries. The horrors of capitalism, and the difficulties which it creates for itself, are both exaggerated by the assumption of constant real-wage rates and, although it would be impossible to defend Rodbertus’ position that a constant rate of exploitation is all that is needed to put everything right, he certainly makes a contribution to the argument which ought to be taken into account.

Tugan-Baranovski also seems to be treated too lightly. His conception is that the rising proportion of constant capital in both departments (machines to make machines as well as machines to make consumers’ goods) provides an outlet for accumulation, and that competition is the driving force which keeps capitalists accumulating. Rosa Luxemburg is no doubt correct in saying that his argument does not carry the analysis beyond the stage at which Marx left it,[39] but he certainly elaborates a point which she seems perversely to overlook. Her real objection to Tugan-Baranovski is that he shows how, in certain conditions, capitalist accumulation might be self-perpetuating, while she wishes to establish that the coming [Pg 24]disintegration of the capitalist system is not merely probable on the evidence, but is a logical necessity.[40]

The authors such as Sismondi, Malthus and Vorontsov, who are groping after the problem of equilibrium between saving and investment, are treated with even less sympathy (though she has a kindly feeling for Sismondi, to whom she considers that Marx gave too little recognition[41] ) for she is either oblivious that there is such a problem, or regards it as trivial.[42]We leave the discussion, at the end of Section II, at the same point where we entered it, with the clue to the inducement to invest still to find.

Section III is broader, more vigorous and in general more rewarding than the two preceding parts. It opens with a return to Marx’s model for a capitalist system with accumulation going on. Our author then sets out a fresh model allowing for technical progress. The rate of exploitation (the ratio of surplus to wages) is rising, for real wages remain constant while output per man increases. In the model the proportion of surplus saved is assumed constant for simplicity, though in reality, she holds, it would tend to rise with the real income of the capitalists.[43] The ratio of constant to variable capital is rising for technical reasons. (The convention by which the annual wear and tear of capital is identified with the stock of capital now becomes a great impediment to clear thinking.) The arithmetical model shows the system running into an impasse because the output of Department I falls short of the requirements of constant capital in the two departments taken together, while the output of Department II exceeds consumption.[44] The method of argument is by no means rigorous. Nothing follows from the fact that one particular numerical example fails to give a solution, and the example is troublesome to interpret as it is necessary to distinguish between discrepancies due to rounding off the figures [Pg 25]from those which are intended to illustrate a point of principle.[45] But there is no need to paddle in the arithmetic to find where the difficulty lies. The model is over-determined because of the rule that the increment of capital within each department at the end of a year must equal the saving made within the same department during the year. If capitalists from Department II were permitted to lend part of their savings to Department I to be invested in its capital, a breakdown would no longer be inevitable. Suppose that total real wages are constant and that real consumption by capitalists increases slowly, so that the real output of Department II rises at a slower rate than productivity, then the amount of labour employed in it is shrinking. The ratio of capital to labour however is rising as a consequence of capital-using technical progress. The output of Department I, and its productive capacity, is growing through time. Capital invested in Department I is accumulating faster than the saving of the capitalists in Department I, and capitalists of Department II, who have no profitable outlet in their own industries for their savings, acquire titles to part of the capital in Department I by supplying the difference between investment in Department I and its own saving.[46] For any increase in the stock of capital of both departments taken together, required by technical progress and demand conditions, there is an appropriate amount of saving, and so long as the total accumulation required and total saving fit, there is no breakdown.

But here we find the clue to the real contradiction. These quantities might conceivably fit, but there is no guarantee that they will. If the ratio of saving which the capitalists (taken together) choose to make exceeds the rate of accumulation dictated by technical progress, the excess savings can only be ‘capitalised’ if there is an outlet for investment outside the system. (The opposite case of deficient savings is also possible. Progress would then be slowed down below the technically possible maximum; but this case is not contemplated by our author, and it would be irrelevant to elaborate upon it.)

Once more we can substitute for a supposed logical necessity [Pg 26]a plausible hypothesis about the nature of the real case, and so rescue the succeeding argument. If in reality the distribution of income between workers and capitalists, and the propensity to save of capitalists, are such as to require a rate of accumulation which exceeds the rate of increase in the stock of capital appropriate to technical conditions, then there is a chronic excess of the potential supply of real capital over the demand for it and the system must fall into chronic depression. (This is the ‘stagnation thesis’ thrown out by Keynes and elaborated by modern American economists, notably Alvin Hansen). How then is it that capitalist expansion had not yet (in 1912) shown any sign of slackening?

