The previous chapter established that if commodities are exchanged for prices which are their values then capitals in different branches of industry have different rates of profit because different branches of industry have different organic compositions and turnovers. Organic composition is the value composition $c/v$ insofar it is determined by the technical composition. Organic composition depends on the technical composition – how many means of production are needed to put a certain amount of labour into motion – and on the price of the means of production.¹

Differing rates of profit, however, are in contradiction to the capitalist mode of production. Spheres of production with a low rate of profit would not be adequate means for the accumulation of capital, which would undermine the reproduction of total social capital. Capital demands a general rate of profit. This, however, is not the result if commodities are exchanged for prices which are their values. This apparent contradiction between the law of value and general rate of profit is to be resolved.

1. Law of value: capitals in their respective branches of industry produce heaps of commodities which have value. These commodities contain surplus-value, a surplus over the advance, which depends on the rate of surplus-value and on the advance in $v$.

2. General rate of profit: capitals realise a surplus proportionally to their advance in $c+v$, not proportionally to their advance in $v$.

The prices realised by capitals in their respective branches of industry cannot match $c+v+s$, they must deviate: $c+v+p$ where $p$ is the general profit for a given overall advance in $c$ and $v$.

However, it is not possible to withdraw overall more from circulation than is put into it. If the law of value holds, then there is no more value to distribute than surplus-value was created. The general rate of profit cannot be 100%, if only 50% surplus-value were created relative to the advance. On the other hand, all surplus-value must be distributed. The general rate of profit can only realise a proportion of surplus-value. The general rate of profit is the average rate of profit.

This is a systematic reason why prices must deviate from price: capitals do not realise the surplus-value they produced but the average profit. The law of value and general rate of profit are only reconcilable if prices deviate from values systematically, i.e. we are not only talking about fluctuations here.

Example. Let the rate of surplus-value be 100% in all branches of industry. We abstract from the effect of turnover on the mass of surplus-value, i.e. for all capitals the yearly rate of surplus-value $M/v$ is equal.

All in all, the spheres I-V advanced 500 and produced a surplus-value of 110. The average composition of all five spheres is

$390c (80c + 70c + 60c + 85c + 95c) + 110v$
or as parts of 100: $78c\ (390/500) + 22v\ (110/500)$.

The average surplus-value is $22s = 100\% · 22v = 110s/5$ and the average value of products per sphere is $122 = 100 + 22 = 610/5$. The average rate of profit is $22\% = 22/100$. For all capitals to realise the same profit they must sell their collections of commodities at a price of 122 each. This way, they can realise the general rate of profit of $22\%$.

For the formation of the general rate of profit the distinction between fixed and circulating capital is irrelevant. The surplus is related to the advance, regardless of how this advance is split between fixed and circulating capital. However, the distinction between fixed and circulation capital plays a role for the cost price, as part of fixed capital was applied by not worn out yet.

If every capital still realises the general rate of profit, i.e. the average rate of profit, then the prices of their respective heaps of commodities are as follows:

The deviation of prices from value cancel each other out on average: what one gains, another looses. It has to be this way, as we are dealing with redistribution to achieve a general rate of profit of 22% here.

Price of production. The unity of law of value and general rate of profit necessitates a modification of the commodity. Commodities are not exchanged at value, but at prices of production: the sum of cost price and average profit²

1. Capitals advance money and produce surplus-value. If organic composition or turnover differ, then the relationship of surplus-value to advance differ even if the rate of surplus-value is the same.

2. The sum of these surplus-values related to the sum of advances gives the average rate of profit.

3. Average profit is the average rate of profit multiplied with the individual advance, regardless of organic composition. Average profit is related to advance not to consumed capital.

4. The price of production of a commodity is the sum of the particular cost price of a commodity and general average profit related to the advance.

Individual and general part. The two components of the price of production – cost price and average profit – are different in to what they relate:³

• The cost price replaces the capital actually consumed in a particular branch of industry. It is related to the actually consumed individual capital in a sphere.

• Average profit is not the surplus-value actually produced in a sphere, but a general profit. Every capital draws a part of the surplus-value produced in society depending on how big it is. This is analogously to stock holders who draw dividends according to the shares they hold.

Value. Prices of production presume a general rate of profit which is the average rate of profit, which in turn presupposes individual rates of profit which are averaged. Otherwise, we are left with “average of what?”. These individual profit rates are explained from value. Without value we cannot explain the average rate of profit and the permanent deviation from values.⁴

For all of society the sum of prices of production is the sum of cost prices (transferred and reproduced value) + the sum of surplus-values (newly created additional value). Hence, the sum of prices of production is the sum of values.⁵

Total profit. That we have “sum of cost prices + sum of profits = sum of values of commodities in society” might be confusion, since the cost price in industry A includes the profits of industries B, C, D, i.e. those industries which produce the means of production for the production in A. Hence, we have to be careful not count profit twice. Once as profit for B, C, D and once as component of the cost price for A.

