Part Two — The Transformation of Profit into Average Profit Chapters 8–12. Differing compositions of capital, the formation of the general rate of profit, and the transformation of values into prices of production.

This Part contains the analysis for which Volume III is most fought over: the transformation of values into prices of production. Part One left a puzzle. Since the rate of profit depends on the composition of capital, capitals of different composition but equal size, exploiting labour at the same rate, would produce different rates of profit — a capital rich in living labour (low composition) yielding more surplus-value, and therefore more profit, than a capital rich in machinery (high composition). Yet competition will not tolerate lasting differences in the profit rate; capital flows from low-profit to high-profit branches until a general, average rate is established across the whole economy. The consequence is that commodities cannot, in general, sell at their values. They sell at prices of production — cost price plus the average profit on the capital advanced — and these diverge systematically from values, above value where composition is high, below value where it is low. Chapter 8 poses the problem of differing compositions; Chapter 9 forms the general rate of profit as the average and derives the price of production, showing that at the level of the whole social product the two great aggregate equalities hold — total profit equals total surplus-value, total price of production equals total value; Chapter 10 shows how competition enforces the equalization; Chapters 11 and 12 add the effects of wage movements and supplementary remarks. The "transformation problem" — whether Marx's procedure of transforming outputs while leaving inputs in value terms is consistent — is the great battlefield of twentieth-century value theory. This brief lays out Marx's own construction and the two aggregate equalities he rests it on, and holds the debate in view for the later read-through without adjudicating it.

Marx sets out the problem with worked examples. Five capitals of equal size but differing organic composition, applied at the same rate of surplus-value, produce different masses of surplus-value — the more variable capital a given total contains, the more living labour it sets in motion and the more surplus-value it yields. If each sold its product at value, each would show a different rate of profit. This directly contradicts the observed fact that capitals of equal size tend to earn equal profits regardless of the trade they are in. The chapter fixes the contradiction precisely, so that Chapter 9 can resolve it: the profit rate as it actually rules the market cannot be the value-determined rate of the individual capital, because competition will not let unequal rates on equal capitals survive.

The chapter’s conclusion states the result of the whole demonstration.

We have shown, therefore, that in different branches of industry unequal profit rates prevail, corresponding to the different organic composition of capitals, and, within the indicated limits, corresponding also to their different turnover times; so that at a given rate of surplus-value it is only for capitals of the same organic composition – assuming equal turnover times – that the law holds good, as a general tendency, that profits stand in direct proportion to the amount of capital, and that capitals of equal size yield equal profits in the same period of time..

Marx, Capital III, page 252.

And Marx immediately names the scandal this creates for the theory of value — the problem the next chapter exists to resolve.

The above argument is true on the same basis as our whole investigation so far: that commodities are sold at their values. There is no doubt, however, that in actual fact, ignoring inessential, accidental circumstances that cancel each other out, no such variation in the average rate of profit exists between different branches of industry, and it could not exist without abolishing the entire system of capitalist production. The theory of value thus appears incompatible with the actual movement, incompatible with the actual phenomena of production, and it might seem that we must abandon all hope of understanding these phenomena..

Marx, Capital III, page 252.