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Part One
The Transformation of Surplus-Value into Profit, and of the Rate of
Surplus-Value into the Rate of Profit

1

Chapter 1: Cost Price and Profit
Marx begins by summarising where we are in our analysis, in order to lay out the purpose of this, the third, volume:
In volume 1[1] we investigated the [...] process of capitalist production, taken by itself, i.e. the immediate production
process, in which connection all secondary influences external to this process were left out of account. But this
immediate production process does not exhaust the life cycle of capital. In the world as it actually is, it is
supplemented by the process of circulation, and this formed our object of investigation in the second volume.[2] Here
we showed [...] that the capitalist production process, taken as a whole, is a unity of the production and
circulation processes. It cannot be the purpose of the present, third volume simply to make general reflections
on this unity. Our concern is rather to discover and present the concrete forms which grow out of the process of
capital’s movement considered as a whole. In their actual movement, capitals confront one another in certain concrete
forms, and, in relation to these, both the shape capital assumes in the immediate production process and its
shape in the process of circulation appear merely as particular moments. The configurations of capital, as
developed in this volume, [...] approach step by step the form in which they appear on the surface of society, in
the action of different capitals on one another, i.e. in competition [...]. 3

***
I Cost Price 4

The value of any commodity (let us call this value C) is given by: C = c + v + s; c + v simply replaces the capital
expenditure, what the capitalist has laid out on constant capital.
Let us call the cost of replacing capital expenditure (c + v), i.e. what the commodity has cost the capitalist, the cost
price, k. Hence, C, what the commodity really costs, = k + s. 5 The capitalist is unaware of this: ‘since the worker, in
the situation of capitalist production, is himself an ingredient of the functioning productive capital that belongs to
the capitalist, and the capitalist is therefore the actual commodity producer, the cost price of the commodity
necessarily appears to him as the actual cost of the commodity itself.’ 6
Whence this difference (between value and cost price)? ‘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.’ 7 Cost
price here is not an absolute illusion but ‘the false semblance of an actual category of value production.’ 8
Marx proceeds with a numerical example. 9
1

Karl Marx, Capital, vol. 1 (Harmondsworth, 1990) [hereafter C1].

2

Karl Marx, Capital, vol. 2 (Harmondsworth, 1978).

3

Karl Marx, Capital, vol. 3 (Harmondsworth, 1981) [hereafter C3], p. 117.

Where I insert my own subheads they appear, as here, in sans serif type.
Of course, were value and cost price the same, there would be no profit. We investigate what this means to the capitalist
below.

4
5

6

C3, p. 118.

7

C3, p. 118. In other words, cost price is established in the transformation M–C<mp , before the process of production

L

begins.
8

C3, p. 119, italicisation added.

Although maintaining the numerical content of Marx’s example, I shall proceed in a slightly different logical order in setting
it out. Marx, misleadingly to my mind, seems to set up the rate of surplus-value as a condition of the example, whereas I think
it follows from the time necessary to produce the product (i.e. the productivity of labour) and the value of labour-power.

9

2

Let us assume:
an average social 10-hour working day
the value produced by 1 worker in 1 average social working day = 6 shillings 10
the daily value of labour-power = 3 shillings
therefore, the rate of surplus-value = 100%11
A commodity product, C, requires the transformation of £380 of raw materials into finished product form. This
involves £20 wear and tear of fixed capital, and takes 666 social working days to accomplish. 12 Therefore:
c = £380 + £20 = £400 (value equivalent, if 6 shillings new value is produced each day, to the value
produced in 1,333 days)
v (capital advanced for labour-power) = 3 shillings (£
v + s (total new value produced) = 6 shillings (£

)

)

666 (days) = £100

666 (days) = £200

therefore, s = (v + s) – v = £200 – £100 = £100 13
The value of C is composed of:
1 reappearing value of constant capital = £400
2 newly produced value = £200
The cost price of the commodity consists in:
1 reappearing value of constant capital = £400
2 half of the newly produced value, i.e. £100
These two elements composing the value/cost price of the commodity are absolutely distinct.