In chapter xxvi Rosa Luxemburg advances her central thesis—that it is the invasion of primitive economies by capitalism which keeps the system alive. There follows a scorching account of the manner in which the capitalist system, by trade, conquest and theft, swallowed up the pre-capitalist economies,—some reduced to colonies of capitalist nations, some remaining nominally independent—and fed itself upon their ruins. The thread of analysis running through the historical illustrations is not easy to pick up, but the main argument seems to be as follows: As soon as a primitive closed economy has been broken into, by force or guile, cheap mass-produced consumption goods displace the old hand production of the family or village communities, so that a market is provided for ever-increasing outputs from the industries of Department II in the old centres of capitalism, without the standard of life of the workers who consume these commodities being raised.[47] The ever-growing capacity of the export industries requires the products of Department I, thus maintaining investment at home. At the same time great capital works, such as railways, are undertaken in the new territories.[48] This investment is matched partly by savings from surplus extracted on the spot, but mainly by loans from the old capitalist countries. There is no difficulty here in accounting for the inducement to invest, for the new territories yield commodities unobtainable at home.[49] We might set out the essence of the argument as follows: Cloth from Lancashire pays for labour in America, which is used to produce wheat and cotton. These provide wages and raw materials to the Lancashire [Pg 27]mills, while the profits acquired both on the plantations and in the mills are invested in steel rails and rolling stock, which open up fresh territories, so that the whole process is continuously expanding. Moreover, apart from profits earned on capital actually invested in the new territories, great capital gains are made simply by acquiring possession of land and other natural resources.[50] Labour to work the resources may be provided by the local dispossessed peasantry or by immigration from the centres of capitalism.[51] Investment in equipment for it to use is more profitable than in that operated by home labour, partly because the wretched condition of the colonial workers makes the rate of exploitation higher,[52] but mainly just because they are on the spot, and can turn the natural resources seized by the capitalists into means of production. No amount of investment in equipment for British labour would produce soil bearing cotton, rubber or copper. Thus investment is deflected abroad[53] and the promise of profit represented by the natural resources calls into existence, by fair means or foul, the labour and capital to make it come true. The process of building up this capital provides an outlet for the old industries and rescues them from the contradictions inherent in deficiency of demand.

The analysis of militarism in the last chapter over-reaches itself by trying to prove too much. The argument is that armaments are built up out of taxes which fall entirely on wages.[54]This can be regarded as a kind of ‘forced saving’ imposed on the workers. These savings are extra to the saving out of surplus. They are invested in armaments, and that ends the story. On this basis the armaments, in themselves, cannot be held to provide an outlet for the investment of surplus (though the use of the armaments, as in the Opium War,[55] to break up primitive economies is a necessary condition for the colonial investment already described) and capital equipment to produce armaments is merely substituted for capital formerly producing consumers’ goods. The analysis which best fits Rosa Luxemburg’s own argument, and the facts, is that armaments provide an outlet for the investment of surplus (over and above any contribution there may be from forced saving out of wages), which, unlike other kinds of investment, creates no further problem by [Pg 28]increasing productive capacity (not to mention the huge new investment opportunities created by reconstruction after the capitalist nations have turned their weapons against each other).

All this is perhaps too neat an account of what our author is saying. The argument streams along bearing a welter of historical examples in its flood, and ideas emerge and disappear again bewilderingly. But something like the above seems to be intended. And something like it is now widely accepted as being true. Rosa Luxemburg, as we have seen, neglects the rise in real wages which takes place as capitalism develops, and denies the internal inducement to invest provided by technical progress, two factors which help to rescue capitalism from the difficulties which it creates for itself. She is left with only one influence (economic imperialism) to account for continuous capital accumulation, so that her analysis is incomplete. All the same, few would deny that the extension of capitalism into new territories was the mainspring of what an academic economist has called the ‘vast secular boom’ of the last two hundred years,[56] and many academic economists account for the uneasy condition of capitalism in the twentieth century largely by the ‘closing of the frontier’ all over the world.[57] But the academic economists are being wise after the event. For all its confusions and exaggerations, this book shows more prescience than any orthodox contemporary could claim.




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