In fact, Marx does explain this, even in Capital I. He explains it in even greater detail, in Capital II, as well as in Theories of Surplus Value, and The Grundrisse. In the latter, in particular, Marx explains the difference between the manifestation of the surplus labour as either surplus product or surplus value. The essence of the solution to this problem resides in the distinction between the social cost of production and the private cost of production, and the role of the producer as consumer. If we take product A, it takes, let us say, 10 hours of labour to produce. If, however, only 8 hours of labour are required to reproduce the labourer themselves, they will have undertaken 2 hour of surplus labour. Now, let's consider how this appears under different sets of social relations.
Firstly, if the labourer is a free, independent commodity producer, the fact that they only required 8 hours of labour for their own reproduction, does not change the fact that they expended 10 hours of labour on the production of A. If we ignore, for the sake of simplicity, here, the question of simple or complex labour etc., then, when they come to exchange A, as a commodity, for some other commodity, B, they will value A as equal to 10 hours labour, including the 2 hours of surplus labour, and will exchange it for a quantity of B, also, equal to 10 hours of labour. The producer of B will do the same.
In both cases, the commodities exchange at their value, which, inherently, includes the 2 hours of surplus labour, which, in this case, assumes the form of both a surplus product, and a surplus value. In other words, for both labourers, the product of their labour includes a surplus product, over and above what was required for the reproduction of their labour-power. This surplus product is what was physically produced in the 2 hours of surplus labour. Because, in this set of social relations, based on commodity production and exchange, the labour expended is manifest as the value of he commodity, and forms the basis of the proportions in which different commodities exchange with each other, their exchange-values, this surplus labour, in the surplus product, also, takes the form of a surplus value.
If A and B are not produced by commodity producers but simply self sustaining, direct producers, the surplus labour does not take the form of a surplus value, but, only, of a surplus product. That surplus product may be used to save for the future, as insurance, or to cover the needs of population growth, i.e. the expansion of the household, or to allow time to be spent on other forms of production, and so on. The only basis upon which the labour expended will play a role in terms of the value of the production, is in terms of setting this value/labour expended against the use-value obtained, as against the use-value of what could have been produced instead.
In terms of the producers of A and B, no force is required to obtain this surplus product or surplus value; it is the inevitable consequence of their performance of surplus labour. Nor is any force, compulsion or exploitation required to realise the produced surplus value, when commodity A is exchanged with commodity B, by two, free, commodity producers. A and B have a value of 10 hours labour, which includes 2 hours of surplus labour. When the producer of A obtains a quantity of B, and vice versa, they both obtain a quantity of surplus labour/value proportionate to the surplus labour they performed, and which is contained in the 10 hours value of both A and B.
In both cases, the 10 hours value is equal to the social cost of production of these commodities, i.e. if society desires them, this is the quantity of social labour-time it must expend. In both cases, this is also equal to their private cost of production. In other words, the producers of A and B both had to expend 10 hours of their own labour in their production. Note that this cost of production/socially necessary labour-time is quite different from the value of the labour-power of the labourers that produced them. That value was only equal to 8 hours of labour. It is the difference between these two that is the basis of the surplus labour/product/value.
In a society based on commodity production and exchange, where commodities are produced and exchanged by free labourers, it is the social cost of production which forms the basis of the value of commodities, and, thereby, their exchange-values. There is no greater problem, therefore, in realising the surplus-value, inherent within that value than were the labourer to be simply a direct producer, who expends 2 hours of surplus labour in producing a surplus product for their own future consumption.
Each commodity producer, here, is, also, an independent consumer. They enter the market in search of commodities to buy for their own consumption (personal or productive) and, consequently, are confronted by other commodity producers who seek to exchange their own commodities at their value, i.e. the labour-time expended on their production.
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