Rosa Luxemburg's political economy

Tony Cliff's Rosa Luxemburg

The Accumulation of Capital

During the years 1906-13 Rosa Luxemburg lectured on political economy at a German Social Democratic Party school of activists. While doing so she prepared a book on Marxian economics entitled Introduction to Political Economy. When about to conclude the basic draft she met with an unexpected difficulty:

I could not succeed in depicting the total process of capitalist production in all its practical relations and with its objective historical limitations with sufficient clarity. Closer examination of the matter then convinced me that it was a question of rather more than the mere art of representation, and that a problem remained to be solved which is connected with the theoretical matter of Volume II of Marx's Capital and at the same time closely connected with present-day imperialist politics and their economic roots.

In this way Rosa Luxemburg came to write her major theoretical work, The Accumulation of Capital: A Contribution to an Economic Explanation of Imperialism (Berlin, 1913). The book is not at all easy to follow, especially for anyone not conversant with Marx's Capital. At the same time, without doubt, Rosa Luxemburg's contribution, whether one agrees with it or not, is one of the most, if not the most, important and original contributions to Marxian economic doctrine since Capital.

Marx, in analysing the laws of motion of capitalism, abstracted from it all non-capitalist factors, in the same way as a scientist studying the law of gravity would study it in a vacuum.

The problem with which Rosa Luxemburg deals is as follows: can enlarged reproduction, i.e. production on an increasing scale, take place under the conditions of abstract, pure capitalism, where non-capitalist countries do not exist, or where any classes besides capitalists and workers do not exist? Marx assumed that it can. Rosa Luxemburg argued that, while in general, for the purposes of the analysis of capitalist economy, abstraction from non-capitalist factors is justified, it is not justified when dealing with the question of enlarged reproduction.

The question is, of course, purely theoretical, as in fact pure capitalism has never existed: enlarged reproduction has always taken place while capitalism has been invading pre-capitalist spheres, either inside the capitalist country itself – invasion into feudalism with the destruction of peasants, artisans, etc – or into wholely agricultural, pre-capitalist countries.

If capitalism has never existed in pure form, one may well ask: what is the importance of the question whether enlarged reproduction is theoretically possible in pure capitalism? After all, neither Marx nor Rosa Luxemburg assumed that capitalism would continue to exist until all pre-capitalist formations had been overthrown. However, the answer to this question may throw light on the effect of the non-capitalist sphere on the accentuation or mitigation of the contradictions in capitalism, and on the factors impelling capitalism to imperialist expansion.

Let us begin by explaining how Marx described the process of reproduction as a whole under capitalism.

Marx starts with an analysis of simple reproduction, i.e. on the assumption – which, of course, could never exist under capitalism – that there is no accumulation of capital, that the whole of the surplus value is spent on the personal consumption of the capitalists, production thus not expanding.

For the capitalist to carry on simple reproduction certain conditions must exist. He must be able to sell the product of his factory, and with the money obtained buy the means of production (machines, raw materials, etc) that he needs for his particular industry; also he must get the labour power he needs from the market, as well as the means of consumption required to feed, clothe, and provide other necessities for the labourers. The product produced by the workers with the help of the means of production must again find a market, and so on.

While from the standpoint of the individual capitalist it makes no difference what his factory produces, whether machinery, stockings, or newspapers, provided he can find buyers for his product so that he can realise his capital plus the surplus value, to the capitalist economy as a whole it is extremely important that the total produce will be made up of certain determined use values, in other words, the total product must provide the means of production necessary to renew the process of production and the means of consumption needed by the workers and capitalists. The quantities of the different products cannot be arbitrarily determined: the means of production produced must be equal in value to the size of the constant capital c: the means of consumption produced must be equal in value to the size of the wages bill – the variable capital v – plus the surplus value s.

To analyse simple reproduction Marx divided industry as a whole into two basic departments: that producing means of production (Department I) and that producing means of consumption (Department II). Between these two departments a certain proportionality must obtain for simple reproduction to take place. It is clear, for instance, that if Department I produced more machines than this department together with Department II needed, machinery would be over-produced, production in Department I consequently paralysed, and a whole sequence of events would follow from this. Similarly, if Department I produced too few machines, reproduction, instead of repeating itself on the same level, would retrogress. The same would apply to Department II if it produced more or less means of consumption than the combined wages bill, or variable capital, and surplus value (v + s) in both departments. [79] The proportion between the demand for means of production and that for means of consumption in the economy as a whole depends on the ratio between the portion of capital devoted to the purchase of machinery and raw materials, i.e. on the constant capital (c) of the whole economy on the one hand, and that portion of capital expended on paying wages, v, plus the profits of the capitalists in the whole economy.