If we already added the profit in a cost price as profit, we cannot add it again as cost price, i.e. we must subtract it before we add up. If, for example, the cost price of commodity A contains a profit $p$ – this is the profit of producers of means of production – and if the producer of A realises a profit of $p_1$, then total profit in A is $P = p + p_1$. The total cost price $k$ of the commodity is then the price of the commodity minus overall profit (Marx writes “cost price minus total profit” but that makes no sense). The price of the commodity is then $k + P = k + p + p_1$.⁶ This is analogous to surplus-value: the surplus-value of a producer of means of production enters the value of means of production. If we want to express a separation of the commodity in transferred and reproduced value on the one hand and surplus-value on the other hand, then we cannot count surplus-value twice: once as part of $c$ and then as part of $m$.

Turnover and average rate of profit. For the appropriation of profit the individual turnover does not matter any more, all capitals draw a part of total social surplus-value in relation to their advance, also independent of their turnover. However, the turnover enters into the average rate of profit, since it enters individual rates of profit over which the average is taken. This is analogous to organic composition: organic composition and turnover determine individual profit rates from which the average rate of profit is derived. When capitals draw profit depending on their advance organic composition and turnover play no role any more.

Average of masses of capital per sphere. In the example above all branches of industry saw the same amount of capital invested in them, 100, to highlight the differences in the profit rates and their average. The individual rate of profit is not affected by size: 10% stay 10% regardless of whether 10/100 or 100/1000 are meant.

However, it does make a difference for the average how much capital is advanced in each sphere with a given organic composition. If sphere I has a profit rate of 10% and sphere II has a profit rate of 20% then the average rate of profit is 15% if in both spheres the same amount of capital is invested and 12.5% if in sphere I three times as much capital is invested as in sphere II:

a. $A = 200C, B=200C → (20s + 40s)/(200C + 200C) = 60/400 = 15\%$
b. $A = 300C, B=100C → (30s + 20s)/(300C + 100C) = 50/400 = 12.5\%$

In case (b) all spheres produce $50s$ with an advance of $400C$ and all realise a part of the produced $50s$ in accordance with their share of $400C$. We, hence, cannot simply average over the profit rates of the branches but must weight the branches depending on how much capital is advanced in them. It is not the average of spheres of production but of capitals, for which each sphere is merely a means for profit.

The general rate of profit is hence determined by two factors:⁷

1. organic composition of capitals (and their turnovers) in different spheres of production and
2. the distribution of capitals over branches.

Above and below value. Capitals with a bigger part of constant capital than average we call capitals of higher composition. Capitals with a smaller part of constant capital than average we call capitals of lower composition.⁸

A capital of higher composition produces less surplus-value than it realises (e.g. $90c + 10v$ produce $10s$ but that capital realises $20s$), a capital of lower composition produces more surplus-value than it realises (e.g. $70c + 30v$ produce $30s$ but that capital only realises $20s$).

Prices of production of $c$ and $v$. The prices of commodities which form the cost price are themselves determined as cost price + average profit. That is, constant and variable capital are not purchased for prices which correspond to value. The cost price of $c+v$ is not the value of components of $c+v$. The prices of constant capital and of the means of subsistence of workers are composed of cost price + average profit of another capitalist which can be more or less than cost price + surplus-value.

In Chapter 1 of Volume 3 $c+v$ are transformed into the cost price of the commodity $k$, i.e. what the commodity costs capital. The value of a commodity was determined as cost price + surplus-value $k + s$. The value of a commodity is now expressed as cost price + average profit $k + p$ = price of production.⁹ Whereas the price of production and commodity value are distinguished by whether surplus-value or average profit enters, both include the same cost price. The value of a commodity includes its cost price, not its “real cost price“. Thus, when Marx writes:

264:1 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.

then this is not an admission of an error in the earlier tables but an indication that the profit rate is related to the actual (socially necessary) advance not to “true” or “authentic” values.

He continues:

264:1 It still remains correct that the cost price of commodities is always smaller than their value. For even if a commodity’s cost price may diverge from the value of the means of production consumed in it, this error in the past is a matter of indifference to the capitalist. The cost price of the commodity is a given precondition, independent of his, the capitalist’s, production, while the result of his production is a commodity that contains surplus-value, and therefore an excess value over and above its cost price. As a general rule, the principle that the cost price of a commodity is less than its value has been transformed in practice into the principle that its cost price is less than its price of production. For the total social capital, where price of production equals value, this assertion is identical with the earlier one that the cost price is less than the value. Even though it has a different meaning for the particular spheres of production, the basic fact remains that, taking the social capital as a whole, the cost price of the commodities that this produces is less than their value, or than the price of production which is identical with this value for the total mass of commodities produced. The cost price of a commodity simply depends on the quantity of paid labour it contains, while the value depends on the total quantity of labour it contains, whether paid or unpaid; the price of production depends on the sum of paid labour plus a certain quantity of unpaid labour that is independent of its own particular sphere of production.

