Marx’s Economic Manuscripts of 1861-63
[III-95] The view presented here is also correct in strictly mathematical terms. Thus in the differential calculus let us take e.g. y = f(x) + c, where c is a constant magnitude. The change of x into x + Dx does not alter the value of c. dc would = 0, because the constant magnitude does not alter. Hence the differential of a constant is zero. 
At the end of the production process capital has a surplus value, which means, expressed in accordance with the general concept of exchange value: The labour time objectified in the product (or the quantity of labour contained in it) is greater than the labour time contained in the original capital, the capital advanced during the production process. This is only possible (assuming that the commodity is sold at its value) because the labour time objectified in the price of labour (the wage of labour) is less than the living labour time by which it is replaced in the production process. What appears as surplus value on the side of capital, appears as surplus labour on the side of the worker. Surplus value is nothing but the excess labour provided by the worker over and above the quantity of objectified labour he has received in his own wage as the value of his labour capacity.
We have seen that equivalents are exchanged in the exchange between capital and labour capacity. But the result of the transaction, as it appears in the production process and as it forms on the part of the capitalist the whole purpose of the transaction, is this, that the capitalist buys a greater quantity of living labour for a definite quantity of objectified labour, or that the labour time which is objectified in the wage is less than the labour time which the worker works for the capitalist and which is accordingly objectified in the product. The mediatory role of the exchange between capital and labour capacity (or the fact that the labour capacity is sold at its value) is a circumstance which is irrelevant in this context, where the question at issue is the analysis of surplus value. What is at stake here is rather the magnitude of the labour time objectified in the wage (the value of labour capacity), on the one hand, and on the other hand the magnitude of the labour time the worker really gives to the capitalist in return, or how much use is made of his labour capacity.
The relation in which objectified labour is exchanged for living labour — hence the difference between the value of labour capacity and the valorisation of that labour capacity by the capitalist — assumes another form in the production process itself. For there it presents itself as a splitting up of living labour itself into two quantities, both measured by time, and as the ratio between these two quantities. For firstly the worker replaces the value of his labour capacity.
Let us assume the value of his daily means of subsistence to be equal to 10 hours of labour. He reproduces this value by working for 10 hours. Let us call this part of the labour time the necessary labour time. Let us assume that the material of labour and the means of labour — the objective conditions of labour — are the property of the worker himself. On our assumption he would have to work 10 hours a day, reproduce a value of 10 hours of labour time a day, in order to be able every following day to appropriate for himself means of subsistence to the amount of 10 hours of labour, to reproduce his own labour capacity, to be able to continue living. The product of his 10 hours of labour would be equal to the labour time contained in the worked up raw material and the tool used up in the process of labour + the 10 hours of new labour he would have added to the raw material. He could only consume the latter portion of the product if he wished to continue producing, i.e. to preserve his conditions of production.
For he must deduct the value of the raw material and the means of labour from the value of his product every day in order to be able to replace constantly the raw material and the means of labour; in order to have afresh at his disposal every day as much raw material and means of labour as is required for the realisation (application) of ten hours of labour. If the value of the worker’s average daily necessary means of subsistence is equal to 10 hours of labour, he must work a daily average of 10 hours of labour to be able to replace his daily consumption, and provide himself with the conditions needed for his life as a worker. This labour would be necessary for him personally, for his [III-96] own self-preservation, quite irrespective of whether he is or is not himself the owner of the conditions of labour-material of labour and means of labour, whether his labour is or is not subsumed under capital. This labour time is necessary for the preservation of the working class itself, and we can call this part of labour time necessary labour time.
But we can also call it this from another point of view.
The labour time which is necessary to reproduce the value of labour capacity itself — i.e. the daily production of the worker which is required so that the worker’s consumption can be repeated every day — or the labour time with which the worker adds to the product the value he himself receives every day and destroys every day in the form of wages — is also necessary labour time from the standpoint of the capitalist in so far as the whole capital-relation presupposes the continuous existence of the working class, its continuing reproduction, and capitalist production has as its necessary prerequisite the continuous availability, preservation and reproduction of a working class.
Further: Let us suppose that the value of the capital advanced for production has to be simply preserved and reproduced, i.e. the capitalist creates no new value in the production process. It is then clear that the value of the product will only be equal to the value of the capital advanced, if the worker adds to the raw material as much labour time as he has received in the form of wages, i.e. if he reproduces the value of his own wage. The labour time which is necessary for the worker to reproduce the value of his own daily means of subsistence is at the same time the labour time necessary for capital simply to preserve and reproduce its value.
We have assumed that a labour time of 10 hours = the labour time contained in the wage; hence the labour time during which the worker only gives back to the capitalist an equivalent for the value of the wage is at the same time the necessary labour time, the labour time necessary both for the preservation of the working class itself and for the simple preservation and reproduction of the capital advanced, and, finally, for the possibility of the capital-relation altogether.
