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.

Marx fixes the category at the outset: what the commodity costs the capitalist and what its production really costs are two different magnitudes.

When we combine the various portions of commodity value that simply replace the capital value spent in the commodity’s production, under the heading of cost price, we express on the one hand the specific character of capitalist production. The capitalist cost of the commodity is measured by the expenditure of capital, whereas the actual cost of the commodity is measured by the expenditure of labour..

Marx, Capital III, page 118.

And he warns at once that the category, though it explains nothing about the production of value, will nonetheless come to pose as one of its real determinants.

If I know that five-sixths of a commodity value of £600, i.e. £500, is simply an equivalent, a replacement value, for the capital of £500 that has been spent, and that this is therefore just sufficient to buy back, the material elements of this capital, I still neither know how this five-sixths of the commodity’s value which forms its cost price was produced, nor can I explain the origin of the last sixth that forms its surplus-value. Our investigation will show, however, that cost price does none the less, in the economy of capital, present the false semblance of an actual category of value production..

Marx, Capital III, page 119.

Because the surplus appears indifferent to the internal division of the advance, it presents itself as sprung from the capital as a whole — the step by which surplus-value takes on the profit form.

However this might be, the upshot is that the surplus-value springs simultaneously from all parts of the capital applied. The deduction may be substantially abbreviated, as in the clear and simple words of Malthus: ‘The capitalist… expects an equal profit upon all the parts of the capital which he advances.’ As this supposed derivative of the total capital advanced, the surplus-value takes on the transformed form of profit. A sum of value is therefore capital if it is invested in order to produce a profit, or alternatively profit arises because a sum of value is employed as capital..

Marx, Capital III, page 126.

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.

Marx spells out how the capitalist’s own standpoint consolidates the illusion, to the point where the surplus seems to arise from the act of sale.

From this standpoint alone, the capitalist is inclined to treat the cost price as the real inner value of the commodity, as it is the price he needs merely to preserve his capital. Added to this, however, is the fact that the cost price of the commodity is the purchase price which the capitalist has himself paid for its production, i.e. the purchase price determined by the production process itself. The excess value or surplus-value realized with the sale of the commodity thus appears to the capitalist as an excess of its sale price over its value, instead of an excess of its value over its cost price, so that the surplus-value concealed in the commodity is not simply realized by its sale, but actually derives from the sale itself..

Marx, Capital III, page 128.

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.

Historically and phenomenally, moreover, the order of discovery runs the other way round: the surface form comes first, and the essence has to be excavated from it.

It is the transformation of surplus-value into profit that is derived from the transformation of the rate of surplus-value into the profit rate, not the other way round. In actual fact, the rate of profit is the historical starting-point. Surplus-value and the rate of surplus-value are, relative to this, the invisible essence to be investigated, whereas the rate of profit and hence the form of surplus-value as profit are visible surface phenomena..

Marx, Capital III, page 134.

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 chapter’s summary formulation carries the whole argument of the Part.

Thus even if the rate of profit is numerically different from the rate of surplus-value, while surplus-value and profit are in fact the same and even numerically identical, profit is still for all that a transformed form of surplus-value, a form in which its origin and the secret of its existence are veiled and obliterated. In point of fact, profit is the form of appearance of surplus-value, and the latter can be sifted out from the former only by analysis. In surplus-value, the relationship between capital and labour is laid bare. In the relationship between capital and profit, i.e. between capital and surplus-value as it appears on the one hand as an excess over the cost price of the commodity realized in the circulation process and on the other hand as an excess determined more precisely by its relationship to the total capital, capital appears as a relationship to itself, a relationship in which it is distinguished, as an original sum of value, from another new value that it posits..

Marx, Capital III, page 139.

The mystification, Marx adds, only deepens as the analysis moves toward the concrete forms.

It appears to consciousness as if capital creates this new value in the course of its movement through the production and circulation processes. But how this happens is now mystified, and appears to derive from hidden qualities that are inherent in capital itself. The further we trace out the valorization process of capital, the more is the capital relationship mystified and the less are the secrets of its internal organization laid bare..

Marx, Capital III, page 139.

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 decisive corollary is stated in both directions: the two rates have come apart as magnitudes.

We saw above, with the variations in ν/C, how one and the same rate of surplus-value can be expressed in the most varied rates of profit. Here we see that one and the same rate of profit can be based on very different rates of surplus-value..

Marx, Capital III, page 160.