In other words, the products of Department I (P1) must be equal to the constant capital of Department I (c1) plus the constant capital of Department II (c2):

P1 = c1 + c2.

Similarly, the products of Department II (P2) must be equal to wages and surplus value in both departments together:

P2 = v1 + s1 + v2 + s2.

These two equations can be combined in one equation:

c2 = v1 + s1.

In other words, the value of machinery and raw materials, etc, needed by Department II must be equal to the wages plus surplus value of workers and capitalists in Department I.

These equations are for simple reproduction. The formulae for enlarged reproduction are more complicated. Here part of the surplus value is expended on the personal consumption of the capitalists – this we shall denote by the letter r – and part is accumulated – this we shall denote by the letter a. a itself is divided into two portions: part serves to buy added means of production, i.e. is spent on adding to available constant capital – ac – and part goes to pay wages to workers newly employed in production – av.

If the social demand for means of production under simple reproduction were expressed by the formula c1 + c2, enlarged reproduction would be expressed as c1 + ac1 + c2 + ac2.

Similarly the social demand for consumer goods, from

v1 + s1 + v2 + s2

becomes:

v1 + r1 + av1 + v2 + r2 + av2

Hence the conditions necessary for enlarged reproduction can be formulated thus:

P1 = c1 + ac1 + c2 + ac2

P2 = v1 + r1 + av1 + v2 + r2 + av2

Or:

c2 + ac2 = v1 + r1 + av1 [80]

Now for Rosa Luxemburg's criticism of Marx's schemas. [81] Rosa Luxemburg showed that a comparison of the formula for simple reproduction with that for enlarged reproduction produced a paradox. In the case of simple reproduction c2 must be equal to v1 + s1. In the case of enlarged reproduction, c2 + ac2 must be equal to v1 + r1 + av1. Now v1 + r1 + av1 are smaller than v1 + s1 (as ac1 is deducted from s1). So that if equilibrium were achieved under conditions of simple reproduction, the transition to enlarged reproduction would demand not only non-accumulation in Department II but the absurd position of disaccumulation.

And it is no accident, she said, that when Marx used diagrams to illustrate enlarged reproduction, he gave a smaller figure for c2 than the one he used to illustrate simple reproduction:

Diagram of simple reproduction
I 4000c + 1000v + 1000s = 6000
II 2000c + 500v + 500s = 3000
Total = 9000

Initial diagram for accumulation on an expanded scale
I 4000c + 1000v + 1000s = 6000
II 1500c + 750v + 750s = 3000
Total = 9000 [82]

Thus the constant capital of Department II is 500 smaller in enlarged than in simple reproduction.

Marx goes on to elaborate the diagram of enlarged reproduction and he shows that, assuming that in Department I as well as in Department II no change in the organic composition of capital (i.e., in the ratio of constant capital to variable capital) takes place, that the rate of exploitation remains constant, and that half the surplus value in Department I is capitalised, then the reproduction of capital will result in the following progression:

First year
I 4400c + 1100v + 1100s = 6600
II 1600c + 800v + 800s = 3200
Total = 9800

Second year
I 4800c + 1210v + 1210s = 7260
II 1760c + 880v + 880s = 3520
Total = 10780

Third year
I 5324c + 1331v + 1331s = 7986
II 1936c + 968v + 968s = 3872
Total = 11858

Fourth year
I 5856c + 1464v + 1464s = 7986
II 2129c + 1065v + 1065s = 4259
Total = 13043

Fifth year
I 6442c + 1610v + 1610s = 9662
II 2342c + 1172v + 1172s = 4686
Total = 14348 [83]

Analysing the above diagram, Rosa Luxemburg correctly points out a peculiarity they show:

While in Department I half the surplus value is capitalised every time, and the other half consumed, so that there is an orderly expansion both of production and of personal consumption by the capitalists, the twofold process in Department II takes the following erratic course:

