# Das Kapital (Moore, 1906)/Chapter 11

Capital by Karl Marx, edited by Frederick Engels, translated by
Chapter XI.—Rate and Mass of Surplus-Value

CHAPTER XI.

rate and mass of surplus-value.

In this chapter, as hitherto, the value of labour-power, and therefore the part of the working-day necessary for the reproduction or maintenance of that labour-power, are supposed to be given constant magnitudes.

This premised with the rate, the mass is at the same time given of the surplus-value that the individual labourer furnishes to the capitalist in a definite period of time. If, e.g., the necessary labour amounts to 6 hours daily, expressed in a quantum of gold = 3 shillings, then 3s. is the daily value of one labour-power or the value of the capital advanced in the buying of one labour-power. If, further, the rate of surplus-value be = 100%, this variable capital of 3s. produces a mass of surplus-value of 3s., or the labourer supplies daily a mass of surplus-labour equal to 6 hours.

But the variable capital of a capitalist is the expression in money of the total value of all the labour-powers that he employs simultaneously Its value is, therefore, equal to the average value of one labour-power, multiplied by the number of labour-powers employed. With a given value of labour-power, therefore, the magnitude of the variable capital varies directly as the number of labourers employed simultaneously. If the daily value of one labour-power = 3s., then a capital of 300s. must be advanced in order to exploit daily 100 labour-powers, of n times 3s., in order to exploit daily n labour-powers.

In the same way, if a variable capital of 3s., being the daily value of one labour-power, produce a daily surplus-value of 3s., a variable capital of 300s. will produce a daily surplus-value of 300s., and one of n times 3s. a daily surplus-value of n × 3s. The mass of the surplus-value produced is therefore equal to the surplus-value which the working-day of one labourer supplies multiplied by the number of labourers employed. But as further the mass of surplus-value which a single labourer produces, the value of labour-power being given, is determined by the rate of the surplus-value, this law follows: the mass of the surplus-value produced is equal to the amount of the variable capital advanced, multiplied by the rate of surplus-value; in other words: it is determined by the compound ratio between the number of labour-powers exploited simultaneously by the same capitalist and the degree of exploitation of each individual labour-power.

Let the mass of the surplus-value be S, the surplus-value supplied by the individual labourer in the average day s, the variable capital daily advanced in the purchase of one individual labour-power v, the sum total of the variable capital V, the value of an average labour-power P, its degree of exploitation a′ (surplus-labor)a (necessary-labor) and the number of labourers employed n; we have:

 S = ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}}$ sv×V P×a′a×n

It is always supposed, not only that the value of an average labour-power is constant, but that the labourers employed by a capitalist are reduced to average labourers. There are exceptional cases in which the surplus-value produced does not increase in proportion to the number of labourers exploited, but then the value of the labour-power does not remain constant.

In the production of a definite mass of surplus-value, therefore, the decrease of one factor may be compensated by the increase of the other. If the variable capital diminishes, and at the same time the rate of surplus-value increases in the same ratio, the mass of surplus-value produced remains unaltered. If on our earlier assumption the capitalist must advance 300s., in order to exploit 100 labourers a day, and if the rate of surplus-value amounts to 50%, this variable capital of 300s. yields a surplus-value of 150s. or of 100×3 working hours. If the rate of surplus-value doubles, or the working day, instead of being extended from 6 to 9, is extended from 6 to 12 hours and at the same time variable capital is lessened by half, and reduced to 150s., it yields also a surplus-value of 150s. or 50×6 working hours. Diminution of the variable capital may therefore be compensated by a proportionate rise in the degree of exploitation of labour-power, or the decrease in the number of the labourers employed by a proportionate extension of the working-day. Within certain limits therefore the supply of labour exploitable by capital is independent. of the supply of labourers.[1] On the contrary, a fall in the rate of surplus-value leaves unaltered the mass of the surplus-value produced, if the amount of the variable capital, or number of the labourers employed, increases in the same proportion.

