Capital Vol. III Part I

The Conversion of Surplus-Value into Profit and of the Rate of Surplus-Value into the Rate of Profit

The effect of the turnover on the production of surplus-value, and consequently of profit, has been discussed in Book II. Briefly summarised it signifies that owing to the time span required for turnover, not all the capital can be employed all at once in production; some of the capital always lies idle, either in the form of money-capital, of raw material supplies, of finished but still unsold commodity-capital, or of outstanding claims; that the capital in active production, i.e., in the production and appropriation of surplus-value, is always short by this amount, and that the produced and appropriated surplus-value is always curtailed to the same extent. The shorter the period of turnover, the smaller this idle portion of capital as compared with the whole, and the larger, therefore, the appropriated surplus-value, provided other conditions remain the same.

It has already been shown in detail in Book II [English edition: Vol. II,
pp. 293-98. — *Ed*.] how the quantity of produced surplus-value is
augmented by reductions in the period of turnover, or of one of its two
sections, in the time of production and the time of circulation. But since the
rate of profit only expresses the relation of the produced quantity of
surplus-value to the total capital employed in its production, it is evident
that any such reduction increases the rate of profit. Whatever has been said
earlier in Part II of Book II in regard to surplus-value, applies equally to
profit and the rate of profit and needs no repetition here. We wish only to
stress a few of the principal points.

The chief means of reducing the time of production is higher labour productivity, which is commonly called industrial progress. If this does not involve a simultaneous considerable increase in the outlay of total capital resulting from the installation of expensive machinery, etc., and thus a reduction of the rate of profit, which is calculated on the total capital, this rate must rise. And this is decidedly true in the case of many of the latest improvements in metallurgy and in the chemical industry. The recently discovered methods of producing iron and steel, such as the processes of Bessemer, Siemens, Gilchrist-Thomas, etc., cut to a minimum at relatively small costs the formerly arduous processes. The making of alizarin, a red dye-stuff extracted from coal-tar, requires but a few weeks, and this by means of already existing coal-tar dye-producing installations, to yield the same results which formerly required years. It took a year for the madder to mature, and it was customary to let the roots grow a few years more before they were processed.

The chief means of reducing the time of circulation is improved
communications. The last fifty years have brought about a revolution in this
field, comparable only with the industrial revolution of the latter half of the
18th century. On land the macadamised road has been displaced by the railway, on
sea the slow and irregular sailing vessel has been pushed into the background by
the rapid and dependable steamboat line, and the entire globe is being girdled
by telegraph wires. The Suez Canal has fully opened East Asia and Australia to
steamer traffic. The time of circulation of a shipment of commodities to East
Asia, at least twelve months in 1847 (cf. Buch II, S. 235 [English edition: Karl
Marx, *Capital*, Vol. II, pp. 251-52. — *Ed*.]), has now been
reduced to almost as many weeks. The two large centres of the crises of 1825-57,
America and India, have been brought from 70 to 90 per cent nearer to the
European industrial countries by this revolution in transport, and have thereby
lost a good deal of their explosive nature. The period of turnover of the total
world commerce has been reduced to the same extent, and the efficacy of the
capital involved in it has been more than doubled or trebled. It goes without
saying that this has not been without effect on the rate of profit.

To single out the effect of the turnover of total capital on the rate of
profit we must assume all other conditions of the capitals to be compared as
equal. Aside from the rate of surplus-value and the working-day it is also
notably the per cent composition which we must assume to be the same. Now let us
take a capital A composed of 80_{c} + 20_{v} = 100 C, which makes two turnovers yearly at
a rate of surplus-value of 100%. The annual product is then:

160_{c} + 40_{v} + 40_{s}. However, to determine the rate of profit we do not calculate
the 40s on the turned-over capital-value of 200, but on the advanced capital of
100, and thus obtain p' = 40%.

Now let us compare this with a capital B = 160_{c} + 40_{v} = 200 C, which has the same
rate of surplus-value of 100%, but which is turned over only once a year. The
annual product of this capital is, therefore, the same as that of A:

160_{c} + 40_{v} + 40_{s}. But this time the 40s are to be calculated on an advance of
capital amounting to 200, which yields a rate of profit of only 20%, or one-half
that of A.

We find, then, that for capitals with an equal per cent composition, with equal rates of surplus-value and equal working-days, the rates of profit of the two capitals are related inversely as their periods of turnover. If either the composition, the rates of surplus-value, the working-day, or the wages, are unequal in the two compared cases, this would naturally produce further differences in the rates of profit; but these are independent of the turnover and, for this reason, do not concern us at this point. They have already been discussed in Chapter III.

