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Increased productiveness and greater intensity of labour, both have a like effect. They both augment the mass of articles produced in a given time. Both, therefore, shorten that portion of the working-day which the labourer needs to produce his means of subsistence or their equivalent. The minimum length of the working-day is fixed by this necessary but contractile portion of it. If the whole working-day were to shrink to the length of this portion, surplus-labour would vanish, a consummation utterly impossible under the régime of capital. Only by suppressing the capitalist form of production could the length of the working-day be reduced to the necessary labour-time. But, even in that case, the latter would extend its limits. On the one hand, because the notion of "means of subsistence" would considerably expand, and the labourer would lay claim to an altogether different standard of life. On the other hand, because a part of what is now surplus-labour, would then count as necessary labour; I mean the labour of forming a fund for reserve and accumulation.
The more the productiveness of labour increases, the more can the working-day be shortened; and the more the working-day is shortened, the more can the intensity of labour increase. From a social point of view, the productiveness increases in the same ratio as the economy of labour, which, in its turn, includes not only economy of the means of production, but also the avoidance of all useless labour. The capitalist mode of production, while on the one hand, enforcing economy in each individual business, on the other hand, begets, by its anarchical system of competition, the most outrageous squandering of labour-power and of the social means of production, not to mention the creation of a vast number of employments, at present indispensable, but in themselves superfluous.
The intensity and productiveness of labour being given, the time which society is bound to devote to material production is shorter, and as a consequence, the time at its disposal for the free development, intellectual and social, of the individual is greater, in proportion as the work is more and more evenly divided among all the able-bodied members of society, and as a particular class is more and more deprived of the power to shift the natural burden of labour from its own shoulders to those of another layer of society. In this direction, the shortening of the working-day finds at last a limit in the generalisation of labour. In capitalist society spare time is acquired for one class by converting the whole life-time of the masses into labour-time.
 Note in the 3rd German edition. — The case considered at pages 300-302 is here of course omitted. — F. E.
 To this third law MacCulloch has made, amongst others, this absurd addition, that a rise in surplus-value, unaccompanied by a fall in the value of labour-power, can occur through the abolition of taxes payable by the capitalist. The abolition of such taxes makes no change whatever in the quantity of surplus-value that the capitalist extorts at first-hand from the labourer. It alters only the proportion in which that surplus-value is divided between himself and third persons. It consequently makes no alteration whatever in the relation between surplus-value and value of labour-power. MacCulloch's exception therefore proves only his misapprehension of the rule, a misfortune that as often happens to him in the vulgarisation of Ricardo, as it does to J. B. Say in the vulgarisation of Adam Smith.
 "When an alteration takes place in the productiveness of industry, and that either more or less is produced by a given quantity of labour and capital, the proportion of wages may obviously vary, whilst the quantity, which that proportion represents, remains the same, or the quantity may vary, whilst the proportion remains the same." ("Outlines of Political Economy, &c.," p. 67.)  "All things being equal, the English manufacturer can turn out a considerably larger amount of work in a given time than a foreign manufacturer, so much as to counterbalance the difference of the working-days, between 60 hours a week here, and 72 or 80 elsewhere." (Rep. of Insp. of Fact. for 31st Oct., 1855, p. 65.) The most infallible means for reducing this qualitative difference between the English and Continental working hour would be a law shortening quantitatively the length of the working-day in Continental factories.
 "There are compensating circumstances... which the working of the Ten Hours' Act has brought to light."(Rep.of Insp. of Fact. for 31st Oct. 1848," p. 7.)  "The amount of labour which a man had undergone in the course of 24 hours might be approximately arrived at by an examination of the chemical changes which had taken place in his body, changed forms in matter indicating the anterior exercise of dynamic force." (Grove: "On the Correlation of Physical Forces.")  "Corn and labour rarely march quite abreast; but there is an obvious limit, beyond which they cannot be separated. With regard to the unusual exertions made by the labouring classes in periods of dearness, which produce the fall of wages noticed in the evidence" (namely, before the Parliamentary Committee of Inquiry, 1814-15), "they are most meritorious in the individuals, and certainly favour the growth of capital. But no man of humanity could wish to see them constant and unremitted. They are most admirable as a temporary relief; but if they were constantly in action, effects of a similar kind would result from them, as from the population of a country being pushed to the very extreme limits of its food." (Malthus: "Inquiry into the Nature and Progress of Rent," Lond., 1815, p. 48, note.) All honour to Malthus that he lays stress on the lengthening of the hours of labour, a fact to which he elsewhere in his pamphlet draws attention, while Ricardo and others, in face of the most notorious facts, make invariability in the length of the working-day the groundwork of all their investigations. But the conservative interests, which Malthus served, prevented him from seeing that an unlimited prolongation of the working-day, combined with an extraordinary development of machinery, and the exploitation of women and children, must inevitably have made a great portion of the working-class "supernumerary," particularly whenever the war should have ceased, and the monopoly of England in the markets of the world should have come to an end. It was, of course, far more convenient, and much more in conformity with the interests of the ruling classes, whom Malthus adored like a true priest, to explain this "over-population" by the eternal laws of Nature, rather than by the historical laws of capitalist production.
 "A principal cause of the increase of capital, during the war, proceeded from the greater exertions, and perhaps the greater privations of the labouring classes, the most numerous in every society. More women and children were compelled by necessitous circumstances, to enter upon laborious occupations, and former workmen were, from the same cause, obliged to devote a greater portion of their time to increase production."