Nevertheless, the compensation of a decrease in the number of labourers employed, or of the amount of variable capital advanced, by a rise in the rate of surplus-value, or by the lengthening of the working-day, has impassable limits. Whatever the value of labour-power may be, whether the working time necessary for the maintenance of the labourer is 2 or 10 hours, the total value that a labourer can produce, day in, day out, is always less than the value in which 24 hours of labour are embodied, less than 12s., if 12s. is the money expression for 24 hours of realized labour. In our former assumption, according to which 6 working hours are daily necessary in order to reproduce the labour-power itself or to replace the value of the capital advanced in its purchase, a variable capital of 1500s., that employs 500 labourers at a rate of surplus-value of 100% with a 12 hours’ working-day, produces daily a surplus-value of 1500s. or of 6500 working hours. A capital of 800s. that employs 100 labourers a day with a rate of surplus-value of 200% or with a working-day of 18 hours, produces only a mass of surplus-value of 600s. or 12×100 working hours; and its total value-product, the equivalent of the variable capital advanced plus the surplus-value, can, day in, day out, never reach the sum of 1200s. or 24×100 working hours. The absolute limit of the average working-day—this being by Nature always less than 24 hours—sets an absolute limit to the compensation of a reduction of variable capital by a higher rate of surplus-value, or of the decrease of the number of labourers exploited by a higher degree of exploitation of labour-power. This palpable law is of importance for the clearing up of many phenomena, arising from a tendency (to be worked out later on) of capital to reduce as much as possible the number of labourers employed by it, or its variable constituent transformed into labour-power, in contradiction to its. other tendency to produce the greatest possible mass of surplus-value. On the other hand, if the mass of labour-power employed, or the amount of variable capital, increases, but not in proportion to the fall in the rate of surplus-value, the mass of the surplus-value produced, falls.

A third law results from the determination, of the mass of the surplus-value produced, by the two factors: rate of surplus-value and amount of variable capital advanced. The rate of surplus-value, or the degree of exploitation of labour-power, and the value of labour-power, or the amount of necessary working time being given, it is self-evident that the greater the variable capital, the greater would be the mass of the value produced and of the surplus-value. If the limit of the working-day is given, and also the limit of its necessary constituent, the mass of value and surplus-value that an individual capital. ist produces, is clearly exclusively dependent on the mass of labour that he sets in motion. But this, under the conditions supposed above, depends on the mass of labour-power, or the number of labourers whom he exploits, and this number in its turn is determined by the amount of the variable capital advanced. With a given rate of surplus-value, and a given value of labour-power, therefore, the masses of surplus-value produced vary directly as the amounts of the variable capitals advanced. Now we know that the capitalist divides his capital into two parts. One part he lays out in means of production. This is the constant part of his capital. The other part he lays out in living labour-power. This part forms his variable capital. On the basis of the same mode of social production, the division of capital into constant and variable differs in different branches of production, and within the same branch of production, too, this relation changes with changes in the technical conditions and in the social combinations of the processes of production. But in whatever proportion a given capital breaks up into a constant and a variable part, whether the latter is to the former as 1:2 or 1:10 or 1:x, the law just laid down is not affected by this. For, according to our previous analysis, the value of the constant capital reappears in the value of the product, but does not enter into the newly produced value, the newly created value-product. To employ 1000 spinners, more raw material, spindles, &c., are, of course, required, than to employ 100. The value of these additional means of production however may rise fall, remain unaltered, be large or small; it has no influence on the process of creation of surplus-value by means of the labour-powers that put them in motion. The law demonstrated above now, therefore, takes this form: the masses of value and of surplus-value produced by different capitals—the value of labour-power being given and its degree of exploitation being equal—vary directly as the amounts of the variable constituents of these capitals, i.e., as their constituents transformed into living labour-power.

This law clearly contradicts all experience based on appearance. Every one knows that a cotton spinner, who, reckoning the percentage on the whole of his applied capital, employs much constant and little variable capital, does not, on account of this, pocket less profit or surplus-value than a baker, who relatively sets in motion much variable and little constant capital, or the solution of this apparent contradiction, many intermediate terms are as yet wanted, as from the standpoint of elementary algebra many intermediate terms are wanted to understand that may represent an actual magnitude. Classical economy, although not formulating the law, holds instinctively to it, because it is a necessary consequence of the general law of value. It tries to rescue the law from collision with contradictory phenomena by a violent abstraction. It will be seen later[2] how the school of Ricardo has come to grief over this stumbling-block. Vulgar economy which, indeed, “has really learnt nothing,” here as everywhere sticks to appearances in opposition to the law which regulates and explains them. In opposition to Spinoza, it believes that “ignorance is a sufficient reason.”

The labour which is set in motion by the total capital of a society, day in, day out, may be regarded as a single collective working-day. If, e.g., the number of labourers is a million, and the average working-day of a labourer is 10 hours, the social working-day consists of ten million hours. With a given length of this working-day, whether its limits are fixed physically or socially, the mass of surplus-value can only be increased by increasing the number of labourers, i.e., of the labouring population. The growth of population here forms the mathematical limit to the production of surplus-value by the total social capital. On the contrary, with a given amount of population, this limit is formed by the possible lengthening of the working-day.[3] It will, however, be seen in the following chapter that this law only holds for the form of surplus-value dealt with up to the present.