On our assumption, then, the first 10 hours the worker works are necessary labour time and this is at the same time nothing but an equivalent for the objectified labour time he has received in the form of the wage. Let us call surplus labour all the labour time the worker works over and above these 10 hours, this necessary labour time. If he works 11 hours, he has provided 1 hour of surplus labour, if 12, two hours of surplus labour, and so on. In the first case the product possesses a surplus value of one hour in excess of the value of the capital advanced, in the second case a surplus value of 2 hours, and so on. But in all circumstances the surplus value of the product is only the objectification of surplus labour. Surplus value is simply objectified surplus labour time, just as value in general is merely objectified labour time. Thus surplus value amounts to labour time the worker works for the capitalist in excess of the necessary labour time.
We have seen that the capitalist pays the worker an equivalent for the daily value of his labour capacity; but he receives in return the right to extract from that labour capacity a value greater than its own value. If 10 hours of labour a day are necessary for the daily reproduction of labour capacity, he sets the worker to work for e.g. 12 hours. In reality, therefore, he exchanges 10 hours of objectified labour time (objectified in the wage) for 12 hours of living labour time. The ratio in which he exchanges objectified labour time (objectified in the capital advanced) for living labour time is the same as the ratio of the worker’s necessary labour time to his surplus labour, the labour time he works over and above the necessary labour time. It therefore presents itself as a ratio between two portions of the labour time of the worker himself — necessary labour time and surplus labour. The necessary labour-time is the same as the labour time necessary to reproduce the wage. It is therefore a simple equivalent given back to the capitalist by the worker. The latter has received a certain labour time in money; he gives it back in the form of living labour time.
The necessary labour time is therefore paid labour time. On the other hand, no equivalent has been paid for the surplus labour. [Id est, it has not been objectified in an equivalent for the worker himself.] It is rather the valorisation of labour [III-97] capacity by the capitalist in excess of that capacity’s own value. It is therefore unpaid labour time. The ratio in which objectified labour is exchanged for living labour can be resolved into the ratio between the necessary labour time of the worker and his surplus labour, and the latter ratio can be resolved into the ratio of paid to unpaid labour time. Surplus value is equal to surplus labour is equal to unpaid labour time. Surplus value can therefore be resolved into unpaid labour time, and the level of surplus value depends on the ratio in which surplus labour stands to necessary labour, or unpaid to paid labour time.
If we look now at capital, we find that it is originally split up into 3 constituent parts (only two in some industries, such as the extractive industries; but we are taking the most complete form, that of manufacturing industry): raw material, instrument of production, and finally the part of capital which is exchanged for labour capacity in the first instance. Here we are concerned only with the exchange value of capital. As regards the part of the capital’s value that is contained in the used up raw material and means of production, we have seen that it simply re-appears in the product. This part of capital never adds more to the value of the product than the value it itself possesses independently of the production process. In reference to the value of the product, we can call this part of the capital its constant part. As noted under heading 1, its value may rise or fall, but this rising or falling has nothing to do with the production process, in which these values enter as values of the material and the instrument of production.
If 12 hours are worked instead of 10, more raw material is of course necessary so as to absorb the two hours of surplus labour. What we call constant capital will therefore enter the production process in an amount, i.e. an amount of value, a magnitude of value, which varies according to the quantity of labour the raw material has to absorb, in general the quantity of labour to be objectified in the production process. But it is constant in so far as its magnitude of value, whatever its ratio towards the total amount of capital advanced, re-appears unchanged in the product. We have seen that it is not itself reproduced in the proper sense of the word. It is rather just preserved because the material and means of labour are (in accordance with their use value), made into factors of the new product by labour, as a result of which the constant capital’s value re-appears in this product. And this value is determined simply by the labour time required for its own production. They add to the labour time contained in the product only as much labour time as they themselves contained before the production process.
It is therefore only the 3rd part of capital, the part exchanged for labour capacity or advanced in wages, which is variable. Firstly, it is really reproduced. The value of labour capacity, or the wage of labour, is annihilated (the value and the use value), consumed by the worker. But it is replaced by a new equivalent; an equal quantity of living labour time, added by the worker to the raw material or materialised in the product, steps into the place of the labour time objectified in the wage. And secondly, this part of the value of the capital is not only reproduced, and simply replaced by an equivalent, but also exchanged in the actual production process for a quantity of labour = the labour contained in it + an excess quantity of labour, the surplus labour the worker performs over and above the labour time which is necessary for the reproduction of his own wage, hence is contained in the component of the value of the capital which can be resolved into wages. Therefore, if we call the labour time contained in constant capital c, that contained in variable capital v, and the time the worker has to work over and above the necessary labour time s, the labour time contained in P, or the value of the product, = c + (v + s). The original capital was equal to c + v. The excess of its value over its original value therefore = s. But the value of c simply re-appears in the product, whereas the value of v is firstly reproduced in v and secondly increased by s. It is therefore only the part of the value of the capital denoted by v which has changed, in that v has reproduced itself as v + s. s is therefore only a result of an alteration in v; [If it is assumed that c = 0 and that the capitalist has advanced wages alone (variable capital), the magnitude of s remains the same although no part of the product replaces c] and the ratio in which surplus value is created is expressed as v:s, the ratio in which the labour time contained in the v component of the value of the total capital has been exchanged for living labour time, [III-98] or, which is the same thing, the ratio of necessary to surplus labour, of v:s. The newly created value results from the alteration in v alone, its transformation into v + s. It is only this part of capital which increases its value or posits surplus value. The ratio, therefore, in which surplus value is posited, is the ratio in which s stands to v, in which the part of the value of capital expressed in v is not only reproduced but magnified. The best demonstration of this is that if v is simply replaced by an amount of labour time equal to that contained in v itself, no surplus value at all is created; on the contrary, the value of the product is equal to the value of the capital advanced.
