(The effect of the turnover on the production of surplus-value, and consequently also of profit, has already been discussed in Volume 2. To summarize it in brief, the time required for the turnover has the effect that the whole capital cannot be simultaneously employed in production. One part of this capital therefore always lies fallow, whether in the form of money capital, stocks of raw materials, finished but still unsold commodity capital, or outstanding debts that are not yet due for payment. The capital that is in active production, active in the production and appropriation of surplus-value, is always reduced by this amount, and the surplus-value that is produced and appropriated is reduced in the same proportion. The shorter the turnover time, the smaller is this idle portion of capital compared with the whole; the greater therefore is the surplus-value appropriated, other conditions being equal.
We explained in detail in the second volume how a reduction in the turnover time or in one of its two component sections, production time and circulation time, raises the mass of surplus-value produced.† But since the rate of profit simply expresses the ratio of the mass of surplus-value produced to the total capital engaged in producing it, it is evident that any reduction of this kind raises the rate of profit as well. The points made in Part Two of the second volume with respect to surplus-value apply equally here to profit and the rate of profit, and do not need to be repeated. There are simply a few key aspects we would like to emphasize.
The main means whereby production time is reduced is an increase in the productivity of labour, which is commonly known as industrial progress. If this does not also involve a major increase in the total capital investment, due to the installation of expensive machinery etc., and therefore a fall in the rate of profit as reckoned on the total capital, then this profit rate must rise. And this is decidedly the case with many of the most recent advances in the metallurgical and chemical industries. The newly discovered methods of iron and steel preparation associated with Bessemer, Siemens, Gilchrist-Thomas and others shorten what were previously very protracted processes to a minimum. The preparation of alizarin dye from coal-tar gives the same result in a few weeks, and using apparatus that is already in use for coal-tar dyes, as previously took several years. The madder from which the dye was previously prepared needed a year to grow, and the roots were left to mature for several years after that before they were used.
The main means of cutting circulation time has been improved communications. And the last fifty years have brought a revolution in this respect that is comparable only with the industrial revolution of the second half of the last century. On land the Macadamized road has been replaced by the railway, while at sea the slow and irregular sailing ship has been driven into the background by the rapid and regular steamer line; the whole earth has been girded by telegraph cables. It was the Suez canal that really opened the Far East and Australia to the steamer. The circulation time for a shipment of goods to the Far East, which in 1847 was at least twelve months (see Volume 2, p. 329), has now been more or less reduced to as many weeks. The two major foci of crisis between 1825 and 1857, America and India, have been brought 70 to 90 per cent closer to the industrial countries of Europe by this revolution in the means of commerce, and have lost in this way a good deal of their explosive potential. The turnover time of world trade as a whole has been reduced to the same extent, and the efficacy of the capital involved in it has been increased two or three times and more. It is evident that this cannot but have had its effect on the profit rate.
In order to present the effect of the turnover of the total capital on the profit rate in its pure form, we must assume that all other circumstances are equal for the two capitals we are comparing. The percentage composition in particular must be taken as the same, as well as the rate of surplus-value and the length of the working day. Let us take a capital A with a composition of 80c + 20ν = 100C, a rate of surplus-value of 100 per cent, and a twice-yearly turnover. Its annual product is then 160c + 40ν + 40s. But for the purposes of the profit rate we calculate this 40s not on the capital value of 200 turned over, but rather on the capital value of 100 that was advanced, and we thus get p′ = 40 per cent.
Let us compare this with a capital B = 160c + 40ν = 200C, with the same rate of surplus-value, but turning over only once in the year. Its annual product is then 160c + 40ν + 40s, the same as above. This time however the 40s has to be calculated on a capital advance of 200, which results in a profit rate of 20 per cent, i.e. only half the rate for A.
The result is therefore that for capitals of the same percentage composition, with the same rate of surplus-value and the same working day, the profit rates of two capitals vary inversely as their turnover times. If either the composition or the rate of surplus-value or the working day or the wage of labour is not the same in the two cases to be compared, further differences in the rate of profit are also brought about, but these are independent of the turnover, and do not concern us here; they have already been discussed in Chapter 3.