And the chapter’s governing statement of the determinants:

The rate of profit is thus determined by two major factors: the rate of surplus-value and the value composition of the capital. The effects of these two factors can be briefly summarized as follows, and we are able now to express the composition in percentages, since it is immaterial here in which of the two portions of capital the change originates..

Marx, Capital III, page 161.

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.

On turnover, the Volume II result enters the profit calculation directly.

The effect of the turnover on the production of surplus-value, and consequently also of profit, has already been discussed in Volume 2. To summarize it in brief, the time required for the turnover has the effect that the whole capital cannot be simultaneously employed in production. One part of this capital therefore always lies fallow, whether in the form of money capital, stocks of raw materials, finished but still unsold commodity capital, or outstanding debts that are not yet due for payment. The capital that is in active production, active in the production and appropriation of surplus-value, is always reduced by this amount, and the surplus-value that is produced and appropriated is reduced in the same proportion. The shorter the turnover time, the smaller is this idle portion of capital compared with the whole; the greater therefore is the surplus-value appropriated, other conditions being equal..

Marx, Capital III, page 163.

On economy in the use of constant capital, Marx names what the “economy” consists of.

The contradictory and antithetical character of the capitalist mode of production leads it to count the squandering of the life and health of the worker, and the depression of his conditions of existence, as itself an economy in the use of constant capital, and hence a means for raising the rate of profit. Since the worker spends the greater part of his life in the production process, the conditions of this process are to a great extent conditions of his active life process itself, his conditions of life, and economy in these conditions of life is a method of increasing the profit rate..

Marx, Capital III, page 179.

The indictment is generalized a few pages on.

If we consider capitalist production in the narrow sense and ignore the process of circulation and the excesses of competition, it is extremely sparing with the realized labour that is objectified in commodities. Yet it squanders human beings, living labour, more readily than does any other mode of production, squandering not only flesh and blood, but nerves and brain as well. In fact it is only through the most tremendous waste of individual development that the development of humanity in general is secured and pursued, in that epoch of history that directly precedes the conscious reconstruction of human society..

Marx, Capital III, page 182.

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.

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 category is defined the moment the averaging is posed.

The prices that arise when the average of the different rates of profit is drawn from the different spheres of production, and this average is added to the cost prices of these different spheres of production, are the prices of production. Their prerequisite is the existence of a general rate of profit, and this presupposes in turn that the profit rates in each particular sphere of production, taken by itself, are already reduced to their average rates..

Marx, Capital III, page 257.

Marx then derives the divergence of profit rates and their equalization in a single movement.

As a result of the differing organic composition of capitals applied in different branches of production, as a result therefore of the circumstance that according to the different percentage that the variable part forms in a total capital of a given size, very different amounts of labour are set in motion by capitals of equal size, so too very different amounts of surplus labour are appropriated by these capitals, or very different amounts of surplus-value are produced by them. The rates of profit prevailing in the different branches of production are accordingly originally very different..

Marx, Capital III, page 257.

These 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.

From the average follow the two category definitions on which the rest of the volume runs.

The profit that falls to a capital of given size according to this general rate of profit, whatever its organic composition might be, we call the average profit. That price of a commodity which is equal to its cost price, plus the part of the annual average profit on the capital applied in its production (not simply the capital consumed in its production) that falls to its share according to its conditions of turnover, is its price of production..

Marx, Capital III, page 257.

The image Marx reaches for is the joint-stock company: each capital draws its dividend on the common surplus.

The various different capitals here are in the position of shareholders in a joint-stock company, in which the dividends are evenly distributed for each 100 units, and hence are distinguished, as far as the individual capitalists are concerned, only according to the size of the capital that each of them has put into the common enterprise, according to his relative participation in this common enterprise, according to the number of his shares..

Marx, Capital III, page 258.

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 265.

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.

Marx states the identity first for the five-capital example, generalizing on the spot.

The total price of commodities I-V would thus be the same as their total value, i.e. the sum of the cost prices I-V plus the sum of the surplus-value or profit produced; in point of fact, therefore, the monetary expression for the total quantity of labour, both past and newly added, contained in commodities I-V. And in the same manner, the sum of prices of production for the commodities produced in society as a whole – taking the totality of all branches of production – is equal to the sum of their values..

Marx, Capital III, page 259.

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 273.

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.

The acknowledgment on which that debate fastened is Marx’s own, made in the course of the chapter: once prices of production exist, they enter into the cost prices of other commodities, so the cost price itself can no longer be read as a sum of values.

