Since, on the one hand, the values of the variable capital and of the labour-power purchased by that capital are equal, and the value of this labour-power determines the necessary portion of the working day; and since, on the other hand, the surplus-value is determined by the surplus portion of the working day, it follows that surplus- value bears the same ratio to variable capital, tliat surplus-labour does to necessary labour, or in other words, the rate of surplus- value \ = neS^^ro^* Both ratios,?^ and i"n>iu8jaT>our express the same thinor in different ways; in the one case by reference to materialised, incorporated labour, in tlie other by reference to living, fluent labour.
The rate of surplus-value is therefore an exact expression 1 Herr Wilhelm Thucy elides Eoscher has found a mare's nest. He has made the important discovery that if, on the one hand, the formation of surplus-value, or surplus-produce, and the consequent accumulation of capital, is now-a-days due to the thrift of the capitalist, on the other hand, in the lowest stages of civilisation it is the strong who compel the weak to economise (1. c. p. 78). To economise what? Labour? Or superfluous wealth that does not exist? What is it that makes such men as Roscher account for the origin of surplus-value, by a mere rechauffe of the more or less plausible excuses by the capitalist, for his appropriation of surplus-value? It is, besides their real ignorance, their apologetic dread of a scientific analysis of value and surplus-value, and of obtaining a result, possibly not altogether palatable to the powers that be.
The Rate of Surphis-value, 201 for the degree of exploitation of labour-power by capital, or of the labourer by the capitalist.^ We assumed in our example, that the value of the product =£410 const. + £90 var. + £90 surpL, and that the capital advanced = £500. Since the surplus- value = £90, and the advanced capital = £500, we should, according to the usual way of reckoning, get as the rate of surplus value (generally confounded with rate of profits) 18%, a rate so low as possibly to cause a pleasant surprise to Mr. Carey and other harraonisers. But in truth, the rate of surplus-value is not equal to ^ cr -^ but to ^: thus it is not i§ but fg or 100%, which is more than five times the apparent degree of exploitation. Although, in the case we have supposed, we are ignorant of the actual length of the working day, and of the duration in days or weeks of the labour-process, as also of the number of labourers employed, yet the rate of surplus-value ^ accurately discloses to us, by means of its equivalent expression, ^2^^^SSr the relation between the two parts of the working day. This relation is here one of equality, the rate being 100%. Hence, it is plain, the labourei-, in our example, works one half of the day for himself, the other half for the capitalist.
The method of calculating the rate of surplus- value is therefore, shortly, as follows. We take the total value of the product and put the constant capital which merely re-appears in it, equal to zero. What remains, is the only value that has, in the process of producing the commodity, been actually created. If the amount of surplus-value be given, we have only to deduct it from this remainder, to find the variable capital. And vice versdy if the latter be given, and we require to find the surplusvalue. If both be given, we have only to perform the concluding operation, viz., to calculate ^, the ratio of the surplus- value to the variable capital.
1 Although the rate of surplus-value is an exact expression for the degree of exploitation of labour-power, it is, in no sense, an expression for the absolute amount of exploitation. For example, if the necessary labour?=^ 5 hours and the surpluslabour =i 5 hours, the degree of exploitation is 100%. The amount of exploitation is here measured by 5 hours. If, on the other hand, the necessary labour;= 6 hours and the surplus-labour ^= 6 hours, the degree of exploitation remains, as before, 100%, while the actual amount of exploitation has increased 20%, namely from five hou s to six.
2'02 Capitalist Production, Though the method is so simple, yet it may not be amiss, by means of a few examples, to exercise the reader in the application of the novel principles underlying it.
First we will take the case of a spinning mill containing 10,000 mule spindles, spinning No. 32 yarn from American cotton, and producing 1 lb. of yarn weekly per spindle. We assume the waste to be 6 %: under these circumstances 10,600 lbs. of cotton are consumed weekly, of which 600 lbs. go to waste. The price of the cotton in April, 1871, was 7|d. ])er lb.; the raw material therefo^-e costs in round numbers £342.