The direct effect of the abbreviated turnover time on the production of surplus-value, and therefore also on profit, consists in the increased effectiveness which this gives to the variable portion of capital, as discussed in Volume 2, Chapter 16: ‘The Turnover of Variable Capital’. There it was seen how a variable capital of 500 which turns over ten times in the year appropriates just as much surplus-value in this period as a variable capital of 5,000, with the same rate of surplus-value and the same wages, which turns over only once in the year.
Let us take a capital I, consisting of 10,000 fixed capital, its annual depreciation being 10 per cent = 1,000, 500 circulating constant capital, and 500 variable capital. With a rate of surplus-value of 100 per cent, the variable capital turns over ten times in the year. For the sake of simplicity we shall assume in all the following examples that the circulating constant capital turns over in the same period as the variable, which will generally be the case in practice. The product of such a turnover period will then be:
100c (depreciation) + 500c + 500ν + 500s = 1,600,
and the product of the whole year, with ten turnovers:
1,000c (depreciation) + 5,000c + 5,000ν + 5,000s = 16,000;
C = 11,000, s = 5,000, p′ = 5,000/11,000 = 45 5/11 per cent.
Let us now take a capital II: fixed capital 9,000 with annual depreciation 1,000, circulating constant capital 1,000, variable capital 1,000, rate of surplus-value 100 per cent, turnovers of variable capital five per year. The product of one of these turnover periods of the variable capital will then be:
200c (depreciation) + 1,000c + 1,000, + 1,000, = 3,200,
and the total annual product over five turnovers:
1,000c (depreciation) + 5,000c + 5,000, + 5,000s = 16,000;
C = 11,000, s = 5,000, p′ = 5,000/11,000 = 45 5/11 per cent.
We may also take a capital III in which there is no fixed capital, but simply 6,000 circulating constant capital and 5,000 variable capital. It turns over once a year, say, with a rate of surplus-value of 100 per cent. The total annual product is then:
6,000c + 5,000ν + 5,000s = 16,000;
C = 11,000, s = 5,000, p′ = 45 5/11 per cent.
In all three cases, therefore, we have the same annual mass of surplus-value = 5,000, and since the total capital is the same in all these cases, i.e. 11,000, we have the same profit rate of 45 per cent.
If in the case of the above capital I there took place not ten but only five turnovers of its variable portion, the matter would be different. The product of one turnover would then be:
200c (depreciation) + 500c + 500e + 500s = 1,700;
or the annual product:
1,000c (depreciation) + 2,500c + 2,500ν + 2,500s = 8,500;
C = 11,000, s = 2,500, p′ = 2,500/11,000 = 22 8/11 per cent.
The profit rate has now fallen by half, as the turnover time has doubled.
The mass of surplus-value appropriated in the course of a year is therefore equal to the mass of surplus-value appropriated in one turnover period of the variable capital, multiplied by the number of such turnovers in a year. If we call the surplus-value or profit annually appropriated S, the surplus-value appropriated in one turnover period s, and the number of turnovers made by the variable capital in a year n, then S = sn and the annual rate of surplus-value S′ = s′n, as already set out in Volume 2, Chapter 16, 1.
It goes without saying that the formula for the profit rate p′ = s′ ν/C = s′ ν/c + ν is correct only if the v in the numerator is the same as that in the denominator. The v in the denominator is the entire part of the total capital that is spent on average as variable capital, on wages. The v in the numerator is initially determined simply by the fact that a certain quantity of surplus-value = s has been produced and appropriated by it, related to it by the rate of surplus-value s′, which equals s/ν. It is only in this way that the equation p′ = s/c + ν was transformed into the equation p′ = s′ ν/c + ν. The v in the numerator can now be more accurately defined by the condition that it must be equal to the v in the denominator, i.e. to the entire variable part of the capital C. In other words, the equation p′ = s/C can be transformed into p′ = s′ ν/c + ν without risk of error only if s stands for the surplus-value produced in a single turnover period of the variable capital. If s comprises only a part of this surplus-value, s = s′v is still correct, but this v is now smaller than the v in C = c + v, as it is smaller than the whole of the variable capital that is laid out on wages. But if s comprises more than the surplus-value of one turnover of v, a part of this v or even the whole of it functions twice, firstly in the first turnover, then in the second or further turnovers; the v that produces surplus-value and is the sum of all wages paid is thus greater than the v in c + v, and the calculation is false.