From the treatment of the production of surplus-value, so far, it follows that not every sum of money, or of value, is at pleasure transformable into capital. To effect this transformation, in fact, a certain minimum of money or of exchange-value must be presupposed in the hands of the individual possessor of money or commodities. The minimum of variable capital is the cost price of a single labour-power, employed the whole year through, day in, day out, for the production of surplus-value. If this labourer were in possession of his own means of production, and were satisfied to live as a labourer, he need not work beyond the time necessary for the reproduction of his means of subsistence, say 8 hours a day. He would, besides, only require the means of production sufficient for 8 working hours. The capitalist, on the other hand, who makes him do, besides these 8 hours, say 4 hours’ surplus-labour, requires an additional sum of money for furnishing the additional means of production. On our supposition, however, he would have to employ two labourers in order to live, on the surplus-value appropriated daily, as well as, and no better than a labourer, i.e., to be able to satisfy his necessary wants. In this case the mere maintenance of life would be the end of his production, not the increase of wealth; but this latter is implied in capitalist production. That he may live only twice as well as an ordinary labourer, and besides turn half of the surplus-value produced into capital, he would have to raise, with the number of labourers, the minimum of the capital advanced 8 times. Of course he can, like his labourer, take to work himself, participate directly in the process of production, but he is then only a hybrid between capitalist and labourer, a “small master.” A certain stage of capitalist production necessitates that the capitalist be able to devote the whole of the time during which he functions as a capitalist, i.e., as personified capital, to the appropriation and therefore control of the labour of others, and to the selling of the products of this labour.[4] The guilds of the middle ages therefore tried to prevent by force the transformation of the master of a trade into a capitalist, by limiting the number of labourers that could be employed by one master within a very small maximum. The possessor of money or commodities actually turns into a capitalist in such cases only where the minimum sum advanced for production greatly exceeds the maximum of the middle ages. Here, as in natural science, is shown the correctness of the law discovered by Hegel (in his “Logic”), that merely quantitative differences beyond a certain point pass into qualitative changes.[5]

The minimum of the sum of value that the individual possessor of money or commodities must command, in order to metamorphose himself into a capitalist, changes with the different stages of development of capitalist production, and is at given stages different in different spheres of production, according to their special and technical conditions. Certain spheres of production demand, even at th~ very outset of capitalist production, a minimum of capital that is not as yet found in the hands of single individuals. This gives rise partly to state subsidies to private persons, as in France in the time of Colbert, and as in many German states up to our own epoch; partly to the formation of societies with legal monopoly for the exploitation of certain branches of industry and commerce, the fore-runners of our own modern joint-stock companies.[6]

Within the process of production, as we have seen, capital acquired the command over labour, i. e., over functioning labouring-power or the labourer himself. Personified capital, the capitalist takes care that the labourer does his work regularly and with the proper degree of intensity.

Capital further developed into a coercive relation, which compels the working class to do more work than the narrow round of its own life-wants prescribes. As a producer of the activity of others, as a pumper-out of surplus-labour and exploiter of labour-power, it surpasses in energy, disregard of bounds, recklessness and efficiency, all earlier systems of production based on directly compulsory labour.

At first, capital subordinates labour on the basis of the technical conditions in which it historically finds it. It does not, therefore, change immediately the mode of production. The production of surplus-value—in the form hitherto considered by us—by means of simple extension of the working-day, proved, therefore, to be independent of any change in the mode of production itself. It was not less active in the old-fashioned bakeries than in the modern cotton factories.

If we consider the process of production from the point of view of the simple labour-process, the labourer stands in relation to the means of production, not in their quality as capital, but as the mere means and material of his own intelligent productive activity. In tanning, e. g., he deals with the skins as his simple object of labour. It is not the capitalist whose skin he tans. But it is different as soon as we deal with the process of production from the point of view of the process of creation of surplus-value. The means of production are at once changed into means for the absorption of the labour of others. It is now no longer the labourer that employes the means of production, but the means of production that employ the labourer. Instead of being consumed by him as material elements of his productive activity, they consume him as the ferment necessary to their own life-process, and the life-process of capital consists only in its movement as value constantly expanding, constantly multiplying itself. Furnaces and workshops that stand idle by night, and absorb no living labour, are “a mere loss” to the capitalist. Hence, furnaces and workshops constitute lawful claims upon the night-labour of the workpeople. The simple transformation of money into the material factors of the process of production, into means of production, transforms the latter into a title and a right to the labour and surplus-labour of others. An example will show, in conclusion, how this sophistication, peculiar to and characteristic of capitalist production, this complete inversion of the relation between dead and living labour, between value and the force that creates value, mirrors itself in the consciousness of capitalists. During the revolt of the English factory lords between 1848 and 1850, “the head of one of the oldest and most respectable houses in the West of Scotland, Messrs. Carlile Sons & Co., of the linen and cotton thread factory at Paisley, a company which has now existed for about a century, which was in operation in 1752, and four generations of the same family have conducted it” … this “very intelligent gentleman” then wrote a letter[7] in the “Glasgow Daily Mail” of April 25th, 1849, with the title, “The relay system,” in which among other things the following grotesquely naïve passage occurs: “Let us now … see what evils will attend the limiting to 10 hours the working of the factory.… They amount to the most serious damage to the mill-owner’s prospects and property. If he (i. e., his “hands”) worked 12 hours before, and is limited to 10, then every 12 machines or spindles in his establishment shrink to 10, and should the works be disposed of, they will be valued only as 10, so that a sixth part would thus be deducted from the value of every factory in the country.”[8]