First year 150 are capitalised, 600 consumed
Second 240 660
Third 254 626
Fourth 290 678
Fifth 320 745

And she adds:

Needless to say, the absolute figures of the diagram are arbitrary in every equation, but that does not detract from their scientific value. It is the quantitative ratios which are relevant, since they are supposed to express strictly determinate relationships. Those precise logical rules that lay down the relations of accumulation in Department I seem to have been gained at the cost of any kind of principle in construing these relations for Department II; and this circumstance calls for a revision of the immanent connections revealed by the analysis. [84]

Here there is no rule in evidence for accumulation and consumption to follow; both are wholly subservient to the requirements of accumulation in Department I. [85]

As regards the progress of the enlarged reproduction, if we assumed that in Department II as well as in Department I there was an orderly expansion of both capital accumulation, and of the personal consumption of the capitalists, there would then have appeared an increasing disequilibrium between the two departments.

Rosa Luxemburg therefore shows clearly that, if any logical rules were laid down for the relations of accumulation in Department I, these rules seem to "have been gained at the cost of any kind of principle in constructing these relations for Department II"; or otherwise, if the same logical rules were applied to the relations of accumulation in Department II as those applied in Department I, a disequilibrium in the form of overproduction in Department II would appear and grow progressively.

It will now be easy to show, assuming as a point of departure for enlarged reproduction that the constant capital in Department II was not 500 smaller than in simple reproduction, that there would have been disequilibrium between Department I and Department II: the demand of Department I for means of consumption would have been 500 smaller at the beginning of the process than the supply available in Department II of the means of consumption looking for exchange: there would have been overproduction of consumer goods to the value of 500 at the start of the process of enlarged reproduction.

If Rosa Luxemburg did not abstract from a number of other factors, such as the rise in the rate of exploitation and the rise in the organic composition of capital, her argument would have been even stronger. It is easy to prove that if the rate of exploitation rises, so that the ratio of surplus value to wage (s:v) is rising, the relative demand for consumer goods as against producer goods will decline, and hence either the rate of accumulation in Department II would be even more erratic than in Marx's diagrams, or increasing surpluses would appear in Department II. Any rise in the portion of the surplus value accumulated would work in the same direction, as well as any growth of the organic composition of capital.

The above-mentioned three tendencies – the rise in the rate of exploitation, rise in the rate of accumulation, and rise in the organic composition of capital – Marx assumed to be absolute and immanent laws of capitalism.

If these were taken into account, Rosa Luxemburg's contention, that under pure capitalism economic disequilibrium would be an absolute, unavoidable, permanent phenomenon, would be greatly strengthened.

However, there is one important factor which cancels out all the above factors and is immanently connected with them: the rise in the relative weight of Department I as compared with Department II. The rise in the organic composition of capital, the improvement of technique, has been historically and logically connected with the rise of Department I compared with Department II. Thus it was calculated that the ratio of net output of capital goods to that of consumer goods was in Britain as follows:

1851, 100:470; 1871, 100:390; 1901, 100:170; 1924, 100:150.

The figures for the United States were:

1850, 100:240; 1890, 100:150; 1920, 100:80.

The figures for Japan:

1900, 100:480; 1913, 100:270; 1925, 100:240. [86]

To show that the rise in Department I compared with Department II counteracts the factors mentioned by Rosa Luxemburg (as well as those added by the present writer to strengthen Rosa Luxemburg's argument about the tendency of overproduction in Department II), some diagrammatic representation of the effect of the change in the relative weight of Department I to Department II on the exchange relationship between the two departments will be given.

The capital invested in Department I can grow comparatively to Department II in two ways:

1. by having a higher rate of accumulation in Department I than in Department II;
2. by the transference of capital from Department II to Department I.

We shall give a diagrammatic example for each of these two processes.

Let us assume that the rate of accumulation in Department I is higher than in Department II, say, half the surplus value in Department I compared with only a third in Department II. We shall assume also that the other factors (the rate of exploitation at 100 percent, the organic composition of capital where constant capital is five times bigger than variable capital) remain unchanged. Then, using Marx's diagram quoted above as a point of departure, the reproduction of capital will result in the following progression (figures are rounded for simplicity) [87]:

Point of departure:
I 5000c + 1000v + 1000s = 7000
II 1500c + 300v + 300s = 2100

End of first year:
I 5000c + 1000v + 500r + 417ac + 83av = 7000
II 1500c + 300v + 200r + 80ac + 20av = 2100
c2 + ac2 = 1580
while v1 + r1 + av1 = 1583.