The 10,000 spindles, inchiding preparation -machinery, and motive power, cost, we will assume, £1 per spindle, amounting to a total of £10,000. The wear and tear we put at 10 %, or £1000 yearly =: £20 weekly. The rent of the building we suppose to be £300 a year, or £6 a week. Coal consumed (for 100 horse-power indicated, at 4 lbs. of coal per horse-power per hour durinor 60 hours, and inclusive of that consumed in heatinor the mill), 11 tons a week at 8s. 6d. a ton, amounts to about £4J a week: gas, £1 a week, oil,«fec.,£4J a week. Total costof theabove auxiliary materials, £10 weekly. Therefore the constant portion of the value of the week s product is £378. Wages amount to £52 a week. The price of the yarn is 12Jd. per lb., which gives for the value of 10,000 lbs. the sum of £510. The surplus value is therefore in this case £510 — £430 ~ £80. We put the constant part of the value of the product •=. 0, as it plays no part in the creation of value. There remains £132 as the weekly value cieated, which =: £52 var. £80 surpl. The rate of surplus-value is therefore |o = 153H %. In a working day of 10 hours with average labour the result is: necessary labour = 3f^ hours, and surplus-labour = 61?%.^ One mora example. Jacob gives the following calculation for the year 1815. Owing to the previous adjustment of several items it is very imperfect; nevertheless for our purpose it is sufficient. In it he assumes the price of wheat to be 8s. a quarter, and the average yield per acre to be 22 bushels.
1 The above data, which may be relied upon, were given me by a Manchester spinner. In England the horse-power of an engine was formerly calculated from the diameter of its cylinder, now the actual horse-power shown by the indicator is taken.
The Rate of Surplus-value. 20, Value Produced Per Acre.
Seed, Tithes, Rates, and Manure, Wages, Total, - Assuming that the price of the product is the same as its value, we here find the surplus-value distributed under the various heads of profit, interest, rent, &c. We have nothing to do with these in detail; we simply add them together, and the sum is a surplus- value of £3 lis. Od. The sum of £3 19s. Od., paid for seed and manure, is constant capital, and we put it equal to zero. There is left the sum of £3 lOs. Od., which is the variable capital advanced: and we see that a new value of £3 lOs. Od. + £3 lis. Od. has been produced in its place. Tlierefore ~ == -||-J^-^;, giving a rate of surplus-value of more than 100 %. The labourer employs more than one half of his working day in producing the surplus- value, which different persons, under different pretexts, share amongst themselves.^ SECTION 2. — THE UEPKESENTATION OF THE COMPONENTS OF THE VALUE OF THE PRODUCT BY CORRESPONDING PROPORTIONAL PARTS OF THE PRO-DUCT ITSELF.
Let US now return to the example by which we were shown how the capitalist converts money into capital.
The product of a working day of 12 hours is 20 lbs. of yarn, having a value of 30s. No less than ^ths of this value, or 24s., is due to mere re-appearance in it, of the value of the means of production (20 lbs. of cotton, value 20s., and spindle worn away, 4s.): it is therefore constant capital. The remaining ^ths or 6s. is the new value created during the spinning process: of 1 The calculations given in the text are intended merely as illustrations. We have in fact assumed that prices = values. We shall, however, see, in Book III., that even in the case of average prices the assumption cannot be made in this very simple manner.
2Q4 Capitalist Production, this one half replaces the value of the day's labour-power, or the variable capital, the remaining half constitutes a surplus-value of 3s. The total value then of the 20 lbs. of yarn is made up as follows: Since the whole of this value is contained in the 20 lbs. of yarn produced, it follows that the various component parts of this value, can be represented as being contained respectively in corresponding parts of the product.