To this West of Scotland bourgeois brain, inheriting the accumulated capitalistic qualities of “four generations,” the value of the means of production, spindles, &c. is so inseparably mixed up with their property, as capital, to expand their own value, and to swallow up daily a definite quantity of the unpaid labour of others, that the head of the firm of Carlile & Co. actually imagines that if he sells his factory, not only will the value of the spindles be paid to him, but, in addition, their power of annexing surplus-value, not only the labour which is embodied in them, and is necessary to the production of spindles of this kind, but also the surplus-labour which they help to pump out daily from the brave Scots of Paisley, and for that very reason he thinks that with the shortening of the working-day by 2 hours, the selling-price of 12 spinning machines dwindles to that of 10!

1. This elementary law appears to be unknown to the vulgar economists, who, upsidedown Archimedes, in the determination of the market-price of labour by supply and demand, imagine they have found the fulcrum by means of which, not to move the world, but to stop its motion.
2. Further particulars will be found in “Theories of Surplus-Value,” edited by Karl Kautsky.
3. "The labour, that is the economic time, of society, is a given portion, say ten hours a day of a million of people, or ten million hours.… Capital has its boundary of increase. This boundary may, at any given period, be attained in the actual extent of economic time employed.” (“An Essay on the Political Economy of Nations.” London, 1821, pp. 47, 49.)
4. “The farmer cannot rely on his own labour, and if he does, I will maintain that he is a loser by it. His employment should be a general attention to the whole: his thresher must he watched, or he will soon lose his wages in corn not threshed not; his mowers, reapers, &c., must be looked after; he must constantly go round his fences; he must see there is no neglect; which would be the case if he was confined to any one spot.” (“An Inquiry into the connection between the Price of Provisions and the Size of Farms, &c. By a Farmer.” London, 1773, p. 12.) This book is very interesting. In it the genesis of the “capitalist farmer” or “merchant farmer,” as he is explicitly called, may be studied, and his self-glorification at the expense of the small farmer who has only to do with bare subsistence, be noted. "The class of capitalists are from the first partially, and they become ultimately completely, discharged from the necessity of the manual labour.” ("Text-book of Lectures on the Political Economy of Nations, By the Rev. Richard Jones." Hertford, 1852, Lecture III. p. 39.)
5. The molecular theory of modern chemistry first scientifically worked out by Laurent and Gerhardt rests on no other law. (Addition to 3rd Edition.) For the explanation of this statement, which is not very clear to non-chemists, we remark that the author speaks here of the homologous series of carbon compounds, first so named by C. Gerhardt in 1848, each series of which has its own general algebraic formula. Thus the series of paraffins: Cn H²n+², that of the normal alcohols: Cn H²n+²0; of the normal fatty acids: Cn H²n O² and many others. In the above examples, by the simply quantitative addition of C H² to the molecular formula, a qualitatively different body is each time formed. On the share (overestimated by Marx) of Laurent and Serhardt in the determination of this important fact see Kopp, ‘“Entwicklung der Chemie.’ München, 1873, pp. 709, 716, and Schorlemmer, "Rise and Progress of Organic Chemistry.” London, 1879, p. 54.—Ed.
6. Martin Luther calls these kinds of institutions: "The Company Monopolia.”
7. Reports of Insp. of Fact., April 30th, 1849, p. 59.
8. l. c., p. 60. Factory Inspector Stuart, himself a Scotchman, and in contrast to the English Factory Inspectors, quite taken captive by the capitalistic method of thinking, remarks expressly on this letter which he incorporates in his report that it is “the most useful of the communications which any of the factory-owners working with relays have given to those engaged in the same trade, and which is the must calculated to remove the prejudices of such of them as have scruples respecting any change of the arrangement of the hours of work."