Thus at the end of the first year, instead of a surplus in Department II as presumed by Rosa Luxemburg, a surplus appears in Department I, amounting to 3.

End of second year:
I 5417c + 1083v + 541r + 450ac + 90av = 7583
II 1580c + 320v + 213r + 90ac + 18av = 2220
c2 + ac2 = 1670
while v1 + r1 + av1 =1714. The surplus in Department I is now 44.

End of third year:
I 5867c + 1173v + 586r + 489ac + 98av = 8213
II 1670c + 338v + 225r + 94ac + 19av = 2346
c2 + ac2 = 1764
while v1 + r1 + av1 =1857. The surplus in Department I is now 93.

From the above diagrams it is clear that if we assume that the rate of exploitation and the organic composition of capital remain unchanged, while the rate of accumulation in Department I is higher than in Department II, then overproduction appears in Department I. [88]

As we have said above, Department I can increase relatively to Department II also by transference of surplus value from Department II to Department I. Let us illustrate this process diagrammatically. We shall assume that the rate of exploitation, the organic composition of capital and the rate of accumulation are the same in both departments and they remain unchanged. At the same time, we shall assume that half the surplus value produced in Department II is being transferred to Department I.

The progress of enlarged production could then be described by the following diagrams:

Point of departure:
I 5000c + 1000v + 1000s = 7000
II 1500c + 300v + 300s = 2100

End of first year:
I 5000c + 1000v + 500r + 417ac + 83av = 7000
II 1500c + 300v + 150r + 63ac + 12av
(plus surplus value transferred to Department I: 63ac + 12av) = 2100
c2 + ac2 = 1563
while v1 + r1 + av1 (plus the av transferred from Department II) = 1595

Thus at the end of the first year, instead of a surplus in Department II as presumed by Rosa Luxemburg, we are faced with overproduction in Department I amounting to 32.

End of second year:
I 5840c + 1095v + 547r + 455ac + 91av = 7670
II 1563c + 312v + 156r + 65ac + 13av
(plus surplus value transferred to Department I: 65ac + 13av) = 2187
c2 + ac2 = 1628
while v1 + r1 + av1 (plus the av transferred from Department II) = 1746
The surplus in Department I is 118.

End of third year:
I 6000c + 1200v + 600r + 500ac + 100av = 8400
II 1628c + 325v + 162r + 67ac + 14av
(plus surplus value transferred to Department I: 67ac + 14av) = 2278
c2 + ac2 = 1695
while v1 + r1 + av1 (plus the av transferred from Department II) = 1914
The surplus in Department I is 219.

Now Rosa Luxemburg argues against this idea that the transfer of surplus value from one department to another can help to bring about an exchange balance between the departments, saying that the "intended transfer of part of the capitalised surplus value from Department II to Department I is ruled out, first because the material form of this surplus value is obviously useless to Department I, and secondly because of the relations of exchange between the two departments which would in turn necessitate an equivalent transfer of the products of Department I into Department II". [89] In other words, Rosa Luxemburg argues that Marx's schema is based on the assumption that the realisation of surplus value can take place only through an exchange between departments, and secondly that the presumed surplus in Department II takes a natural form, i.e. remains as means of consumption, and cannot serve directly as means of production. Now the first argument falls through owing to the fact that exchange between enterprises in the same department can serve to realise the surplus value: when an owner of a hat factory sells his hats to workers who produce biscuits, he realises the surplus value produced by his workers. Secondly, quite a large number of consumer goods can serve also as means of production: if a building contractor builds factories instead of flats, this signifies the transference of capital from Department II to Department I; electricity can serve to light flats as well as to move machinery; grain can feed man (consumption) as well as pigs (productive consumption), etc. Thirdly, without the possibility of transference of capital from one department to another, the postulate that the rate of profit throughout the economy tends to equality, which is basic Marxian economics, loses its foundation.

From the diagrams given above it becomes clear that a relative increase of Department I compared with Department II, if all other conditions remain unchanged, brings in its wake surpluses in the exchange relations in Department I.

