MARX AND ROSA LUXEMBURG
 In the second part of Capital Marx dealt with the general conditions of capitalist production as a whole. In the abstract case of pure capitalist production all production is carried on for the market, all products are bought and sold as commodities. The value of the means of production is passed on to the product and a new value is added by labour. This new value is broken down into two parts: the value of the labour power, which is paid as wages and used by the workers to buy means of subsistence, and the remainder, the surplus value, which goes to the capitalist. Where the surplus value is used for means of subsistence and luxury goods then there is simple reproduction; where a part of it is accumulated as new capital there is reproduction on an extended scale. For the capitalists to find on the market the means of production they need and for the workers to likewise find the means of subsistence they need, a given proportion must exist between the various branches of production. A mathematician would easily express this in algebraic formulae. Marx gives instead numerical examples to express these proportions, making up cases with selected figures, to serve as illustrations. He distinguishes two spheres, two main departments of production: the means of production department (I) and the means of consumption department (II). In each of these departments a given value of the means of production used is transferred to the product without undergoing any change (constant capital, c); a given part of the newly added value is used to pay for labour-power (variable capital, v), the other part being the surplus value (s). If it is assumed for the numerical example that the constant capital is four times greater than the variable capital (a figure which rises with technical progress) and that the surplus value is equal to the variable capital (this ratio is determined by the rate of exploitation), then, in the case of simple reproduction, the following figures satisfy these conditions:
Each of these lines satisfies the conditions. Since v+s, which are used as means of consumption, are together equal to a half of c, the value of the means of production, Department II must produce a value equal to a half the value produced in Department I. Then the exact proportion is found: the means of production produced (6000) are just the amount needed for the next turnover period: 4000c for Department I and 2000c for Department II; and the means of subsistence produced in Department II (3000) are exactly what must be supplied for the workers (1000+500) and the capitalists (1000+500). To illustrate in a similar way the case of capital accumulation the part of surplus value going to accumulation must be indicated; this part is added to the capital in the following year (for reasons of simplicity a production period of a year is assumed each time) so that a larger capital is then employed in each department. We will assume in our example that half the surplus value is accumulated (and so used for new c and new v) and that the other half is consumed (consumption, k). The calculation of the proportion between Department I and Department II becomes a little more complicated but can of course still be found. It turns out that, on the assumptions given, this proportion is 11 : 4, as is shown in the following figures:
The capitalists need 4400+1600 for the renewal and 440+160 for the extension of their means of production, and in fact they find 6600 means of production on the market. The capitalists need 550+200 for their consumption, the original workers need 1100+400 and the newly engaged workers 110+40 as means of subsistence; which together is equal to the 2400 in fact produced as means of subsistence. In the following year all the figures are increased by 10 per cent:
Production can thus continue increasing each year in the same proportion. This is of course a grossly oversimplified example. It could be made more complicated, and thus nearer to reality, if it is assumed that there are different compositions of capital (the ratio c:v) in the two departments, or different rates of accumulation or if the ratio c:v is made to grow gradually, so changing the proportion between Department I and Department II each year. In all these cases the calculation becomes more complicated, but it can always be done, since an unknown figure - the proportion of Department I to Department II - can always be calculated to satisfy the condition that demand and supply coincide. Examples of this can be found in the literature. In the real world, of course, complete equilibrium over a period is never found; commodities are sold for money and money is only used later to buy something else so that hoards are formed which act as a buffer and a reserve. And commodities remain unsold; and there is trade with non-capitalist areas. But the essential, important point is seen clearly from these reproduction schemes: for production to expand and steadily progress given proportions must exist between the productive sectors; in practice these proportions are approximately realised; they depend on the following factors: the organic composition of capital, the rate of exploitation, and the proportion of surplus value which is accumulated. Marx did not have the chance to provide a carefully prepared presentation of these examples (see Engels' introduction to the second volume of Capital). This is no doubt why Rosa Luxemburg believed that she had discovered an omission here, a problem which Marx had overlooked and so left unsolved and whose solution she had worked out in her book The Accumulation of Capital (1912). The problem which seemed to have been left open was who was to buy from each other more and more means of production and means of subsistence this would be a pointless circular movement from which nothing would result. The solution would lie in the appearance of buyers situated outside capitalism, foreign overseas markets whose conquest would therefore be a vital question for capitalism. This would be the economic basis of imperialism. But from what we have said before it is clear that Rosa Luxemburg has herself made a mistake here. In the schema used as the example it can be clearly seen that all the products are sold within capitalism itself. Not only the part of the value transmitted (4400+1600) but also the 440+160 which contain the surplus value accumulated are brought, in the physical form of means of production, by the capitalists who wish to start the following year with in total 6600 means of production. In the same way, the 110+40 from surplus value is in fact bought by the additional workers. Nor is it pointless: to produce, to sell products to each other, to consume, to produce more is the whole essence of capitalism and so of men's life in this mode of production. There is no unsolved problem here which Marx overlooked. |