Capital: A Critique of Political Economy, Vol. III. The Process of Capitalist Production as a Whole

Karl Marx
Marx, Karl
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Frederick Engels, ed. Ernest Untermann, trans.
First Pub. Date
Chicago: Charles H. Kerr and Co.
Pub. Date
Das Kapital, based on the 1st edition.

Part I, Chapter IV


THE effect of the turn-over on the production of surplus-value, and consequently of profit, has been discussed in volume II. It may be briefly summarized in the statement that the entire capital cannot be employed all at once in production, because the turn-over requires a certain lapse of time; for this reason a portion of the capital is always lying fallow, either in the form of money-capital, of a supply of raw materials, of finished but still unsold commodity-capital, or of outstanding bills not yet due; hence the capital active in the production and appropriation of surplus-value is always short by this amount, and the production and appropriation of surplus-value is curtailed to that extent. The shorter the period of turn-over, the smaller is the fallow portion of capital as compared with the whole, and the larger will be the appropriated surplus-value, other conditions remaining the same.


It has been shown explicitly in the second volume to what extent the mass of the produced surplus-value is augmented by the reduction of the period of turn-over, or of one of its two sections, the time of production and the time of circulation. But it is evident that any such reduction increases the rate of profit, since this rate expresses but the mass of surplus-value produced in proportion to the total capital employed in production. Whatever has been said in the second part of the second volume in regard to surplus-value, applies just as well to profit and the rate of profit, and requires no repetition at this place. We shall touch only upon a few of the principal points.


A reduction of the time of production is mainly due to an increase in the productivity of labor, a thing commonly called the progress of industry. If this does not require at once a considerable extra-outlay of capital for 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 the case with many of the latest improvements in metallurgy and chemical industry. The recently discovered methods of making iron and steel, such as the processes of Bessemer, Siemens, Gilchrist-Thomas, etc., shorten formerly tedious processes to a minimum with relatively small expense. The making of alizarin, a red coloring substance extracted from coal-tar, produces in a few weeks, by the help of already existing installations for the manufacture of coal-tar colors, the same results which formerly required years. It took at least one year to mature the plants from which this coloring matter was formerly extracted, and it was customary to let them grow a few years before the roots were used for the purpose of making color.


The time of circulation is reduced principally by improved means of communication. In this respect the last fifty years have brought about a revolution, which can be compared only with the industrial revolution of the last half of the eighteenth century. On land the macademized road has been displaced by the railroad, on sea the slow and irregular sailing vessel by the rapid and regular steamboat line, and the entire globe has been circled by telegraph wires. The Suez Canal has fully opened Eastern Asia and Australia for steamer traffic. The time of circulation of a shipment of commodities to Eastern Asia was at least twelve months as late as 1847, and it has now been reduced to almost as many weeks. The two large centers of commercial crises, 1825-1857, America and India, have been brought from 70 to 90 per cent. nearer to Europe by this revolution of the means of communication, and have thereby lost a good deal of their explosive nature. The period of turn-over of the world's commerce has been reduced to the same extent, and the productive capacity of the capital engaged in it has been doubled or trebled. It goes without saying that this has not been without effect on the rate of profit.


In order to view the effect of the turn-over of the total capital on the rate of profit in its purest form, it is necessary to assume all other conditions of two compared capitals as equal. Aside from the rate of surplus-value and the working day it is especially the percentages of composition which we assume to be the same. Now let us select a capital A composed of 80 c + 20 v = 100 C. Let this have a rate of surplus-value of 100%, and let it be turned over twice per year.


The annual product is then 160 c + 40 v + 40 s. But for the purpose of ascertaining the rate of profit we do not calculate the 40 s on the turned-over capital-value of 200. We calculate it on the advanced capital of 100, and we obtain thus a rate of profit of 40%.


Now let us compare this with a capital B composed of 160 c + 40 v = 200 C, which has the same rate of surplus-value, 100%, but which is turned over only once a year.


The annual product of this capital is the same as that of A, namely 160 c + 40 v + 40 s. But the 40 s in this case are to be calculated on an advance of capital amounting to 200, so that the rate of profit of B is only 20%, or one-half that of A.


