But, in aggregate, as we have seen, the consequence of all these transactions is a mass exchange between Department 1 and 2, with the former providing the latter with necessary means of production and the latter providing the former with consumer goods. Within the context of this mass social exchange, we have seen how it is possible to break the different components of the physical output down into its value components of c+v+s, as Marx did in Volume 1.
So, for example, of Department 2 output, of £3,000, £2,000 constitutes c, £500 v, and another £500 s. Of the physical product then, two-thirds could be equated with c, and one sixth each to v and s. Similarly, with Department 1, it broke down £4,000 c, £1,000 v, and £1,000 s. Two thirds of its output was needed to replace its constant capital, and one sixth each to replace the variable capital and surplus value.
On this basis, it becomes apparent that one third of Department 1's output is exchanged for two-thirds of Department 2's output. The one third of Department 1 output that is exchanged is equal to that portion of its output that is equal to the new value created, i.e. equal to v+s, and the two-thirds of Department 2 output that is exchanged for it, is equal to that portion of its output that is equal to c.
Looking at it from the perspective of these physical components is central to Marx’s analysis and explanation here. In setting it out this way, Marx can then argue in relation to the physical output that is exchanged.
“The entire constant capital-value contained in the commodity mass II representing a value of 3,000 is therefore comprised in 2,000 c, and neither 500 v nor 500 s hold an atom of it. The same is true of v and s respectively.
In other words, the entire share of commodity mass II that represents constant capital-value and therefore is reconvertible either into its bodily or its money-form, exists in 2,000 c. Everything referring to the exchange of the constant value of commodities II is therefore confined to the movement of 2,000 II c. And this exchange can be made only with I (1,000 v+ 1,000 s).
Similarly, as regards class I, everything that bears in the exchange of the constant capital-value of that class is to be confined to a consideration of 4,000 I c.” (p 456)
In other words, using the same method he used in Volume I, it is as though the two-thirds of output is equal to the value of c, containing only constant capital, that the one sixth equivalent of the variable capital contained no constant capital at all etc. This way of looking at things simplifies the important exchange to be considered here between II(c) and I(v+s).