Can this factor not counteract the one pointed out by Rosa Luxemburg to be the cause of a surplus in Department II? Are the different counteracting factors not in fact two sides of one coin, the progress of capitalist economy? Of course this is so.

Rosa Luxemburg came to the conclusion that a surplus must appear in Department II because she paid attention to only one side of the coin. Considering both sides, it is clear that it is possible in pure capitalism for proportionality between the two departments to exist, while the accumulation in both is regular, not erratic.

However, the theoretical possibility of the preservation of correct proportionalities between the two departments, which will prevent overproduction by their mutual exchange while accumulation goes forward on an even keel, does not mean that in actual life the anarchic and atomistic working of capitalism leads to continuous and stable preservation of the proportionalities needed. And here the factor Rosa Luxemburg pointed to – the existence of non-capitalist formations into which capitalism expands – is extremely important. If it is not a prerequisite for enlarged reproduction as Rosa Luxemburg argued, it is, at least, a factor that eases the process of enlarged reproduction, of accumulation, by making the interdependence of the two departments less than absolute. One cannot but agree with Rosa Luxemburg when she says, "Accumulation is more than an internal relationship between the branches of capitalist economy"; as a result of the relationship between the capitalist and non-capitalist environment:

... the two great departments of production sometimes perform the accumulative process on their own, independently of each other, but even then at every step the movements overlap and intersect. From this we get most complicated relations, divergencies in the speed and direction of accumulation for the two departments, different relations with non-capitalist modes of production as regards both material elements and elements of value. [90]

As a matter of fact, the number of factors determining whether certain proportionalities between the departments lead to equilibrium or not are numerous and contradictory (the rate of exploitation, the rate of accumulation in different industries, changes in the organic composition of capital in different industries, and so on) and, once the economy leaves the state of equilibrium, what was proportionality before turns into disproportionality with snowball effect. Hence the exchange between capitalist industry and the non-capitalist sphere, even if it is small in absolute terms, may have a tremendous effect on the elasticity, and hence stability, of capitalism.

In her book Rosa Luxemburg goes backwards and forwards between analyses of the schemas of reproduction – which describe exchange relationships between the two departments of industry – and another set of relations between the two departments: the potentiality of means of production to become means of consumption – means of production not only being exchanged for means of consumption, but in time being realised in new means of consumption. The proportionalities expressed in Marx's schemas are conditions without which accumulation cannot take place; but in order that accumulation should actually take place there is need for a progressively enlarged demand for commodities, and the question that arises is: where does this demand come from?

Capitalist prosperity depends upon the increasing output and absorption of capital goods. But this depends in the last analysis upon the capacity of industry to sell an increasing output of consumer goods. However, in trying to sell its products, capitalist industry enters into deepening contradictions, the most fundamental of which is that between production and the limited market: "The last cause of all real crises always remains the poverty and restricted consumption of the masses as compared to the tendency of capitalist production to develop the productive forces in such a way that only the absolute power of consumption of the entire society would be their limit". [91]

Rosa Luxemburg argued that the factor making it possible for capitalism to get away from the absolute impediment to accumulation of the limiting market was the penetration of capitalist industry into the non-capitalist territories. [92]

Rosa Luxemburg, more than any Marxist or non-Marxist economist, drew attention to the effect of the non-capitalist frontier on capitalism. Relying on this factor – even if she herself did not develop all the main consequences of it – one can try and sum up the effect of the expansion of capitalism into non-capitalist territories thus:

(1) The markets of the backward colonial countries, by increasing demand for goods from the industrial countries, weaken the tendency for overproduction there, decrease the reserve army of unemployed, and so bring about an improvement in the wages of workers in the industrial countries.

(2) The increase in wages brought about in this way has a cumulative effect. By increasing the internal market in the industrial countries, the tendency for overproduction is weakened, unemployment decreases, wages rise.

