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 resolution treats the whole social capital as one. The total surplus-value produced by all capitals is pooled and redistributed over them in proportion to their size, yielding a single general rate of profit — the ratio of total surplus-value to total social capital. This general rate is the weighted average of the individual rates.

the different rates of profit are balanced out by competition to give a general rate of profit which is the average of all these different rates.

Marx, Capital III, pages 256–257.

Each capital then draws profit at this common rate on its advance, and the price at which its commodity sells becomes cost price plus that average profit: the price of production. Marx restates the formula exactly once the general rate is in hand.

The formula that the price of production of a commodity = k + p, cost price plus profit, can now be stated more exactly; since p = kp′ (where p′ is the general rate of profit), the price of production = k + kp′.

Marx, Capital III, page 264.

Prices of production therefore deviate from values: a high-composition capital sells its product above value (it draws more profit than the surplus-value it produced), a low-composition capital sells below value. Surplus-value is redistributed among capitals by competition, so that each receives a share proportional to its capital rather than to the labour it exploited. This is why individual prices no longer show values. But the redistribution is a redistribution, not a creation: at the level of the total social product, nothing is added or lost, and the two aggregate identities hold.

The sum of the profits for all the different spheres of production must accordingly be equal to the sum of surplus-values, and the sum of prices of production for the total social product must be equal to the sum of its values.

Marx, Capital III, page 272.

These two equalities are the anchor of Marx's claim that the price-of-production system is only a redistributed form of the value system, not a departure from the labour theory of value: total value governs total price, total surplus-value governs total profit, and the deviations at the level of individual commodities cancel in the aggregate. The consistency of this claim — given that Marx transforms the outputs into prices of production but leaves the cost-price inputs reckoned in values — is exactly what Bortkiewicz, and after him the whole twentieth-century literature, contested. The brief records Marx's construction and its two anchoring equalities; the adjudication belongs to the later read-through against the transformation debate.

Chapter 10 shows the mechanism that produces the general rate: competition, working through the migration of capital. Where the profit rate is high, capital pours in, output expands, prices fall; where it is low, capital withdraws, output contracts, prices rise — until rates are levelled. Marx distinguishes two levels of this process. Within a single branch, competition among the many producers establishes a market value (the value of the commodity produced under the socially average conditions of that branch), around which market prices oscillate. Between branches, competition establishes the general rate of profit and the prices of production. He is careful to insist that value remains the regulator behind the surface: prices of production are governed by, and gravitate around, the values from which they are derived, and the market price oscillates around the price of production as the price of production oscillates around value. The law of value is not abolished by the equalization of profit rates; it operates through it, one level removed. This is the point at which the "esoteric" categories of Volumes I and II and the "exoteric" categories of competition are shown to be connected rather than opposed — the connection that vulgar economics, seeing only the surface, cannot make.

Two shorter chapters close the Part. Chapter 11 examines what a general rise or fall in wages does to prices of production. Because a wage change alters the rate of surplus-value uniformly and therefore lowers or raises the general rate of profit, it shifts prices of production in opposite directions according to composition: a wage rise lowers the price of production of commodities made by high-composition capitals and raises that of low-composition capitals, while the price of a commodity of average composition (where price of production coincides with value) is unchanged. This refutes the Ricardian and vulgar view that wage rises simply raise all prices. Chapter 12 gathers supplementary remarks, including the observation that the capitalist's own consciousness registers the price of production, not the value, as the "natural" price, and that the whole apparatus of average profit makes the connection between profit and surplus labour invisible to the agents who live inside it — preparing the ground for the still deeper mystifications of interest and rent in the Parts to come.