The direct effect of a reduced period of turnover on the production of surplus-value, and consequently of profit, consists of an increased efficiency imparted thereby to the variable portion of capital, as shown in Book II, Chapter XVI, "The Turnover of Variable Capital". This chapter demonstrated that a variable capital of 500 turned over ten times a year produces as much surplus-value in this time as a variable capital of 5,000 with the same rate of surplus-value and the same wages, turned over just once a year.

Take capital I, consisting of 10,000 fixed capital whose annual depreciation is 10% = 1,000, of 500 circulating constant and 500 variable capital. Let the variable capital turn over ten times per year at a 100% rate of surplus-value. For the sake of simplicity we assume in all the following examples that the circulating constant capital is turned over in the same time as the variable, which is generally the case in practice. Then the product of one such period of turnover will be:

100_{c} (depreciation) + 500_{c} + 500_{v} + 500_{s} = 1,600

and the product of one entire year, with ten such turnovers, will be

1,000_{c} (depreciation) + 5,000_{c} + 5,000_{v} + 5,000_{s} = 16,000,

C = 11,000, s = 5,000, p' = 5,000/11,000 = 45 5/11 %.

Now let us take capital II: 9,000 fixed capital, 1,000 annual wear and tear, 1,000 circulating constant capital, 1,000 variable capital, 100% rate of surplus-value, 5 turnovers of variable capital per year. Then the product of each of the turnovers of the variable capital will be:

200_{c} (depreciation) + 1,000_{c} + 1,000_{v} + 1,000_{s} = 3,200,

and the total annual product after five turnovers:

1,000_{c} (depreciation) + 5,000_{c} + 5,000_{v} + 5,000_{s} = 16,000,

C = 11,000, s = 5,000, p' = 5,000/11,000 = 45 5/11 %

Further, take capital III with no fixed capital, 6,000 circulating constant capital and 5,000 variable capital. Let there be one turnover per year at a 100% rate of surplus-value. Then the total annual product is:

6,000_{c} + 5,000_{v} + 5,000_{s} = 16,000,

C = 11,000, s = 5,000, p' = 5,000/11,000 = 45 5/11%.

In all the three cases we therefore have the same annual quantity of surplus-value = 5,000, and, since the total capital is likewise equal in all three cases, namely = 11,000, also the same rate of profit of 45 5/11%.

But should capital I have only 5 instead of 10 turnovers of its variable part per year, the result would be different. The product of one turnover would then be:

200_{c} (depreciation) + 500_{c} + 500_{v} + 500_{s} = 1,700.

And the annual product:

1,000_{c} (depreciation) + 2,500_{c} + 2,500_{v} + 2,500_{s} = 8,500,

C = 11,000, s = 2,500; p' = 2,500/11,000 = 22 8/11%.

The rate of profit has fallen one-half, because the period of turnover has doubled.

The quantity of surplus-value appropriated in one year is therefore equal to
the quantity of surplus-value appropriated in one turnover of the *variable*
capital multiplied by the number of such turnovers per year. Suppose we call the
surplus-value, or profit, appropriated in one year S, the surplus-value
appropriated in one period of turnover s, the number of turnovers of the
variable capital in one year n, then S = sn, and the annual rate of surplus-value
S' = s'n, as already demonstrated in Book II, Chapter XVI, I. [English edition:
Vol. II, p. 305. — *Ed*.]

It goes without saying that the formula p' = s' (v/C) = s' v/(c + v) is correct only so long as the v in the numerator is the same as that in the denominator. In the denominator v stands for the entire portion of the total capital used on an average as variable capital for the payment of wages. The v of the numerator is primarily only determined by the fact that a certain quantity of surplus-value = s is produced and appropriated by it, whose relation to it s/v, is m', the rate of surplus-value. It is only along these lines that the formula p' = s/(c + v) is transformed into the other: p' = s' v/(c + v). The v of the numerator will now be more accurately determined by the fact that it must equal the v of the denominator, that is, the entire variable portion of capital C. In other words, the equation p' = (s/C) may be correctly transformed into the equation p' = s' v/(c + v) only if s stands for surplus-value produced in one turnover of the variable capital. Should s be only a portion of this surplus-value, then s = s'v is still correct, but this v is then smaller than the v in C = c + v, because it is smaller than the entire variable capital expended for wages. But should s stand for more than the surplus-value of one turnover of v, then a portion of this v, or perhaps the whole of it, serves twice, namely in the first and in the second turnover, and eventually in subsequent turnovers. The v which produces the surplus-value and represents the sum of all paid wages, is therefore greater than the v in c + v and the calculation falls into error.