1. The cost price is always smaller than the production price, as the purpose of production is more wealth counted in money.

2. The value of commodities is cost price + surplus-value and hence always bigger than cost price. If the cost price corresponded to the value of the means of production is irrelevant: “this error in the past is a matter of indifference to the capitalist” is not a criticism of bourgeois ideology but expresses the socially valid economic standpoint: how much does $c+v$ cost capital?

3. On a social level the sum of prices of production are equal to the sum of values, since these prices of production only redistribute surplus-value. Hence, on a social level the sum of cost prices ($c+v$) is smaller than the sum of values ($c+v+s$).

Profit per commodity. If the average value composition is $80c + 20v$ and the rate of surplus-value is $m’ = 100\%$ then the average rate of profit is $20\%$. A capital of 100 then realise 20 surplus-value, regardless of what the cost price of its commodities. If the sum of cost prices is $K$, then a capital earns $K + 20$. Average profit does not depend on cost price but on advance.

In order to relate profit to a single commodity, a single commodity must be related to total advance. That is, if an advance produces $w$ commodities per year then the price per commodity is $k + p’ ⋅ C/w$ where $k$ is the cost price of one commodity.¹⁰ The fraction $C/w$ can be read as advance per commodity or we can read $p’ ⋅ C/w$ as profit per commodity, such that the average rate of profit is realised for $C$.

An example: Let $C=1,100$, of which 1,000 are fix and 100 circulation, $m’ = 100\%$, average profit rate $20\%$, annual depreciation of fixed capital 500 and the annual product 100 commodities. Turnover is once per year. Then the cost price of each commodity is $1,000/200 + 100/100 = 4 + 1 = 6$. Overall profit by the general rate of profit is $1,100/ ⋅ 20\% = 220$ per year or $2.2$ per commodity. The price of production is hence $6 + 2.2 = 8.2$. Expressed differently: a capital of $1100$ realises a profit of $220$ per year. If 100 commodities are produced per year, each commodity must realise a profit of $2.2$.

This consideration, however, does not fit with Marx’ development from $k + p$ to $k + k⋅p’$ where $p’$ is the general rate of profit.¹¹ For the example above we would get $6 + 6 ⋅ 20\% = 6 + 1.2 = 7.2$:

265:1 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 $= k + kp’$.

Changes of magnitude of prices of production. Changes to the magnitude of prices of production are caused by:¹²

1. A change in the general rate of profit.
2. A particular change in the value of commodities of a sphere of production; either because production is changed or because the value of the means of production changes.
3. A combination of 1. and 2.

Changes of magnitude of the profit rate. The general rate of profit does not fluctuate much but changes slowly, because different movements cancel each other out, which is why short-term changes are caused by changes in value.¹³

The general rate of profit changes when $m/C$ changes, which in turn means — if rate of surplus-value, turnover and technical composition are constant — that either the value of $v$ or of $c$ changes. In this case a general change in the overall rate of profit is caused by a change of value of commodities.

On the other hand, the general rate of profit can change if the rate of surplus-value changes or organic composition. These, however, impact the values of commodities, too.

Surplus-value and profit. In Part 1 surplus-value and profit were the same. Instead, the rate of surplus-value and the profit rate were distinguished. The profit rate relates surplus-value to all advanced capital and therewith extinguishes the distinction between variable and constant capital. Profit was the transformed form of surplus-value and differences in magnitude only concerned the rates: the profit rate can rise and fall independently of the rate of surplus-value. The masses, however, were equal.

With the general rate of profit surplus-value and profit diverge. The magnitude of profit now depends on advance and not on the mass of surplus-value produced. The mass of surplus-value of a given capital does not determine what mass of profit it appropriates. Only insofar this mass is part of the total mass of surplus-value of society which is distributed amongst all capitals it plays a role.

Laws of the profit rate. What is the place of the laws of the rising and falling of the profit rate from the first part now?¹⁴

1. These laws apply to the general rate of profit. However, the general rate of profit does not fluctuate much as opposing movements in different branches cancel out, because opposing movements in one branch cancel out and because movement of capital between the branches limits its movement.

2. Within a branch there is room within which the local profit rate can fluctuate, but which does not affect the average of profit. The laws from part one apply to these fluctuations.

Appearance. That labour is the source of profit disappears completely: the mass of profit does not immediately depend on the successful exploitation of a single capital. Profit appears external to (own) production.

The effects of the general rate of profit seem to confirm that the source of profit is not living labour. Capitalists save on wage costs and increase the productivity of labour (less work per use-value) and this does not affect their profit rate or increases it temporarily (extra profit).

Changes in the prices of means of production (constant capital part of the cost part) confront the capitalist on the market. If productivity of labour is increased then the wage might stay the same, but wage per commodity drops. Since, however, price of production = cost price + average profit, the capitalist still receives her average profit of, say, $10\%$ (this might appear differently when presented with respect to a single commodity, though, as discussed above).

The capitalist sees that with increases in productivity the price of production drops, a fall of profit, however, is not apparent.