If the value of 30s. is contained in 20 lbs. of yarn, then ^ ths of this value, or the 24s. that form its constant part, is contained in ^ths of the product or in 16 lbs. of yarn. Of the latter 13J lbs. represent the value of the raw material, the 20s. worth of cotton spun, and 2| lbs. represent the 4s. worth of spindle, &c., worn away in the process.
Hence the whole of the cotton used up in spinning the 20 lbs. of yarn, is represented by 13 J lbs. of yarn. This latter weight of yarn contains, it is true, by weight, no more than 13J lbs. of cotton, worth 13 J shillings; but the 6| shillings additional value contained in it, are the equivalent for the cotton consumed in spinning the remaining 6| lbs. of yarn. The effect is the same as if these 6| lbs. of yarn contained no cotton at all, and the whole 20 lbs. of cotton were concentrated in the 13 J lbs. of yarn. The latter weight, on the other hand, does not contain an atom either of the value of the auxiliary materials and implements, or of the value newly created in the process.
In the same way, the 2| lbs. of yarn, in which the 4s., the remainder of the constant capital, is embodied, represents nothing but the value of the auxiliary materials and instruments of labour consumed in producing the 20 lbs. of yarn.
We have, therefore, amved at this result: although eighttenths of the product, or 16 lbs. of yarn, is, in its character of an article of utility, just as much the fabric of the spinner's labour, as the remainder of the same product, yet when viewed in this connexion, it does not contain, and has not absorbed any labour expended during the process of spinning. It is just as if the cotton had converted itself into yarn, without help; as if the shape it had assumed was mere trickery and deceit: The Rate of Siirplus-value, 205 for so soon as our capit-alist sells it for 24s., and with the money replaces his means of production, it becomes evident that this 16 lbs. of yarn is nothing more than so much cotton and spindlewaste in disguise.
On the other hand, the remaining y^ ths of the product, or 4 lbs. of yarn, represent nothing but the new value of 6s., created during the 12 hours' spinning process. All the value transferred to those 4 lbs., from the raw material and instruments of labour consumed, was, so to say, intercepted in order to be incorporated in the 16 lbs. first spun. In this case, it is as if the spinner had spun 4 lbs. of yarn out of air, or, as if he had spun them with the aid of cotton and spindles, that, being the spontaneous gift of Nature, transferred no value to the product.
Of this 4 lbs. of yarn, in which the whole of the value newly created during the process, is condensed, one half represents the equivalent for the value of the labour consumed, or the 3s. variable capital, the other half represents the 8s. surplus-value.
Since 12 workingjiours of the spinner are embodied in 6s., it follows that in yarn of the value of 30s., there must be embodied 60 working hours. And this quantity of labour-time does in fact exist in the 20 lbs. of yarn; for in ^^^ths or 16 lbs. there are materialised the 48 hours of labour expended, before the commencement of the spinning process, on the means of production; and in the remaining y^ths or 4 lbs. there are materialised the 12 hours' work done during the process itself On a former page we saw that the value of the yarn is equal to the sum of the new value created during the production of that yarn plus the value previously existing in the means of production.
It has now been shown how the various component parts of the value of the product, parts that differ functionally from each other, may be represented by corresponding proportional parts of the product itself.
To split up in this manner the product into different parts, of which one represents only the labour previously spent on the means of production, or the constant capital, another, only the necessary labour spent during the process of production, or the variable capital, and another and last part, only -the surplus- 2o6 Capitalist Production.
labour expended during the same process, or the surplus-value f to do this, is, as will be seen later on from its application to complicated and hitherto unsolved problems, no less important than it is simple.
In the preceding investigation we have treated the total product as the final result, ready for use, of a working day of 12 hours. We can however follow this total product through all the stages of its production; and in this way we shall arrive at the same result as before, if we represent the partial products, given off at the different stages, as functionally different parts of the final or total product.