(3) The export of capital adds to the prosperity of the industrial countries as it creates a market for their goods – at least temporarily. The export of cotton goods from Britain to India presupposes that India is able to pay for it straight away, by exporting cotton, for instance. On the other hand, the export of capital for the building of a railway presupposes an export of goods – rails, locomotives, etc – beyond the immediate purchasing power or exporting power of India. In other words, for a time the export of capital is an important factor in enlarging markets for the industries of the advanced countries. However, in time this factor turns into its opposite: capital once exported puts a brake on the export of goods from the "mother" country after the colonial countries start to pay profit or interest on it. In order to pay a profit of £10 million to Britain (on British capital invested in India) India has to import less than it exports, and thus save the money needed to the tune of £10 million. In other words, the act of exporting capital from Britain to India expands the market for British goods; the payment of interest and profit on existing British capital in India restricts the markets for British goods. Hence the existence of great British capital investments abroad does not at all exclude overproduction and mass unemployment in Britain. Contrary to Lenin's view, the high profit from capital invested abroad may well be not a concomitant of capitalist prosperity and stabilisation in the imperialist country, but a factor of mass unemployment and depression.

(4) The export of capital to the colonies affects the whole capital market in the imperialist country. Even if the surplus of capital looking vainly for investment were very small, its cumulative influence could be tremendous, as it would create pressure in the capital markets, and strengthen the downward trend of the rate of profit. This in turn would have a cumulative effect of its own on the activity of capital, on the entire economic activity, on employment, and so on the purchasing power of the masses, and so again in a vicious circle on the markets. The export of surplus capital can obviate these difficulties and can thus be of great importance to the whole of capitalist prosperity, and thus to reformism.

(5) By thus relieving pressure in capital markets the export of capital diminishes competition between different enterprises, and so diminishes the need of each to rationalise and modernise its equipment. (This to some extent explains the technical backwardness of British industry, the pioneer of the industrial revolution, as compared with that of Germany today, for example.) This weakens the tendencies to overproduction and unemployment, wage cuts, and so on. (Of course, in changed circumstances, in which Britain has ceased to hold a virtual monopoly in the industrial world, this factor may well cause the defeat of British industry in the world market, unemployment and cuts in wages.)

(6) Buying cheap raw materials and foodstuffs in the colonies allows real wages in the industrial countries to be increased without cutting into the rate of profit. This increase of wages means widened domestic markets without a decrease in the rate and amount of profit, in other words, without weakening the motive of capitalist production.

(7) The period during which the agrarian colonial countries serve to broaden markets for the industrial countries will no longer be in proportion to:

1. the size of the colonial world compared with the productive power of the advanced industrial countries, and
2. the extent that the industrialisation of the former is postponed.

(8) All the beneficial effects of imperialism on capitalist prosperity would disappear if there were no national boundaries between the industrial imperialist countries and their colonies. Britain exported goods and capital to India and imported cheap raw materials and foodstuffs, but it did not let the unemployed of India – increased by the invasion of British capitalism – enter Britain's labour market. If not for the barrier (a financial one) to mass Indian immigration into Britain, wages in Britain would not have risen throughout the last century. The crisis of capitalism would have got deeper and deeper. Reformism would not have been able to replace revolutionary Chartism. [93]

One may agree or disagree with Rosa Luxemburg's criticism of Marx's schemas in Volume II of Capital, and with all or some of the links in her chain of reasoning leading to the final conclusion that, if the capitalist mode of production was not only the predominant one but the only one, of necessity in a short time capitalism would have collapsed from its internal contradictions. Whatever one thinks, one cannot doubt the tremendous service Rosa Luxemburg did in drawing attention to the effect of non-capitalist spheres on the stability of capitalism. As Professor Joan Robinson states in her introductory essay to the English edition of The Accumulation of Capital: "... 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 200 years, and many academic economists account for the uneasy condition of capitalism in the 20th century largely by the 'closing of the frontier' all over the world". [94] Joan Robinson mixes praise of Rosa Luxemburg's analysis with a criticism that Rosa Luxemburg ignored the rise in real wages that occurred throughout the capitalist world – a factor enlarging the market – and thus presented an incomplete picture. However, even if Rosa Luxemburg did not include this factor in her analysis – and it is extraneous to the main line of her argument about the possibility or impossibility of enlarged reproduction in pure capitalism – one cannot explain the rise in real wages itself independently of the main feature Rosa Luxemburg pointed out: the expansion of capitalism into non-capitalist spheres. [95]

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Notes

79. Actually, what is needed for smooth reproduction is not only that a certain proportionality be kept between the production of Department I and that of Department II in the whole economy, but that the proportionality between the departments be kept also in every branch of the economy. Thus, for instance, the production of clothing machinery (Department I) will need to fit the demand for this kind of machinery in the clothing industry (Department II).