To make the formula precise for the annual rate of profit, we must substitute the annual rate of surplus-value for the simple rate of surplus-value, that is, substitute S' or s'n for s'. In other words, we must multiply the rate of surplus-value s', or, what amounts to the same thing, the variable capital v contained in C, by n, the number of turnovers of this variable capital in one year. Thus we obtain p' = s'n (v/C), which is the formula for the annual rate of profit.

The amount of variable capital invested in his business is something the capitalist himself does not know in most cases. We have seen in Chapter VIII of Book II, and shall see further along, that the only essential distinction within his capital which impresses itself upon the capitalist is that of fixed and circulating capital. He takes money to pay wages from his cash-box containing the part of the circulating capital he has on hand in the form of money, so far as it is not deposited in a bank; he takes money from the same cash-box for raw and auxiliary materials, and credits both items to the same cash-account. And even if he should keep a separate account for wages, at the close of the year this would only show the sum paid out for this item, hence vn, but not the variable capital v itself. In order to ascertain this, he would have to make a special calculation, of which we propose here to give an illustration.

For this purpose we select the cotton spinnery of 10,000 mule spindles
described in Book I (S. 209/201) [English edition: p. 219. — *Ed*.] and
assume that the data given there for one week of April 1871, are in force during
the whole year. The fixed capital incorporated in the machinery was £10,000.
The circulating capital was not given. We assume it to have been £2,500.
This is a rather high estimate, but justified by the assumption, which we must
always make here, that no credit operations were effected, hence no permanent or
temporary employment of other people's capital. The value of the weekly product
was composed of £20 for depreciation of machinery, £358 circulating
constant advanced capital (rent £6; cotton £342; coal, gas, oil, £10),
£52 variable capital paid out for wages, and £80 surplus-value.
Therefore,

20_{c} (depreciation) + 358_{c} + 52_{v} + 80_{s} = 510.

The weekly advance of circulating capital therefore was 358_{c} + 52_{v} = 410. In
terms of per cent this was 87.3_{c} + 12.7_{v}. For the entire circulating capital of £2,500
this would be £2,182 constant and £318 variable capital. Since the
total expenditure for wages in one year was 52 times £52, or £2,704,
it follows that in a year the variable capital of £318 was turned over
almost exactly 8½ times. The rate of surplus-value
was 80/52 = 153
11/13. We calculate the rate of profit on the basis of
these elements by inserting the above values in the formula p' = s'n (v/C) : s' = 153
11/13, n = 8½, v = 318, C = 12,500; hence:

p' = 153 11/13 × 8½ × 318/12,500 = 33.27%.

We test this by means of the simple formula p' = (s/C). The total annual surplus-value or profit amounts to 52 times £80, or £4,160, and this divided by the total capital of £12,500 gives us 33.28%, or almost an identical result. This is an abnormally high rate of profit, which may only be explained by extraordinarily favourable conditions of the moment (very low prices of cotton along with very high prices of yarn), and could certainly not have obtained throughout the year.

The s'n in the formula p' = s'n (v/C) stands, as has been said, for the thing
called in Book II [English edition: Vol. II, p. 295. — *Ed*.] the annual
rate of surplus-value. In the above case it is 153 11/13%
multiplied by 8½ or in exact figures, 1,307 9/18%.
Thus, if a certain Biedermann [Biedermann — Philistine. A pun, being also the
name of the editor of the
*Deutsche Allgemeine Zeitung*. — *Ed*.] was shocked by the abnormity
of an annual rate of surplus-value of 1,000% used as an illustration in Book II,
he will now perhaps be pacified by this annual rate of surplus-value of more
than 1,300% taken from the living experience of Manchester. In times of greatest
prosperity, such as we have not indeed seen for a long time, such a rate is by
no means a rarity.

For that matter we have here an illustration of the actual composition of capital in modern large-scale industry. The total capital is broken up into £12,182 constant and £318 variable capital, a sum of £12,500. In terms of percent this is 97½c + 2½v = 100 C. Only one-fortieth of the total, but in more than an eight-fold annual turnover, serves for the payment of wages.

Since very few capitalists ever think of making calculations of this sort
with reference to their own business, statistics is almost completely silent
about the relation of the constant portion of the total social capital to its
variable portion. Only the American census gives what is possible under modern
conditions, namely the sum of wages paid in each line of business and the
profits realised. Questionable as they may be, being based on the capitalist's
own uncontrolled statements, they are nevertheless very valuable and the only
records available to us on this subject. [In Europe we are far too delicate to
expect such revelations from our major capitalists. — *F.E*.]

*Transcribed for the Internet by Hinrich Kuhls*