Thus
| c 2 | = | v 1 | + | s 1 |
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 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.
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 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