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.

cvsGross Output
Department I44111166
Department II164424
Total90

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

cvsGross Output
Department I48·412·112·172·6
Department II17·64·44·426·4
Total99

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 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]