Part One — The Transformation of Surplus-Value into Profit and of the Rate of Surplus-Value into the Rate of Profit Chapters 1–7. Cost price and profit, the rate of profit, its relation to the rate of surplus-value, and the effects of turnover, economy, and price change.

Volume III changes the level of analysis. Volumes I and II analysed capital "in general" — the production and circulation of surplus-value in their inner constitution. Volume III follows capital out to the surface of society, into the forms in which it appears to the agents of production themselves and acts through competition: profit, the general rate of profit, interest, rent. The governing thesis of the whole volume is that these surface forms systematically disguise the depths that produced them, so that the origin of surplus-value in unpaid labour becomes ever more thoroughly veiled the closer one gets to the categories of everyday economic consciousness. Part One takes the first step of this descent. It shows how surplus-value assumes the form of profit and how the rate of surplus-value assumes the form of the rate of profit — two transformations that, in one stroke, hide the source of the surplus in the variable capital by referring it instead to the total capital advanced. The cost-price category (k = c + v) obliterates the distinction between constant and variable capital on which the whole theory of exploitation rests; profit (the surplus reckoned against the whole outlay) then appears as an offspring of capital as such rather than of living labour. Chapters 1 through 3 establish the two transformations and the relation between the rates; Chapters 4 through 7 examine how turnover, economies in the use of constant capital, and price fluctuations modify the rate of profit — all of them further loosening the visible tie between profit and its real source.

Marx introduces the cost price, the sum the capitalist actually lays out — constant capital plus variable capital, k = c + v. Because the surplus labour costs the capitalist nothing, the value of the commodity C = c + v + s can be rewritten from his standpoint as k + s, and the surplus, reckoned now against the whole outlay, presents itself as profit. The value-formula becomes the profit-formula, and in the passage the source of the surplus is lost.

If we call profit p, the formula C = c + v + s = k + s is converted into the formula C = k + p, or commodity value = cost price + profit. Profit, as we are originally faced with it, is thus the same thing as surplus-value, save in a mystified form, though one that necessarily arises from the capitalist mode of production. Because no distinction between constant and variable capital can be recognized in the apparent formation of the cost price, the origin of the change in value that occurs in the course of the production process is shifted from the variable capital to the capital as a whole.

Marx, Capital III, page 127.

The cost price is thus the first veil. It sets a floor beneath which the capitalist cannot sell without losing capital, so he treats it as the commodity's "real inner value"; and because the difference between cost price and value is precisely the surplus-value, a whole band of possible selling prices opens up between them, within which a commodity can be sold below its value and still at a profit. This gap — value minus cost price — is what makes competition's price movements possible, and Marx flags here that the general rate of profit and the prices of production analysed in Part Two will rest on exactly this difference.

The second transformation follows. Surplus-value measured against the variable capital that produced it is the rate of surplus-value, s/v — the exact index of exploitation from Volume I. Surplus-value measured against the total capital advanced is the rate of profit, s/C = s/(c+v). To the capitalist only the second is visible, and it necessarily understates the first, since its denominator is larger. Marx first restates plainly where profit comes from.

The capitalist's profit, therefore, comes from the fact that he has something to sell for which he has not paid. The surplus-value or profit consists precisely in the excess of commodity value over its cost price, i.e. in the excess of the total sum of labour contained in the commodity over the sum of labour that is actually paid for.

Marx, Capital III, page 133.

But because the capitalist relates the surplus to his whole capital and not to its variable part alone, the rate of profit obscures the rate of exploitation. The same rate of surplus-value can appear as very different rates of profit depending on the composition of capital, and the same rate of profit can conceal very different rates of surplus-value. The rate of profit is the surface form in which the rate of exploitation is at once expressed and hidden — expressed because it derives from it, hidden because its magnitude no longer reveals it.

The longest chapter of the Part works out the exact mathematical relation between the two rates. The rate of profit equals the rate of surplus-value multiplied by the ratio of variable capital to total capital: p′ = s′ · (v/C). From this single relation Marx derives the behaviour of the profit rate as each of its determinants varies — the rate of surplus-value, the value of labour-power, the length and intensity of the working day, and above all the composition of capital. The upshot that matters for the volume is structural: because the profit rate depends on the composition of capital as well as on the rate of exploitation, two capitals exploiting labour at exactly the same rate will show different rates of profit if their compositions differ, and the higher the proportion of constant to variable capital, the lower the rate of profit for a given rate of surplus-value. This dependence of the profit rate on composition is the hinge on which both Part Two (the equalization of profit rates across differing compositions) and Part Three (the tendency of the profit rate to fall as composition rises) will turn.

The remaining chapters of the Part show how the visible rate of profit is pulled about by circumstances that have nothing to do with the rate of exploitation, widening still further the gap between profit and its source. Chapter 4 (added by Engels) brings in turnover: since the mass of surplus-value produced in a year depends on how many times the variable capital turns over, the annual rate of profit rises with the speed of turnover, so that a faster-turning capital shows a higher profit rate at the same rate of exploitation — the Volume II result carried into the theory of profit. Chapter 5 examines economies in the use of constant capital: by driving down the value of the constant capital advanced (crowding more workers under one roof, working machinery in shifts, recycling waste, cheapening raw materials), the capitalist raises the rate of profit without raising the rate of surplus-value, and Marx notes bitterly that these economies are largely wrung from the worker's life and limb — ventilation, safety, space sacrificed to the profit rate. Chapter 6 analyses the effect of price fluctuations, especially in raw materials, on the profit rate, and the "release" and "tying-up" of capital these produce; Chapter 7 gathers supplementary remarks. Across all of them the lesson is the same: the rate of profit is a surface magnitude, responsive to turnover, economy, and price, and its movements no longer read off the rate of exploitation beneath them — which is exactly why the profit rate can become, for the agents of production and for vulgar economics, an apparently self-standing property of capital.