(Essays on Pol. Econ., in which are illustrated the principal causes of the present national distress. Lond., 1830, p. 248.) Transcribed by Alan Thurrott Html Markup by Stephen Baird (1999) Next: Chapter Eighteen: Various Formula for the Rate of Surplus-Value Capital Volume One- Index Karl Marx Capital Volume One
The Production of Absolute and of Relative Surplus-Value
VARIOUS FORMULA FOR THE RATE OF SURPLUS-VALUE
We have seen that the rate of surplus-value is represented by the following formulae:
Surplus-value (s) Surplus-value Surplus-labor I. —————————— == —————————— == ———————Variable Capital (v) Value of labor-power Necessary labor The two first of these formulae represent, as a ratio of values, that which, in the third, is represented as a ratio of the times during which those values are produced. These formulae, supplementary the one to the other, are rigorously definite and correct. We therefore find them substantially, but not consciously, worked out in classical Political Economy. There we meet with the following derivative formulae.
Surplus-labor Surplus-value Surplus-product II. ———————- == —————————— == ————————Working-day Value of the Product Total Product One and the same ratio is here expressed as a ratio of labor-times, of the values in which those labor-times are embodied, and of the products in which those values exist. It is of course understood that, by "Value of the Product", is meant only the value newly created in a working-day, the constant part of the value of the product being excluded.
In all of these formulae (II.), the actual degree of exploitation of labor, or the rate of surplus-value, is falsely expressed. Let the working-day be 12 hours. Then, making the same assumptions as in former instances, the real degree of exploitation of labor will be represented in the following proportions.
6 hours surplus-labor Surplus-value of 3 sh.
———————————- == —————————————- == 100%.
6 hours necessary labor Variable Capital of 3 sh.
From formulae II. we get very differently, 6 hours surplus-labor Surplus-value of 3 sh.
———————————- == —————————————- == 50%.
Working-day of 12 hours Value created of 6 sh.
These derivative formulae express, in reality, only the proportion in which the working-day, or the value produced by it, is divided between capitalist and laborer. If they are to be treated as direct
expressions of the degree of self-expansion of capital, the following erroneous law would hold good:
Surplus-labor or surplus-value can never reach 100%.  Since the surplus-labor is only an aliquot part of the working-day, or since surplus-value is only an aliquot part of the value created, the surplus-labor must necessarily be always less than the working-day, or the surplus-value always less than the total value created. In order, however, to attain the ratio of 100:100 they must be equal. In order that the surplus-labor may absorb the whole day (i.e., an average dy of any week or year), the necessary labor must sink to zero. But if the necessary labor vanish, so too does the surplus-labor, since it is only a function of the former. The ratio Surplus-labor Surplus-value ———————- or ———————Working-day Value created can therefore never reach the limit 100/100, still less rise to 100+x/100. But not so the rate of surplus-value, the real degree of exploitation of labor. Take, e.g., the estimate of L. de Lavergne, according to which the English agricultural laborer gets only 1/4, the capitalist (farmer) on the other hand 3/4 of the product  or its value, apart from the question of how the booty is subsequently divided between the capitalist, the landlord, and others. According to this, this surplus-labor of the English agricultural laborer is to his necessary labor as 3:1, which gives a rate of exploitation of 300%.
The favorite method of treating the working-day as constant in magnitude became, through the use of formulae II., a fixed usage, because in them surplus-labor is always compared with a working-day of given length. The same holds good when the repartition of the value produced is exclusively kept insight. The working-day that has already been realized in given value, must necessarily be a day of given length.
The habit of representing surplus-value and value of labor-power as fractions of the value created — a habit that originates in the capitalist mode of production itself, and whose import will hereafter be disclosed — conceals the very transaction that characterizes capital, namely the exchange of variable capital for living labor-power, and the consequent exclusion of the laborer from the product. Instead of the real fact, we have false semblance of an association, in which laborer and capitalist divide the product in proportion to the different elements which they respectively contribute towards its formation.  Moreover, the formulae II. can at any time be reconverted into formulae I. If, for instance, we have Surplus-labor of 6 hours —————————————, Working-day of 12 hours then the necessary labor-time being 12 hours less the surplus-labor of 6 hours, we get the following result, Surplus-labor of 6 hours 100 —————————————— == —-.
Necessary labor of 6 hours 100 There is a third formula which I have occassionally already anticipated; it is Surplus-value Surplus-labor Unpaid labor III. —————————— == ————————- == ———————.
Value of labor-power Necessary labor Paid labor After the investigations we have given above, it is no longer possible to be misled, by the formula Unpaid labor ———————, Paid labor into concluding, that the capitalist pays for labor and not for labor-power. This formula is only a popular expression for Surplus-labor ————————-.
Necessary labor The capitalist pays the value, so far as price coincides with value, of the labor-power, and receives in exchange the disposal of the living labor-power itself. His usufruct is spread over two periods. During one the laborer produces a value that is only equal to the value of his labor-power; he produces its equivalent. This the capitalist receives in return for his advance of the price of the labor-power, a product ready made in the market. During the other period, the period of surplus-labor, the usufruct of the labor-power creates a value for the capitalist, that costs him no equivalent.  This expenditure of labor-power comes to him gratis. In this sense it is that surplus-labor can be called unpaid labor.
Capital, therefore, it not only, as Adam Smith says, the command over labor. It is essentially the command over unpaid labor. All surplus-value, whatever particular form (profit, interest, or rent), it may subsequently crystallize into, is in substance the materialization of unpaid labor. The secret of the self-expansion of capital resolves itself into having the disposal of a definite quantity of other people's unpaid labor.