80. These equations, which are algebraic formulations of Marx's analysis in Volume II of Capital were formulated by N Bukharin in his Der Imperialismus und die Akkumulation Des Kapitals (Berlin, 1925) and we find them very useful for summing up Marx's many arithmetical examples.

81. Before describing Rosa Luxemburg's analysis of reproduction, it must be clear that she did not develop a theory explaining the cyclical movement of boom, crisis and slump. She took it that the periodical cycles are phases of reproduction in capitalist economy, but not the whole of the process. Therefore, she abstracted her analysis from the cycles in order to study the process of reproduction in purity and as a whole. As she writes: "... in spite of the sharp rises and falls in the course of a cycle, in spite of crises, the needs of society are always satisfied more or less, reproduction continues on its complicated course, and productive capacities develop progressively. How can this take place, leaving cycles and crises out of consideration? Here the real question begins ... When we speak of capitalist reproduction in the following exposition, we shall always understand by this term a mean volume of productivity which is an average taken over the various phases of a cycle." R. Luxemburg, The Accumulation of Capital (London, 1951), pp.36-37.

82. K. Marx, Capital, vol.II, p.596.

83. K. Marx, Capital, vol.II, pp.598-600.

84. R. Luxemburg, Accumulation, p.122.

85. R. Luxemburg, Accumulation, p.122.

86. W.S. and E.S. Woytinsky, World Population and Production (New York, 1953), pp.415-416.

87. Editor's note: in these examples Cliff ignores decimals when assigning numbers to individual portions of value, so the totals are correct even if the portions do not appear to add up.

88. Rosa Luxemburg's argument against exactly this idea of a higher rate of accumulation in Department I than in Department II (R. Luxemburg, Accumulation, pp.338-339) is absolutely wrong. We have not the space to deal with it here. The reader should consult the source.

89. R. Luxemburg, Accumulation, pp.340-341.

90. R. Luxemburg, Accumulation, p.417.

91. K. Marx, Capital, vol.III, p.568.

92. A different "Marxist" answer to the capitalist dilemma was given by Otto Bauer in his criticism of Rosa Luxemburg's book. Using much more complicated schemes of reproduction than Marx or Rosa Luxemburg, he tried to prove that "the accumulation of capital adapts itself to the increase of population ... the periodic cycle of prosperity, crisis and slump is an empirical expression of the fact that the capitalist apparatus of production automatically overcomes too large or too small accumulation by adapting anew the accumulation of capital to the increase of population" (Die Neue Zeit, 1913, p.871). And this is said not by a disciple of Malthus, but of Marx, for whom the primary factor should not be population increase but capital accumulation!

93. By the way, the "third" buyer – not worker nor capitalist consumer – need not necessarily be the non-capitalist producer, but the non-producing state; hence the permanent war economy can, at least for a time, have a similar effect on capitalist prosperity as the non-capitalist economic sphere. (See T. Cliff, Perspectives of the Permanent War Economy, Socialist Review, May 1957.)

94. R. Luxemburg, Accumulation, p.28.

95. In her argument Rosa Luxemburg made a number of side errors which were discovered subsequently by N. Bukharin in his Der Imperialismus und die Akkumulation des Kapitals, although he did not disprove her central thesis (even though he thought he did). Thus, for instance, Rosa Luxemburg devoted a good deal of attention to purely monetary problems of capital accumulation – whether, for instance, one should include the production of money commodity (gold, silver, etc) in Department I, as Marx did, or, as she herself proposed, should add a third department. It seems that in a number of places in her book Rosa Luxemburg confuses the question: where does the demand come from? with the question: where does the money come from? But as this is of only secondary importance to her main thesis, we shall not deal with it here. Again, while, if we carefully followed Rosa Luxemburg's own reasoning about the schemes of reproduction, we should say that the weight of her argument is that a portion of the surplus value in Department II could not be realised under pure capitalism, Rosa Luxemburg herself sums up the argument as if she proved that no realisation of any portion of the surplus value could take place under pure capitalism. This was pointed out by F. Sternberg, in Der Imperialismus (Berlin, 1926), p.102.