We find, then, that with capitals with equal percentages of composition, equal rates of surplus-value, and equal working days, the rates of profit are proportioned inversely as their periods of turn-over. If either the composition, or the rates of surplus-value, or the working day, or the wages, are unequal in the two compared cases, then other differences are naturally produced in the rates of profit. But these are not directly dependent on the turn-over, and do not concern us at this point. They have already been discussed in chapter III.


The direct effect of a reduced period of turn-over on the production of surplus-value, and consequently of profit, consists in the increased effectiveness given thereby to the variable portion of capital, as shown in volume II, chapter XVI, The Turn-Over of Variable Capital. It was demonstrated in that chapter that a variable capital of 500, which is turned over ten times per year, produces during this time as much surplus-value as a variable capital of 5,000 with the same rate of surplus-value and the same wages, turned over once a year.


Take a capital (I) consisting of 10,000 fixed capital, with an annual wear and tear of 10%, or 1,000, furthermore of 500 circulating constant and 500 variable capital. Let the rate of surplus-value be 100%, and let the variable capital be turned over ten times per year. For the sake of simplicity we assume in all 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 turn-over will be

100 c (wear) + 500 c + 500 v + 500 s = 1,600.


And the product of one entire year, with ten such turn-overs, will be

1,000 c (wear) + 5,000 c + 5,000 v + 5,000 s = 16,000.

Then C is 11,000, s is 5,000, p' is 5000/11000, or 45 5/11%.


Now let us take another capital (II), composed of 9,000 fixed capital, with an annual wear and tear of 1,000, circulating constant capital 1,000, variable capital 1,000, rate of surplus-value 100%, number of annual turn-overs of variable capital 5. Then the product of each one of these turn-overs of the variable capital will be

200 c (wear) + 1,000 c + 1,000 v + 1,000 s = 3,200.

And the annual product (of all five turn-overs) will be

1,000 c (wear) + 5,000 c + 5,000 v + 5,000 s = 16,000.

Then C is 11,000, s is 5,000, and p' is 5000/11000, or 45 5/11%.


Take furthermore a third capital (III) with no fixed capital, 6,000 circulating constant capital, and 5,000 variable capital. Let the rate of surplus-value be 100%, and let there be one turn-over per year. Then the total product of one year is

6,000 c + 5,000 v + 5,000 s = 16,000.

C is 11,000, s is 5,000, and p' is 5000/11000, or 45 5/11%.


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


But now let us assume that capital (I) has only 5 instead of 10 turn-overs of its variable capital per year. In that case the outcome is different. The product of one turn-over is then 200 c (wear) + 500 c + 500 v + 500 s = 1,700. And the product of one year is

1,000 c (wear) + 2,500 c + 2,500 v + 2,500 s = 8,500.

C is 11,000, s is 2,500, p' is 2500/11000, or 22 8/11%. The rate of profit has fallen by one-half, because the time of turn-over has been doubled.


The amount of surplus-value appropriated during one year is therefore equal to the mass of surplus-value appropriated during one turn-over of the variable capital multiplied by the number of such turn-overs per year. If we call the surplus-value, or profit, appropriated during one year S, the surplus-value appropriated during one period of turn-over of the variable capital s, the number of turn-overs of the variable capital in one year n, then S = sn, and the annual rate of surplus-value S' = s'n, as demonstrated in Volume II, chapter XVI, I.


It is understood that the formula p' = s' v/c = s' v/c+v is correct only so long as the v of the numerator is the same as that of 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. In the numerator, v is determined in the first place by the fact that a certain amount of surplus-value s is produced and appropriated by it. The proportion of this surplus-value to the variable capital, s/v, constitutes the rate of surplus-value. It is only in this way that the formula p' = s/c+v is transformed into p' = s' v/c+v. Now the v of the numerator is more definitely described by stating that it must be equal to the v of the denominator, that is to say equal to the entire variable capital of C. In other words, the equation p' = s/C can be transformed into the equation p' = s' v/c+v only in the case that s stands for the surplus-value produced in one turn-over of the variable capital. If s stands for 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 less than the entire variable capital has been employed in the payment of wages. On the other hand, if s stands for more than the surplus-value of one turn-over of v, then a portion of this v, or perhaps the whole, serves twice, namely in the first and in the second turn-over, and eventually it may serve in the subsequent turn-overs. The v which produces the surplus-value, and which represents the sum of all paid wages, is then greater than the v in c + v and the calculation becomes wrong.


