Part Four — The Production of Relative Surplus-Value Chapters 12–15. Relative surplus-value, co-operation, the division of labour in manufacture, and machinery and large-scale industry.

Part Three produced surplus-value by lengthening the working day. But the day has a limit — physical, moral, and now legal — and once the collective worker has forced a normal working day, capital needs another method. Part Four supplies it. If the day cannot be lengthened, the necessary portion of it can be shortened, so that more of a fixed day falls to surplus labour. This is relative surplus-value, and producing it requires revolutionizing the mode of production itself. Chapter 12 defines the concept and shows the individual capitalist's incentive hardening into the coercive law of competition. Chapters 13, 14, and 15 then trace the three historical stages through which capital raises the productivity of labour and reorganizes the labour process to that end: simple co-operation, the manufacturing division of labour, and machinery with large-scale industry.

The through-line is the transformation of the labour process by capital in pursuit of relative surplus-value, and the cost of that transformation to the worker. Each stage raises the social productive power of labour and each stage appropriates that power as a power of capital, so that the collective productivity the workers create confronts them as the property and the domination of another. Chapter 15, on machinery, is the culmination and the longest chapter of the book; its material on the subordination of living labour to the machine is a charter capture-target and is caught here with sustained engagement.

With the working day fixed, surplus labour can be increased only by contracting necessary labour — pushing back the point at which the worker has reproduced the value of his own labour-power. Excluding the option of simply paying below value (ruled out by the assumption that everything sells at its value), this requires that the value of labour-power itself fall, which requires that the means of subsistence be produced more cheaply, which requires higher productivity. From this Marx draws the pair of definitions that names the two methods of producing surplus-value.

I call that surplus-value which is produced by the lengthening of the working day, absolute surplus-value. In contrast to this, I call that surplus-value which arises from the curtailment of the necessary labour-time, and from the corresponding alteration in the respective lengths of the two components of the working day, relative surplus-value.

Marx, Capital I, page 432.

No individual capitalist sets out to cheapen the general value of labour-power; each is driven by a nearer motive. The first to raise productivity produces below the prevailing social value and pockets the difference as an extra surplus-value — until the method spreads. Marx names the mechanism that both rewards the innovator and compels the rest: the law of value operating as the coercive law of competition.

The law of the determination of value by labour-time makes itself felt to the individual capitalist who applies the new method of production by compelling him to sell his goods under their social value; this same law, acting as a coercive law of competition, forces his competitors to adopt the new method.

Marx, Capital I, page 436.

Aggregated across the economy, this drive gives capital a permanent tendency, and Marx states its endpoint bluntly: the cheapening of commodities is, in the end, the cheapening of the worker.

Capital therefore has an immanent drive, and a constant tendency, towards increasing the productivity of labour, in order to cheapen commodities and, by cheapening commodities, to cheapen the worker himself.

Marx, Capital I, pages 436–437.

This solves the riddle Quesnay used to pose — why the producer of exchange-value forever strives to lower exchange-value — since relative surplus-value rises exactly as commodity values fall. And it disposes of the apologists' claim that rising productivity benefits the worker: the aim is never to shorten the worker's day but to shrink the part of it he works for himself and enlarge the part he works for capital.

The objective of the development of the productivity of labour within the context of capitalist production is the shortening of that part of the working day in which the worker must work for himself, and the lengthening, thereby, of the other part of the day, in which he is free to work for nothing for the capitalist.

Marx, Capital I, page 438.