In order that the formula for the annual rate of profit may be completely correct, we must replace the simple rate of surplus-value with the annual rate, S′ or s′n in place of s′. In other words, we must multiply s′, the rate of surplus-value – or else multiply the v, the variable capital v contained in C – by n, the number of turnovers that this variable capital makes in a year, and we then obtain p′ = s′nc̄, the formula for calculating the annual rate of profit.
The capitalist himself does not know in most cases how much variable capital he employs in his business. We have already seen in Chapter 8 of Volume 2, and we shall now see further, that the only distinction within his capital that impresses itself on the capitalist as fundamental is the distinction between fixed and circulating capital. From the same till that contains the part of his circulating capital that exists in his hands in the money form, in so far as this is not placed in the bank, he fetches both money for wages and money for raw and ancillary materials, and enters both of these in the same cash account. Even if he were to keep a separate record for wages paid, this would simply indicate the total sum paid at the end of the year, i.e. vn, and not the variable capital v itself. In order to arrive at this sum he would have to make a special calculation, such as is given in the following example.
Let us take the spinning mill described in Volume 1 [Chapter 9, 1, pp. 327–8], with its 10,000 spindles, and assume that the data given for one week in April 1871 are the same for the whole year. The fixed capital in the form of machinery was £10,000. The circulating capital was not given; we shall take it to be £2,500, a fairly high figure, but one that is justified by the assumption we must constantly make at this stage, that there are no credit operations, i.e. no permanent or temporary use of other people’s capital. The week’s product was composed, as far as its value was concerned, of £20 for depreciation of machinery, £358 advance of circulating constant capital (rent £6, cotton £342, coal, gas and oil £10), £52 laid out as variable capital on wages, and £80 surplus-value, i.e. 20c (depreciation) + 358c + 52ν + 80s = 510.
The weekly advance of circulating capital was therefore 358 c + 52ν = 410, and its percentage composition 87.3C + 12.7ν.* Calculated on the whole circulating capital of £2,500, this gives a constant capital of £2,182 and a variable capital of £318. Since the total outlay on wages for the whole year comes to 52 times £52, i.e. £2,704, the upshot is that the variable capital of £318 has turned over almost exactly 8½ times in the course of the year. The rate of surplus-value is 80/52 = 153 11/13 per cent. From these elements we can calculate the rate of profit by using the formula p′ = s′n ν/C, with s′ = 153 11/13, n = 8 1/2, ν = 318, C = 12,500. The result is that p′ = 153 11/13 × 8 1/2 × 318/12,500 = 33.27 per cent.
We can test this by using the simple formula p′c̄. The total surplus-value or profit over the whole year amounts to £80 × 52 = £4,160, and this divided by the total capital of £12,500 gives 33.28 per cent, pretty well the same figure as above. This is an abnormally high rate of profit, which can only be explained by extremely favourable temporary conditions (very cheap cotton prices combined with very high prices for yarn) and would certainly not have prevailed for a whole year in actual fact.
In the formula p′ = s′n ν/c, s′ n, as already stated, is what was designated in Volume 2 as the annual rate of surplus-value. In the above case it amounts to 153 11/13 per cent. If a certain worthy was shocked by the enormous size of the annual rate of surplus-value of 1,000 per cent given in one of the examples in Volume 2, he can perhaps console himself with the actual fact of an annual rate of surplus-value of more than 1,300 per cent taken from a practical example in Manchester. In periods of greatest prosperity, such as we have of course not seen now for a long while, a rate of this level is by no means rare.
We have here incidentally an example of the actual composition of capital in modern large-scale industry. The total capital is divided into £12,182 constant and £318 variable, making £12,500 altogether. In percentages, 97 1/2c + 2 1/2ν = 100C. Only a fortieth part of the total is needed for the payment of wages, though this serves more than eight times in the course of a year.
Since there are certainly only a few capitalists who make calculations of such a kind about their businesses, statistical material is almost completely absent on the ratio of the constant part o the total social capital to the variable part. Only the U.S. Census gives what is possible under present-day conditions, the sum of the wages paid in each branch of business and the profits made. Dubious as these data are, owing to the way they rely on the unchecked information of the industrialists themselves, they are none the less extremely valuable and the only data that we have on the subject. In Europe we are far too kind-hearted to expect such revelations on the part of our great industrialists. – F.E.)