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Surplus value is defined by Marx as "profit in the form of profit" in the first sentence of the first chapter of Theories of Surplus Value . According to Marxism it is unpaid labour that is extracted from the worker by the capitalist, and serves as the basis for capitalist accumulation. It is the labour that workers perform for their capitalist employers beyond what is necessary to produce enough to pay for their wages. Surplus value is a concept inextricably tied to Marx's labour theory of value, and is central to his account of exploitation under capitalism.
According to Marx, absolute surplus value is extracted simply by the lengthening of the working day (i.e. 'surplus labour time'), whereas relative surplus value is extracted by either: a. The lowering of wages — this can only go to a certain point, because if wages fall bellow the ability of workers to purchase their means of subsistence, they will be unable to reproduce themselves and the capitalists will not be able to find sufficient labor power. b. Or by lowering the value of the means of subsistence — this requires higher productivity with respect to producing the means of subsistence, instruments of production and raw materials (i.e. lowering 'necessary labour time'). The extraction of Surplus-value from workers by capitalists, both individual and corporations, is manifested in and is acquired through the form of profits, interest and rent.
Total value produced = total labour performed = paid labour (the value of labour-power: variable capital) plus unpaid labour. Thus, surplus-value = total value produced minus paid labour.
- Theories of Surplus-Value (1863) "In spite of the fact that Theories of Surplus-Value was left in a form that had not prepared for the press, this work gives a connected and complete picture of that “History of the Theory” which Marx intended to form the final, fourth volume of Capital. In it Marx sets forth the whole course of evolution of bourgeois political economy from the time of its birth up to its “grave”, as vulgar political economy was called by Marx."
- Capital, Volume 1, Volume 2, Volume 3 "Assume that our merchant operates his export business with capital of 30,000 ducats, sequins, pounds sterling or whatever is the case. Of that, say 10,000 are engaged in the purchase of domestic goods, whereas 20,000 are used in the overseas market. Say the capital is turned over once in two years. Annual turnover = 15,000. Now, our merchant wants to become a contractor, to have cloth woven for his own account. How much additional capital must he invest? Let us assume that the production time of the piece of cloth, such as he sells, averages two months — which is certainly very high. Let us further assume that he has to pay for everything in cash. Hence, he must advance enough capital to supply his weavers with yarn for two months. Since his turnover is 15,000 a year, he buys cloth for 2,500 in two months. Let us say that 2,000 of that represents the value of yarn, and 500 weavers' wages; then our merchant requires an additional capital of 2,000. We assume that the surplus-value he appropriates from the weaver by the new method totals only 5 per cent of the value of the cloth, which constitutes the certainly very modest surplus-value rate of 25 per cent.( 2,000 c + 500 v + 125 s; s' = 125/500 = 25%, p' = 125/2,500 = 5%). Our man then makes an extra profit of 750 on his annual turnover of 15,000, and has thus got his additional capital back in 2 2/3 years." from "Law of Value and Rate of Profit" in "Supplement by Frederick Engels" in "Capital Volume III" 
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