The spinner produces in 12 hours 20 lbs. of yarn, or in 1 hour 1| lbs.; consequently he produces in 8 hours 13 J lbs., or a partial product equal in value to all the cotton that is spun in a whole day. In like manner the partial product of the next period of 1 hour and 36 minutes, is 2| lbs. of yarn: this represents the value of the instruments of labour that are consumed in 12 hours. In the following hour and 12 minutes, the spinner produces 2 lbs. of yarn worth 3 shillings, a value equal to the whole value he creates in his 6 hours necessary labour. Finally, in the last hour and 12 minutes he produces another 2 lbs. of yarn, whose value is equal to the surplusvalue, created by his surplus-labour during half a day. This method of calculation serves the English manufacturer for everyday use; it shows, he will say, that in the first 8 hours, or f of the working day, he gets back the value of his cotton; and so on for the remaining hours. It is also a perfectly correct method: being in fact the first method given above with this difference, that instead of being applied to space, in which the different parts of the completed product lie side by side, it deals with time, in which those parts are successively produced. But it can also be accompanied by very barbarian notions, more especially in the heads of those who are as mu*. h interested, practically, in the process of making value beget value, as they are in misunderstanding that process theoretically. Such people may get the notion into their heads, that our spinner, for example, produces or replaces in the first 8 hours of his working day the value of the cotton; in the The Rate of SurphtS'Vahie, 207 following hour and 86 minutes the vilue of the instruments of labour worn away; in the next hour and 12 minutes the value of the wages; and that he devotes to the production of surplusvalue for the manufacturer, only that well known ** last hour." In this way the poor spinner is made to perform the two-fold miracle not only of producing cotton, spindles, steam-engine, coal, oil, fee, at the same time that he spins with them, but also of turning one working day into five; for, in the example we are considering, the production of the raw material and instruments of labour demands four working days of twelve hours each, and their conversion into yarn requires another such day. That the love of lucre induces an easy belief in such miracles, and that sycophant doctrinaires are never wanting to prove them, is vouched for by the following incident of historical celebrity.
One fine morning, in the year 1 836, Nassau W. Senior, who may be called the bel-esprit of English economists, well known, alike for his economical "science," and for, his beautiful style, was summoned from Oxford to Manchester, to learn in the latter place, the political economy that he taught in the former. The manufacturers elected him as their champion, not only against the newly passed Factory Act, but against the still more menacing Ten-hours' agitation. With their usual practical acuteness, they had found out that the learned Professor "wanted a good deal of finishing;" it was this discovery that caused them to write for him. On his side the Professor has embodied the lecture he received from the Manchester manufacturers, in a pamphlet, entitled: " Letters on the Factory Act, as it affects the cotton manufacture." London, 1837. Here we find, amongst others, the following edifying passage: " Under the present law, no mill in which persons under 18 years of age are employed, can be worked more than \\\ hours a day, that is, 12 hours for 5 days in the week, and nine on Saturday.
" Now the following analysis (!) will show that in a mill so 2o8 Capitalist Production, worked, the whole net profit is derived from the last hour. I will suppose a manufacturer to invest £100,000: — £80,000 in his mill and machinery, and £20,000 in raw material and wages. The annual return of that mill, supposing the capital to be turned once a year, and gross profits to be 15 per cent., ought to be goods worth £115,000 Of this £115,000, each of the twenty- three half-hours of work produces 5-115ths or one twenty -third. Of these 23-23rds (constituting the whole £115,000) twenty, that is to say £100,000 out of the £115,000, simply replace the capital; — one twenty-third (or £5000 out of the £115,000) makes up for the deterioration of the mill and machinery. The remaining 2-23rds, that is, the last two of the twenty-three half-hours of every day, produce the net profit of 10 per cent. If, therefore (prices remaining the same), the factory could be kept at work thirteen hours instead of eleven and a half, with an addition of about £2600 to the circulating capital, the net profit. would be more than doubled. On the other hand, if the hours of working were reduced by one hour per day (prices remaining the same), the net profit would be destroyed — if they were reduced by one hour and a half, even the gross profit would be destroyed." ^ 1 Senior, 1. c, p. 12, 13. We let pass such extraordinary notions as are of no importance for our purpose; for instance, the assertion, that manufacturers reckon as part of their profit, gross or net, the amount required to make good wear and tear of machinery, or in other words, to replace a part of the capital. So. too, we pass over any question as to the accuracy of his figures. Leonard Horner has shown in "A Letter to Mr. Senior," &c., London, 1837, that they are worth no more than the socalled " Analysis." Leonard Horner was one of the Factory Inquiry Commissioners in 1833, and Inspector, or rather Censor of Factories till 1859. He rendered undying service to the English working class. He carried on a life-long contest, not only with the embittered manufacturers, but also with the Cabinet, to whom the number of votes given by the masters in the Lower House, was a matter of far greater importance than the number of hours worked by the " hands " in the mills.