The value of the means of production (£400) is transferred from the means of production to the
product through the purposive character of the labour spent during production; this component of
the product’s value exists as such only because it previously existed as a component of the capital
advanced: the constant capital spent is replaced by the portion of commodity value that it itself adds.
This means two things: (1) it forms a part of the cost price because it is a component of commodity value,
replacing capital used up; (2) it forms a component of the commodity value because it is the value of
capital that has been used up (in function of the cost of means of production).



The labour expended during production commodity forms a new value of £200, one part of which
replaces the variable capital advanced. But this value does not enter the product as the value of means
of production did: labour-power counts not as value within the total capital value advanced, but as
the creator of value in production, functioning as productive capital.

We can see this distinction clearly if we change the price (value) of each element in turn.


Suppose the price of the means of production rises to £600. Both the cost price and the value of the

There are 20 shillings to the pound.
s
11 Rate of surplus-value = (cf. C1, pp. 326-7; 977-8).
v
10

12

This latter Marx does not say explicitly at this point, but it is implicit to the example.

13

Therefore, and not because, the rate of surplus-value is 100%.
3

commodity rise by the same amount; respectively, from £500 (£400c + £100v ) to £700 (600c + 100v ),
and from £600 (£400c + £200(v + s) ) to £800 (£600c + £200(v + s) ). A fall would have a similar, but
opposite, effect.


Now suppose the price (value) of labour-power rises by 50 %, from 3 shillings to 4 a day. Now, the
labour-power necessary to produce the commodity product stands at 4

shillings (£

)

666

(days) = £150. The cost price now rises by the same amount, from £500 (£400c + £100v ) to £550
(£400c + £150v ), but the value of the commodity remains the same: £600 (£400c + £200(v + s) ). All
that has happened is that now v = £150 and s = £50 (v + s, new value created, must remain the same
because the time labour-power has been active remains the same). A fall in the price of labour-power
will have the converse effect: the cost price will fall by the same amount, but the value of the
commodity product, for the same reason, will stay the same (s will rise by the amount that v falls). 14
Hence:
[A] change in the absolute size of the variable capital, in so far as this expresses simply a change in the price of
labour-power, does not change in the least the absolute size of the commodity value, because it does not affect
that absolute size of the new value which active labour-power creates. A change of this kind affects only the ratio
between the two components of this new value, one of which forms a surplus-value, while the other simply
replaces the variable capital and thus enters into the cost price of the commodity. 15

How does this appear to the capitalist (‘[f]rom the standpoint of capitalist production’ 16)? The value of labourpower expresses itself as the price of labour, as wages. 17 It appears as if the variable component of capital, rather
than paying for the value of the labour-power which then functions in production, is capital which pays for the
labour actually expended in production. In our numerical example, what is really happening is that the capitalist lays
out 3 shillings to buy labour-power capable of functioning for ten hours (creating six shillings of new value); what
appears to the capitalist to be happening is that ten hours of labour are bought for three shillings. Hence, here, the
‘price’ of one ten-hour working day is three shillings, the value product (we really know) of five hours’ expenditure
of labour-power.
We hence have two very distinct viewpoints on what is going on: that of capital advance, and that of commodity value.
From the point of view of the former, the only distinction between capital advanced on means of production and
capital advanced on labour-power is that between different kinds of elements of production; the distinction
between constant and variable capital is lost. The only distinction from this point of view in terms of the different
kinds of capital bought with the money capital advanced is between fixed (instruments of production) and
circulating (raw materials and labour) capital, in that the former, once deployed, enters into the commodity’s cost
only piecemeal, while the latter enters wholesale.
II Profit

If surplus-value (profit) is value additional to its cost price, and we take the point of view that the only distinction
between capital advanced on means of production and capital advanced on labour-power is that between different
kinds of elements of production, then profit is a value which accrues to the capital (all of it) in production: 18 ‘It is
And the rate of surplus-value will necessarily change, as the ratio s : v changes. As we saw in volume 1 (C1, pp. 429-32) the
rate of surplus-value rises with a cheapening of the value of labour-power, and falls when the value of labour-power rises.
14

15

C3, p. 121.

16

C3, p. 121.

17

C1, pp. 675-82.

