This corresponds to the real modus operandi of the capitalist system. It also points the way to a solution of the technical problem seen by Luxemburg in the fact that the ‘unsaleable’ portion of commodities of department II embodies part of the surplus-value created in that department. As a matter of fact, Luxemburg dismissed out of hand Marx’s convincing solution, which was later developed at length by Otto Bauer.86 Part of the surplus-value produced in department II is periodically transferred to department I, precisely when (and because) department I exhibits, over a considerable length of time, a higher organic composition of capital than that of department II.

At this most abstract level of reasoning, the problem has been posed as one of quasi-static equilibrium. But at a second level which, while still abstract, is a step nearer to the historical reality of the capitalist mode of production, accumulation of capital must be examined as a discontinuous process with a view to understanding its actual dynamics. The first question I posed was the following: can customers be found for those commodities which embody the accumulated part of surplus-value, if we assume that all purchasing power originates as either wages or surplus-value within the capitalist process of production itself? Marx’s simple answer is: yes, so long as we do not take surplus-value to be a single mass, owned by a solitary capitalist (who would then obviously be condemned to ‘buy’ his own goods). The second question may now be re-posed as follows: what is the effect upon the realization of the value of commodities embodying the accumulated part of surplus-value, if and when (1) the organic composition of capital rises in both departments; (2) department I grows at a faster rate than II (which is the unavoidable result of the rising organic composition of capital); and (3) the rate of profit declines (i.e. the growth in the rate of surplus-value is insufficient to compensate for the rising organic composition of capital)? In other words, is full realization of surplus-value possible when the laws of motion of the capitalist mode of production assert themselves?

This second question requires a more complex answer than the previous one. Theoretically, full realization of surplus-value is possible, and several ingenious mathematical models have been constructed – by, among others, O. Benedikt, Shinzaburo Koshimura, Oskar Lange, J. Caridad Mateo and Hosea Jaffe87 – in order to show that it is. By contesting this. Luxemburg denied that ‘pure’ capitalism was possible, thus taking a position exactly opposite to the one which Marx tried to demonstrate with his reproduction schemas. It should be immediately added, however, that the real socio-economic conditions expressed by these algebraic formulas have to be precisely defined.88 Furthermore, those of her critics who replied that the schemas ‘prove’ by themselves the possibility of unlimited, smooth progress of reproduction 89 forgot one small point: capitalism has been generating periodic crises of overproduction for more than 150 years, and continues to do so with the regularity of a ‘natural law’. We can reject out of hand the hypothesis that each successive crisis has been’ due entirely to ‘specific’ causes, unrelated to the inner logic of the capitalist mode of production, and extraneous to the inter-relation of the growth rates of c, v, s/v, accumulated s/total s, both within and between the two departments. The very periodicity of these crises is enough to refute the ‘harmony theorists’ and the view that capital accumulation can go on for ever ‘on the basis of the schemas’. In this respect, the superiority of Luxemburg over certain of her critics is obvious.90

Nevertheless, did she succeed in proving her case in a technically satisfactory manner? We do not believe so; for she narrowed down the problem to an excessively monocausal one. In order to prove that, under capitalism, equilibrium must beget disequilibrium, that expanded reproduction must generate over-production, and that accumulation of capital must lead to devalorization of capital it is necessary to bring all the inter-related variables of the reproduction schemas into play. And this she does not do. Thus, while The Accumulation of Capital raises the correct problems, it does not provide acceptable solutions to them.91

Synthetically, we may say that the equilibrium formula of expanded reproduction: Iv+Isα+Isγ = IIc+IIsβ, implies an identity of the rate of growth of demand for consumer goods generated by department I, and the rate of growth of constant capital in department II. Now, the rise in the organic composition of capital entails that the demand for consumer goods generated in department I will normally grow more slowly than constant capital in that sector (unless the slower rate of growth of variable capital is compensated by a rate of growth of unproductively consumed surplus-value higher than that of constant capital, which is extremely unlikely in the long run). The precondition of equilibrium is consequently a rate of growth of constant capital in department II lower than the one in department I. If the rates in the two departments are equal, the conditions of equilibrium will be upset.

However, a rate of growth of constant capital in department II which is permanently lower than that in department I is incompatible with private property and competition. There is no reason why capitalists engaged in the production of consumer goods should forever abstain from trying to incorporate all existing technology, all means of reducing costs of production, all potentially useable machinery. Therefore, IIc+IIsβ will from time to time be greater than Iv+Isα+Isγ, just as, periodically, under conditions of rising organic composition of capital (biased development of labour-saving technology), A[IIc+IIsβ] will be equal to A[Ic+Isβ] and A[Ic+ Isβ] will be greater than A[Iυ+Isα+Isγ]. It therefore seems impossible to avoid periodic over-production of consumer goods, as well as a decline in the rate of profit and of the ratio ace. sv/sv, entailing an abrupt halt to the accumulation of capital.

Donald Harris has concluded from Marx’s ‘assumptions’ that equilibrium obtains only if (in a value system) there is proportional hiring of labour in the two departments, or if (in a prices of production system) there is an equal ratio of investment – accumulation – of surplus-value.92 However, all these calculations are based upon a misunderstanding of Marx’s method. While Marx does assume an equal rate of exploitation in both departments (an assumption based on the concept of an average national value of labour-power, for which quite strong empirical evidence exists under developed capitalism), he does not ‘assume’ either that the organic composition of capital will remain equal or that the rate of surplus-value will stay the same. His method of successive approximation to the ‘appearances’ of day-to-day capitalist economy led him to abstract, at a given stage of the inquiry, from a number of additional variables, in order to clarify certain preliminary problems. This has nothing to with ‘assuming’ historical trends.

Finally, on the third level, that of the actual historical process of capital accumulation, Luxemburg seems fundamentally correct. Capitalism was born essentially in a non-capitalist milieu; it has immensely enriched itself by plundering that milieu; and the same value-transferring metabolism has continued to this very day.