Apart from errors in j)rinciple, Senior's statement is confused. "WTiat he really intended to say was this: The manufacturer employs the workman for 11^ hours or for 23 half-hours daily. As the working day, so, too, the working year, may be conceived to consist of 11.^ hours or 23 half -hours, but each multiplied by the number of working days in the year. On this supposition, the 23 half -hours yield an annual product of £115,000; one half -hour yields ^V x £115,000; 20 half -hours yield |g x £115,000; = £100,000, i.e., they replace no more than the capital advanced. There remain 3 halfhours, which yield ^^5 x £115,000= £15,000 or the gross i>rofit. Of these 3 half -hours, one yields oV x £115,000 = £5000; i.e., it makes up for the wear and tear of the machinery; the remaining 2 half -hours, i.e., the last hour, yield ^\ x £115,000 = £10,000 or the net profit. In the text Senior converts the last -^^ of the product into portions of the working day itself.
The Rate of Surplus-value, 209 And the professor calls this an " analysis! " If, giving credence to the out-cries of the manufacturers, he believed that the workmen spend the best part of the day in the production, i.e.y the reproduction or replacement of the value of the buildings, machinery, cotton, coal, &;c., then his analysis was superfluous. His answer would simply have been: — Gentlemen! if you work your mills for 10 hours instead of 11|, then, other things being equal, the daily consumption of cotton, machinery, &;c., will decrease in proportion. You gain just as much as you lose. Your work-people will in future spend one hour and a half less time in reproducing or replacing the capital that has been advanced. — If, on the other hand, he did not believe them without further inquiry, but, as being an expert in such matters, deemed an analysis necessary, then he ought, in a question that is concerned exclusively with the relations of net profit to the length of the working day, before all things to have asked the manufacturers, to be careful not to lump together machinery, workshops, raw material, and labour, but to be good enough to place the constant capital, invested in buildings, machinery, raw material, &ic., on one side of the account, and the capital advanced in wages on the other side.
If the profesvsor then found, that in accordance with the calculation of the manufacturers, the workman reproduced or replaced his wages in 2 half-hours, in that case, he should have continued his analysis thus: According to your figures, the workman in the last hour but one produces his wages, and in the last hour your surplusvalue or net profit. Now, since in equal periods he produces equal values, the produce of the last hour but one, must have the same value as that of the last hour. Further, it is only while he labours that he produces any value at all, and the amount of his labour is measured by his labour-time. This you say, amounts to 11 J hours a day. He employs one portion of these 11 J hours, in producing or replacing his wages, and the remaining portion in producing your net profit. Beyond this he does absolutely nothing. But since, on your assumption, his wages, and the surplus-value he yields, are of equal value, it is clear that he produces his wages in 5| hours, and your net ^210 Capitalist Production.
profit in the other oj hours. Again, since the value of the yarn produced in 2 hours, is equal to the sum of the values of his wages and of your net profit, the measure of the value of this yarn must be II2 working hours, of which 5f hours measure the value of the yarn produced in the last hour bub one, and 5f, the value of the yarn produced in the last hour.