Including, Marx makes clear, that part of fixed capital not accounted for as wear and tear in the finished product, for it is
not in function of being used up in production that capital causes profit to accrue to the product (in this view of things), for this
18

4

clear enough to the capitalist that this additional value derives from the productive activities which he undertakes
with his capital, i.e. that it derives from the capital itself. For after the production process he has it, and before the
production process he did not.’ 19
Profit is thus surplus-value, although in ‘mystified’ 20 form. ‘Because the price of labour-power appears at one pole
in the transformed form of wages, surplus-value appears at the other pole in the transformed form of profit.’ 21
It is, in addition, clearly the case that in order to realise a profit, all the capitalist has to do is sell the commodity
profit above its cost price (even if, at the same time, she sells it below its value). 22 For this reason, the capitalist is
inclined to treat the cost price as the commodity’s ‘real’ value; profit appearing as the excess of its sale price over its
‘value’. 23
Finally, Marx (Proudhon in his sights) gives the lie to the notion that the cost price of a commodity really is its ‘real’
price, and that surplus-value therefore results from selling a commodity above its value, by noting that in the case,
say, of our example here, if our commodity is sold for £500 rather than £600, the worker will still have performed
her surplus-labour, but now for the buyer – who receives £100 of commodity for nothing – rather than for the
seller. 24
Nevertheless, he then goes on to make the following remark, of critical importance for what he is going to go on to
expound:
It would be quite wrong to suppose that, if all commodities were sold at their cost prices, the result would in fact
be the same as if they were all sold above their cost prices but at their values. For even if the value of labourpower, the length of the working day and the rate of exploitation are taken as everywhere the same, yet the
amounts. of surplus-value that the values of the various different kinds of commodities contain are completely
unequal, according to the differing organic compositions of the capitals advanced for their production. 25

function is what accounts for the cost price: profit accrues in function of capital advanced. ‘The entire capital is materially
involved in the labour process, even if only a part of it is involved in the process of valorisation.’ C3, p. 126.
19

C3, p. 125.

20

C3, p. 127.

C3, p. 127.
And, Marx adds (C3, pp. 127-8), anticipating substantially: ‘The basic law of capitalist competition, which political economy
has so far failed to grasp, the law that governs the general rate of profit and the so-called prices of production determined by
it, depends, as we shall see, on this difference between the value and the cost price of commodities, and the possibility
deriving from this of selling commodities below their value at a profit.’
21
22

Marx here digresses, commenting on how political economy, in more or less vulgar form, was unable to account for the
source of profit in either production, or in exchange.
23

It is worth recalling here Marx’s demonstration in volume 1 (C1, pp. 258-69) of the impossibility of surplus-value arising
from circulation.
24

25

C3, p. 131.
5

Chapter 2: The Rate of Profit
I The motivation of the capitalist 1

The ‘general formula’ for capital is M–C–M′; put into words, value is cast into circulation in order that a greater sum
be extracted from it. This greater sum is created by production but realised in circulation. The ‘in order’ in the previous
sentence is important here: what the capitalist is interested in is the excess value over that advanced. Other than
being the means to this end the capitalist is disinterested in the product as a product; she is also disinterested in ‘the
different roles that [...] [the] components [of the capital advanced] will play in the production of surplus-value.’ 2 The
capitalist is disinterested in these two things because it makes no difference to what she does as a capitalist:
independently of her initial intentions, a capitalist producing commodities cannot survive as a capitalist – cannot
continue to produce commodities – without producing surplus-value; and, in order to do this, the capitalist needs to
advance capital in the form of means of production and labour-power and recuperate the cost of this capital
advanced in addition to realising a surplus (i.e. profit).
To put this another way, the capitalist, as a capitalist, does not need to know whence profit arises, all the capitalists
as a capitalist needs is that there be one. As Marx is about to go on to discuss the illusions (‘that inversion of subject
and object’ 3), let us be clear here that thus far nothing illusory has occurred. None of the capitalist’s indifference to
the source of profit stems from a misunderstanding of capitalist production, only from the practical necessities of
what she, as a capitalist, needs to do. Illusions (through which ‘the capitalist relation is mystified’ 4) arise when these
practicalities are taken as themselves sufficient for the explanation of the source of profit; for, as Marx will go on to
comment, 5 analysis is necessary to identify and separate out ‘origin’ and ‘form of appearance’, for, through the latter,
the former is ‘veiled and obliterated’.
II The illusions of the capitalist