If therefore, surplus value is, in general, nothing but the excess of living labour for which the labour objectified in capital is exchanged, or, which is the same thing, nothing but the unpaid labour time worked by the worker over and above the necessary labour time, the magnitude of the surplus value, the ratio in which it stands to the value it replaces, the ratio in which it grows, is simply determined by the ratio s:v, surplus labour to necessary labour, or, and this is the same, the ratio of the labour time advanced by the capitalist in wages to the surplus of labour, etc. Thus if the necessary (wage-reproducing) labour time = 10 hours, and the worker works for 12, the surplus value is equal to 2 hours, and the ratio in which the value advanced has increased = 2:10, = 1/5, = 20%, whatever may be the amount of labour time contained in c, the constant part of capital, whether it is 50, 60, 100, in short x hours of labour, whatever may be the ratio of the variable to the constant part of capital. As we have seen, the value of this [the constant] part of capital simply re-appears in the product and has absolutely nothing to do with the value-creation that occurs during the production process itself.
[I-A] // If the original ratio of necessary labour to surplus labour = 10 hours: 2 hours = 5:1, and if now 16 hours are worked instead of 12, hence 4 more hours, the worker would have to receive 3 1/3 and the capitalist only 2/3 of an hour from those 4 hours for the ratio to remain the same; for 10:2 = 3 1/3:2 /3 = 10/3:2 /3 = 10:2. But under the mathematical law that “A ratio of greater inequality is diminished, and of less inequality increased, by adding any quantity to both its terms”, the ratio of wages to surplus value is unchanged if the overtime is divided in accordance with the above ratio. Previously the ratio of [necessary] labour to surplus was 10:2 = 5:1 (5 times greater). Now it will be 13 1/3:2 2/3 = 40/3:8/3 = 40[:8 = 5:1]. // 
It is very important to keep a strong hold on the idea that surplus value = surplus labour, and that the ratio of surplus value is the ratio of surplus labour to necessary labour. In this connection the customary notion of profit and the rate of profit should initially be entirely forgotten. What kind of relation exists between surplus value and profit will be seen later on. 
We shall therefore use a few examples to clarify this conception of surplus value and the rate of surplus value, the ratio in which it grows — the yardstick by which its magnitude is to be measured. These examples are borrowed from statistical sources. Hence labour time always appears here expressed in money. Furthermore, different items bearing different names appear in the calculations, e.g. side by side with profit there is interest, taxes, rent, etc. These are all different portions of surplus value under different names.  How surplus value is distributed among the different classes, i.e. how much of it the industrial capitalist gives up under various headings, and how much he keeps for himself, is completely irrelevant to the conception of surplus value itself. It is, however, entirely clear that all those people — whatever heading they figure under — who do not themselves work, who do not take part in the material process of production themselves as workers, can only participate in the value of the material product in so far as they divide the product’s surplus value among themselves, for the value of raw material and machinery, the constant part of the value of capital, must be replaced. Similarly with the necessary labour time, for the working class absolutely must first of all work the quantity of labour time necessary to preserve its own life before it can work for others. Only the value x, equal to the workers’ surplus labour, hence also the use values that can be purchased with this surplus value, is available for distribution among the non-workers.
It is only the variable part of capital, the quantity of objectified labour which is exchanged in the production process for a greater quantity of living labour time, that undergoes any change at all, that changes its value, posits a surplus value, and the magnitude of this newly created value depends entirely on the ratio between the quantity of living surplus labour obtained in exchange for the variable part of capital and the labour contained in it before the production process.
[III-99] Senior must be cited here as a second example illustrating the political economists’ failure to understand surplus labour and surplus value. 
Now the following points are still to be examined under surplus value:
// 1) Extent of surplus labour. Drive of capital to spin this out to infinity. 2) Surplus value depends not only on the number of hours the individual worker works over and above the necessary labour time, but also on the number of simultaneous working days, or the number of workers the capitalist employs. 3) The relation of capital as producer of surplus labour: working more than is needed. Civilising character of capital, labour time and free time. Opposition. Surplus labour and surplus product. Hence in the last instance relation of population and capital. 4) Mr. Proudhon’s thesis that the worker cannot buy back his own product, or the price of the portion of the product, etc. 145 5) This form of surplus value is the absolute form. Persists in all modes of production which are founded on the opposition between classes one of which is the possessor of the conditions of production and the other of labour. //