We now come to a ticklish point; therefore, attention! The last working hour but one is, like the first, an ordinary working hour, neither more nor less. How then can the spinner produce in one hour, in the shape of yarn, a value that embodies 5f hours labour? The truth is that he performs no such miracle. The use-value produced by him in one hour, is a definite quantity of yarn. The vakie of this yarn is measured by 5f working hours, of which 4f were, without any assistance from him, previously embodied in the means of production, in the cotton, the machinery, and so on; the remaining one hour alone is added by him. Therefore since his wages are produced in 5f hours, and the yarn produced in one hour also contains 5| hours' work, there is no witchcraft in the result, that the value created by his 5| hours* spinning, is equal to the value of the product spun in one hour. You are altogether on the wrong track, if you think that he loses a single moment of his working day, in reproducing or replacing the values of the cotton, the machinery, and so on: On the contrary, it is because his labour converts the cotton and spindles into yarn, because he spins, that the values of the cotton and spindles go over to the yarn of their oww accord. This result is owing to the quality of his labour, not to its quantity. It is true, he will in one hour transfer to the yarn more value, in the shape of cotton, than he will in half an hour; but that is only because in one hour he spins up more cotton than in half an hour. You see then, your assertion, that the workman produces, in the last hour but one, the value of his wages, and in the last hour your net profit, amounts to no more than this, that in the yarn produced by him in 2 working hours, whether they are the 2 first or the 2 last hours of the working day, in that yarn, there are incorporated 11^ working hours, or just a whole day's work, Le.y two hours of his own work and 9^ hours of other people's. And my assertion that, in the first 5f hours, he produces his wages, and in the last 5| hours your net profit, amounts only to this, that you pay him for the former, but not for the latter. In speaking of payment of labour, instead of payment of labour-power, I only talk your own slang. Now, gentlemen, if you compare the working time you pay for, with that which yow. do not pay for, you will find that they are to one another, as half a day is to half a day; this gives a rate of 100%, and a very pretty percentage it is. Further, there is not the least doubt, that if you make your " hands " toil for 13 hours, instead of 11 J, and, as may be expected from you, treat the work done in that extra one hour and a half, as pure surplus-labour, then the latter will be increased from 5| hours' labour to 7i hours' labour, and the rate of surplus-value from 100% to 126 4 %• So that you are altogether too sanguine, in expecting that by such an addition of 1| hours to the working day, the rate will rise from 100% to 200% and more, in other words that it will be "more than doubled." On the other hand — man's heart is a wonderful thing, especially when carried in the purse — you take too pessimist a view, when you fear, that with a reduction of the hours of labour from \\\ to 10, the whole of your net profit will go to the dogs. Not at all. All other conditions remaining the same, the surpluslabour will fall from 5| hours to 4| hours, a period that still gives a very profitable rate of surplus-value, namely 82^^ %. But this dreadful " last hour," about which you have invented more stories than have the millenarians about the day of judgment, is "all bosh." If it goes, it will cost neither you, your net profit, nor the boys and girls whom you employ, their " purity of mind." ^ Whenever your " last hour " strikes in 1 If, on the one hand, Senior proved that the net profit of the manufacturer, the existence of the English cotton industry, and England's command of the markets of the Wi)rld, depend on " the last working hour," on the other hand, Dr. Andrew Ure showed, that if children and young persons under 18 years of age, instead of being kept the full 12 hours in the warm and pure moral atmosphere of the factory, are turned out an hour sooner into the heartless and frivolous outer world, they will be deprived, by idleness and vice, of all hope of salvation for their souls. Since 1848, the factory inspectors have never tired of twitting the masters with this " last," this "fatal hour." Thus Mr. Howell in his report of the 81st May, 1855: "Had the following ingenious calculation (he quotes Senior) been correct, every cotton factory in the United Kingdom would have been working at a loss since the year 1850." (Reports 212 Capitalist Production.
earnest, think on the Oxford Professor. And now, gentleman, " farewell, and may we meet again in yonder better world, but not before/' Senior invented the battle cry of the " last hour " in 1836.*