What then are the illusions that arise (without ‘analysis’; without identifying how the form of appearance obscures
the origin)? Marx identifies two.
1 Given:
(a) that surplus-value, although produced in production, is realised in circulation;
(b) the possibility of selling commodities above or below their value in the market; and
(c) the way that circulation and production ‘constantly run into one another and intertwine, [...] [such that]
their distinguishing features are continuously blurred’, 6 i.e. the ‘evanescent’ 7 nature of production itself;
it appears that the excess value of the commodity over its cost price (which, as we saw in chapter 1, 8 appears
to the capitalist as the intrinsic – ‘real’ – value of the commodity) derives from the circulation process (either
instead of, or in combination with, production).
2 It appears that ‘the actual degree of [...] [the capitalist’s] profit is determined in relation not to his variable
capital but to his total capital.’ 9 Hence, ‘the extortion of unpaid labour appears simply as an economy in the
1

Where I insert my own subheads they appear, as here, in sans serif type.

Karl Marx, Capital, vol. 3 (Harmondsworth, 1981) [hereafter C3], p. 132.
3 C3, p. 136.
2

4

C3, p. 136.

5

C3, p. 139.

6

C3, p. 135.

7

C3, p. 135.

8

C3, p. 128

9

C3, p. 133; not, observes Marx, anticipating, ‘by the rate of surplus-value but by the rate of profit […]’.
1

payment of one of the articles that comprise [...] [the] costs [of production] [...], an economy similar to that
made when raw material is bought more cheaply or wear and tear of material is reduced.’ 10
Now, even if one might derive a relation between the physical quantities of means of production to set a certain
quantity of labour-power to work, i.e. to produce a certain quantity of new value in production (and hence the
profit to be produced), there is no necessary relation between the value of the constant capital advanced (and hence
the total capital advanced) and the profit produced, for the former can change. A relation between the value of
means of production an profit only appears to hold insofar as the price of the former can serve as an indicator of its
physical magnitude, i.e. assuming that its price does not change. ‘There is [...] no inner and necessary relationship
between the value of the constant capital and the surplus-value, nor, hence, [...] between the value of the total
capital [...] and the surplus-value.’ 11
We already know why this is. The value of the commodity product is equal to the labour time contained in it: the
labour objectified in means of production, the necessary labour and the surplus labour – the labour beyond the
value of the labour-power advanced as variable capital – expended in its production. The cost of the commodity to
the capitalist is the cost of the capital advanced. Profit – surplus-value – is the difference between the two.
This excess value can be related to the variable capital advanced, and to the total capital advanced: respectively ,
the rate of surplus-value, and

,

, the rate of profit. While the latter is historically prior to the former, the former

is categorically determining:
It is the transformation of surplus-value into profit that is derived from the transformation of the rate of surplusvalue into profit rate, not the other way round. [...] [T]he rate of profit is the historical starting point. Surplusvalue 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 to profit are visible surface phenomena. 12

Hence:
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 realised 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. 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. 13

10

C3, p. 136. ‘All sections of capital equally appear as sources of the excess value.’

11

C3, p. 138.

12

C3, p. 134.

13

C3, p. 139.
2

Chapter 3: The Relationship between Rate of Profit and Rate of Surplus-Value
I Rate of profit and rate of surplus-value 1

Here we shall work under the assumption that profit = surplus-value, i.e. we shall ignore for now the division of
surplus-value into ‘subordinate’ forms (interest, ground-rent, taxes, etc.). 2
C = total capital
c = constant capital
v = variable capital