In order that the formula for the annual rate of profit may be exact, we must substitute the annual rate of surplus-value for the simple rate of surplus-value, we must 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, the variable capital v contained in C, with n, the number of turn-overs of this variable capital in one year. Thus we obtain p' = s'n v/C, which is the formula for the calculation of the annual rate of profit.


In most cases the capitalist himself does not know the amount of variable capital invested in his business. We have seen in chapter VIII of volume II, and shall see further along, that the only distinction which forces itself upon the capitalist within his capital is that of fixed and circulating capital. From the cash-box containing the money-part of the circulating capital in his hands, so far as it is not deposited in a bank, he takes the money to pay wages, and from the same cash-box he takes the money for raw and auxiliary materials. And he credits both expenditures to the same cash account. And even if he should keep a separate account for wages, it would show at the end of the year the amounts paid out for wages, that is 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 to give an illustration.


We select for this purpose the cotton spinnery of 10,000 mule spindles described in volume I. We assume that the data there given for one week of April, 1871, are in force during the whole year. The fixed capital incorporated in the machinery was valued at 10,000 The circulating capital was not given. We assume it to have been 2,500 This is a rather high estimate, but it is justified by the assumption, which we must always make in this discussion, that no credit was in force, in other words, no permanent or temporary employment of other people's capital. The value of the weekly product was composed of 20 for wear of machinery, 358 of circulating constant capital (rent 6, cotton 342, coal, gas, oil, 10, 52 of variable capital paid out for wages, and 80 of surplus-value. The formula was, therefore

20 c (wear) + 358 c + 52 v + 80 s = 510.


The weekly advance of circulating capital consisted therefore of 358 c + 52 v = 410, and its percentages of composition were 87.3 c + 12.7 v. Calculating the entire circulating capital of 2,500, on this basis, we obtain 2,182 of constant and 318 of variable capital. Since the total expenditure for wages in one year was 52 times 52, or 2,704, it follows that the variable capital of 318 was turned over almost exactly 8½ times in one year. The rate of surplus-value was 80/52, or 153 11/13%. We calculate the rate of profit from these elements by inserting the above values in the formula p' = s'n v/C. Since s' is 153 11/13, n is 8½ v is 318, and C is 12,500, we have

p' = 153 11/13 × 8½ × 818/12,500 = 33.27%.


We test this result by means of the simple formula p' = s/C. The total surplus-value or profit, of one year amounts to 52 times 80, or 4,160 Dividing this by the total capital of 12,500, we obtain 33.28%, or almost the identical result. This is an abnormally high rate of profit, due to the extraordinarily favorable conditions of the moment (very low prices of cotton and very high prices of yarn). In reality this rate was certainly not maintained throughout the year.


The term s'n in the formula p' = s'n v/c stands for the same thing which was called the annual rate of surplus-value in volume II. In the above case it is 153 11/13% multiplied by 8½, or in exact figures 1,307 9/13%. A certain brave soul was shocked to the point of speechlessness over the abnormity of an annual rate of profit of 1,000%, which had been used as an illustration in that volume. Perhaps he will now settle down peacefully and contemplate this annual rate of surplus-value of more than 1,300% taken from the practical life of Manchester. In times of greatest prosperity, such as we have not seen for a long time, a similar rate is by no means rare.


By the way, this is an illustration of the actual composition of capital in modern great industry. The total capital is divided into 12,182 of constant and 318 of variable capital, a total of 12,500 In percentages this is 97½ c + 2½ v = 100 C. Only one-fortieth of the total capital serves for the payment of wages, but it is turned over eight times during the year.


Since very few capitalists take the trouble of making similar calculations with reference to their own business, the science of statistics is almost completely silent regarding the proportion 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 amount of wages paid in each line of business and the profits realized. These data are, of course, very doubtful, because they are based on uncontrollable statements of the capitalists, but they are nevertheless very valuable, and the only records available on this subject. In Europe we are far too delicate to expect such revelations from our great capitalists.—F. E.]

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