Exchange proves not only that the commodity has a use for somebody, but also that another producer is not offering an identical commodity more cheaply. In any particular instance of sale, this does not prove all the labour producing the commodity was socially necessary – the producer may be inefficient relative to the average – but over time inefficient producers either become more efficient or are driven out of the market for their commodity. It is only because of this process of general commodity exchange (leaving ‘capitalism’ out of it for a second), which presupposes a social force driving labour processes to be as efficient as is materially possible, that we can talk about ‘abstract labour’. Even then, ‘abstract labour’ cannot be easily located at the level of the individual because labour processes are collective and it is only the collective product that is subject to testing by exchange on the market.

The interesting question to me is how the discussion of capitalist competition in Vol 3 supercedes the discussion of value in Vol 1, and what this means for the concept of abstract labour. In Vol 1 Marx only seems to discuss competition between producers making the same kind of commodity, when clearly the concept of ‘abstract labour’ requires competition between capitals in all different industries, where the average rate of profit is the enforcer, rather than the going price in any particular industry.

This still means pressure to make labour processes as efficient as possible, but also to make use of capital as efficiently as possible (the value quantity of capital invested, not in the narrow sense of ‘means of production’). Also it really requires some quantitative consideration of demand (as opposed to whether something has a ‘use value’ or not). Marx doesn’t consider either of these properly until Vol 3, and then he doesn’t explicitly revisit the concept of ‘abstract labour’.