C=c+v
s = surplus-value
= rate of surplus-value, δ 3

Since δ = , s = δv
= rate of profit, π 4

=
Given that π =

and s = δv , then π =

, such that

=

, which we can express as π : δ = v : C . In other words,

‘rate of profit is to rate of surplus-value as variable capital is to total capital.’ 5
We should note that it is necessarily the case that π < δ . π = δ when v = C, i.e. when c = 0 . π > δ would require
that v > C , i.e. that c be negative, which is impossible.
For the sake of exposition we shall abstract away from the following factors (which affect the magnitudes of c , v
and s ‘in a decisive way’ 6).
1 The value of money 7
This is assumed constant.
2 Turnover
π=

holds for a single turnover period of v. Considering the annual turnover of v, π =

, where n = the

number of times v turns over in a year. 8 We ignore this here (but return to it in the next chapter).
3 Productivity of labour
The productivity of labour impacts on both the rate of surplus-value and the rate of profit. 9 Here, we assume
1
2
3
4

Where I insert my own subheads they appear, as here, in sans serif type.
How this is not the case will become clear in part 2 of the volume.
Marx uses the symbol s′.
Marx uses the symbol p′.

Karl Marx, Capital, vol. 3 (Harmondsworth, 1981) [hereafter C3], p. 142.
6 C3, p. 142.
5

I.e. the value of the money commodity; effectively here Marx assumes a constant productivity of labour in the sphere of the
production of precious metals.

7

8

See Karl Marx, Capital, vol. 2 (Harmondsworth, 1978), pp. 369-93.

9

See Karl Marx, Capital, vol. 1 (Harmondsworth, 1990), pp. 429-38 and ff.
1

that commodities are produced under normal social conditions and are sold at value; we assume that the
productivity of labour remains constant.
We also disregard the fact that the value composition of capital,

, insofar as it expresses a specific ratio of

constant and variable capital, expresses a certain productivity of labour; changes in the value composition not
due to changes in value of the material components of c, or to changes in wages, are synonymous with changes
in the level of productivity. Changes in the relative proportions of c, v and s necessarily involve changes in the
productivity of labour.

II The effect of the length of the working day, the intensity of labour and wages on the mass and rate of
surplus-value

There are three more factors that influence both the mass and the rate of surplus-value: (1) the length of the
working day; (2) the intensity of labour; and (3) wages.
For example, let us take 80c + 20v + 20s , with 20 workers working a 10-hour day (producing 40(v + s) ).
Let us now extend the working day to 15 hours. Given that 10 : 15 = 40 : 60 the workers now produce 60(v +s) ;
supposing constant wages 20v + 40s .
Previously, π,

,=

= 20 % , and δ,

,=

; now, π =

and δ =

.

Now, instead of changing the working day (which we maintain at 10 hours), the wage falls from 20v to 12v . The
workers still produce 40(v + s) , but this now breaks down as 12v + 28s (hence 80c + 12v + 28s ) , with π =
= 30

, and δ =

=

= 233 .

Conclusions: the extension of the working day (or an increase in the intensity of labour) and a fall in wages both
necessarily increase both the mass and the rate of surplus-value. Evidently a decrease in the working day and a rise
in wages produce the opposite effect. Therefore, changes in the length of the working day, intensity of labour and
wages must involve changes in v and s, and their proportions; and necessarily therefore the proportions s : v and s :
(c + v), hence δ and π. The converse is also true: changes in the ratio s : v must involve a change in at least one of
the length of the working day, the intensity of labour and wages.
This all illustrates ‘precisely the special organic connection that the variable capital has with the movement of the
capital as a whole and its valorisation, as well as its distinction from the constant capital.’ 10
From the point of view of the formation of value, what counts with respect to the constant capital is its value. The physical
quantity of material which this value represents is here irrelevant.
But what counts with respect to variable capital is not the value objectified in it (the value of its reproduction), but
the quantity of labour it sets in motion. The value of labour-power only serves as a measure 11 of this labour set in
motion.
The difference between the latter and the former – between the labour paid for in variable capital and the total
labour set in motion – is surplus-value; hence, once this measure changes – once the labour objectified as labourpower, i.e. the value (price) of labour-power stands in a different relation to the mass of labour set in motion – both
the mass of surplus-value and therefore the rate of surplus-value change in the opposite direction and in inverse
proportion.
10

C3, p. 144.

11

Marx uses the word ‘index’ (‘Index’): C3, p. 144.
2


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