The development given above also involves a modification in the determination of a commodity’s cost price. It was originally assumed that the cost price of a commodity equalled the value of the commodities consumed in its production. But for the buyer of a commodity, it is the price of production that constitutes its cost price and can thus enter into forming the price of another commodity. As the price of production of a commodity can diverge from its value, so the cost price of a commodity, in which the price of production of other commodities is involved, can also stand above or below the portion of its total value that is formed by the value of the means of production going into it. It is necessary to bear in mind this modified significance of the cost price, and therefore to bear in mind too that if the cost price of a commodity is equated with the value of the means of production used up in producing it, it is always possible to go wrong..

Marx, Capital III, page 264.

And the chapter already draws the epistemic consequence that Part Two bequeaths to everything after it: the transformation hides the origin of profit from every agent inside the system.

It is important for him only in so far as the quantity of surplus-value created in his own branch intervenes as a co-determinant in regulating the average profit. But this process takes place behind his back. He does not see it, he does not understand it, and it does not in fact interest him. The actual difference in magnitude between profit and surplus-value in the various spheres of production (and not merely between rate of profit and rate of surplus-value) now completely conceals the true nature and origin of profit, not only for the capitalist, who has here a particular interest in deceiving himself, but also for the worker. With the transformation of values into prices of production, the very basis for determining value is now removed from view..

Marx, Capital III, page 268.

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.

The mechanism itself, in Marx’s words:

Capital withdraws from a sphere with a low rate of profit and wends its way to others that yield higher profit. This constant migration, the distribution of capital between the different spheres according to where the profit rate is rising and where it is falling, is what produces a relationship between supply and demand such that the average profit is the same in the various different spheres, and values are therefore transformed into prices of production..

Marx, Capital III, page 297.

Within each sphere, the regulating magnitude is the market value.

Market value is to be viewed on the one hand as the average value of the commodities produced in a particular sphere, and on the other hand as the individual value of commodities produced under average conditions in the sphere in question, and forming the great mass of its commodities. Only in extraordinary situations do commodities produced under the worst conditions, or alternatively the most advantageous ones, govern the market value, which forms in turn the centre around which market prices fluctuate – these being the same for all commodities of the same species..

Marx, Capital III, page 279.

On the priority of value over price of production, Marx is explicit in both the systematic and the historical register.

The exchange of commodities at their values, or at approximately these values, thus corresponds to a much lower stage of development than the exchange at prices of production, for which a definite degree of capitalist development is needed..

Marx, Capital III, page 277.

Apart from the way in which the law of value governs prices and their movement, it is also quite apposite to view the values of commodities not only as theoretically prior to the prices of production, but also as historically prior to them..

Marx, Capital III, page 277.

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.

Chapter 11’s demonstration begins from the average capital, where profit and surplus-value coincide.

A general rise in wages, everything else being equal, means a fall in the rate of surplus-value. For the average capital, profit and surplus-value coincide. Say that wages rise by 25 per cent. The same amount of labour which previously cost 20 to set in motion now costs 25. We then have a turnover value of 80c + 25ν + 15s, instead of 80c + 20ν + 20s. The labour set in motion by the variable capital still produces a value sum of 40, as before. But if ν rises from 20 to 25, the excess s or p is now only 15. A profit of 15 on 105 is 14 2/7 per cent, and this would be the new average rate of profit.

Marx, Capital III, page 302.

Chapter 12 then names the notion that rules the capitalist’s own consciousness.

The basic notion in this connection is that of average profit itself, the idea that capitals of equal size must yield equal profits in the same period of time. This is based in turn on the idea that capital in each sphere of production has to participate according to its size in the total surplus-value extorted from the workers by the total social capital; or that each particular capital should be viewed simply as a fragment of the total capital and each capitalist in fact as a shareholder in the whole social enterprise, partaking in the overall profit in proportion to the size of his share of capital..

Marx, Capital III, page 312.

And it closes on what that notion makes invisible.

He simply forgets (or rather he no longer sees it, since competition does not show it to him) that all these grounds for compensation that make themselves mutually felt in the reciprocal calculation of commodity prices by the capitalists in different branches of production are simply related to the fact that they all have an equal claim on the common booty, the total surplus-value, in proportion to their capital. It appears to them, rather, that the profit which they pocket is something different from the surplus-value they extort; that the grounds for compensation do not simply equalize their participation in the total surplus-value, but that they actually create profit itself, since profit seems to derive simply from the addition to the cost price made with one justification or another..

Marx, Capital III, page 312.