As was indicated at the close of the previous chapter, we assume here, as throughout this Part, that the sum of profit that accrues to a given capital is the same as the total sum of surplus-value which this capital produces in a given period of circulation. We therefore ignore for the time being the division of this surplus-value into various subordinate forms: interest, ground-rent, taxes, etc., as also the fact that surplus-value by no means coincides in the majority of cases with profit, as the latter is appropriated by way of the prevailing rate of profit, which we shall return to in Part Two.
In so far as profit is taken as quantitatively equal to surplus-value, its magnitude, and the magnitude of the rate of profit, are determined by simple numerical ratios, the numbers involved being given or definable in each individual case. Our investigation is firstly, therefore, a purely mathematical one.
We shall keep the symbols that were used in the first and second volumes. The total capital C is divided into constant capital c and variable capital v, and produces a surplus-value s. The ratio between this surplus-value and the variable capital advanced, i.e. s/ν, we call the rate of surplus-value, and we denote it by s’. Since s/ν = s’, s = s’v. If this surplus-value is related to the total capital instead of just the variable capital, it is called profit (p), and the ratio between the surplus-value and the total capital C, i.e. s/C, is known as the rate of profit, p’. We therefore have:
p′ = s/C = s/c + ν
and if we substitute for s the value s’v, as above, we have
p′ = s′ν/C = s′ν/c + ν,
an equation which can also be expressed as the proportionality:
p′:s’ = v:C;
rate of profit is to rate of surplus-value as variable capital is to total capital.
It follows from this proportionality that p′, the rate of profit, is always smaller than s′, the rate of surplus-value, since v, the variable capital, is always smaller than C, the sum of v + s, variable and constant capital. The only exception is the case, impossible in practice, where v = C, and where the capitalist thus advances no constant capital, no means of production, but simply wages.
But a further series of factors have also to be taken into account in our analysis, factors which affect the sizes of c, v and s in a decisive way, and which must therefore be briefly mentioned.
Firstly, the value of money. This we can take as constant throughout.
Secondly, the turnover. We shall ignore this factor completely, for the time being, since its influence on the profit rate will be dealt with in a later chapter. (Here we shall simply anticipate the point that the formula p′ = s′ν/C is strictly correct only for a single turnover period of the variable capital, while for the annual turnover the simple rate of surplus-value s′ has to be replaced by s’n, the annual rate of surplus-value, n standing for the number of turnovers that the variable capital makes in the course of a year; see Volume 2, Chapter 16, 1 – F.E.)
The third factor involved is the productivity of labour, whose influence on the rate of surplus-value we have already gone into in some detail in Volume 1, Part Four. This can however also exert a direct influence on the rate of profit, at least that of an individual capital, if, as explained in Volume 1, Chapter 12, pp. 433ff., this individual capital operates with a productivity higher than the social average, produces its products at a lower value than the average social value of the same commodity, and in this way realizes an extra profit. But we shall also leave this case out of consideration here, as in this Part we also proceed from the assumption that commodities are produced under normal social conditions and are sold at their values. We therefore assume in each individual case that the productivity of labour remains constant. In actual fact, the value composition of the capital applied in a particular branch of industry, i.e. a specific ratio between variable and constant capital, expresses in each case a definite level of labour productivity. Thus as soon as this ratio experiences any change that is not simply due either to a change in value of the material components of the constant capital, or to a change in wages, the productivity of labour must also have undergone a change, and we shall therefore find often enough that the changes in the factors c, v and s also involve changes in labour productivity.
The same applies to the remaining three factors: length of working day, intensity of labour, and wages. Their influence on the mass and rate of surplus-value was developed in detail in Volume 1 [Chapter 17]. We can well understand, therefore, how, even if we proceed for the sake of simplicity from the assumption that these three factors remain constant, the changes that v and s undergo nevertheless also involve changes in the size of these determining moments of theirs. And we may briefly remind ourselves here that wages affect the size and the rate of surplus-value in the opposite direction to the length of the working day and the intensity of labour; a rise in wages reduces surplus-value, while an extension of the working day and a greater intensity of labour both increase it.
Let us take for example a capital of 100, producing a surplus-value of 20 with 20 workers in a 10-hour working day, and a total weekly wage bill of 20. We then have:
80c + 20ν + 20s; s′ = 100 per cent, p′ = 20 per cent.
If the working day is now extended to 15 hours, without an increase in wages, the total value produced by the 20 workers is increased from 40 to 60 (10:15 = 40: 60). Since v, the wages paid, remains the same, the surplus-value rises from 20 to 40, and we have:
80c + 20ν + 40s; s’ = 200 per cent, p′ = 40 per cent.
If the wage for the same 10 hours’ labour falls from 20 to 12, we then have the same total value product of 40 as before, but differently distributed; v falls to 12 and thus leaves a remainder o 28 for s. We then have:
80c + 12ν + 28s; s’ = 233 1/3 per cent, p′ = 28/92 = 30 10/23 per cent.
We see therefore how an extension of the working day (or, alternatively, an increase in the intensity of labour) and a fall in wages both raise the mass and with it the rate of surplus-value; conversely, a rise in wages, with other circumstances remaining the same, would reduce the rate of surplus-value. If v grows owing to a rise in wages, this does not express an increased quantity of labour but simply its dearer payment; s′ and p′ do not rise but fall.
It is already evident here that changes in the working day, the intensity of labour and wages cannot take place without a simultaneous change in v and s and their relationship, and thus also in p′, the ratio between s and c + v, the total capital; and it is also evident that changes in the ratio of s to v also involve changes in at least one of the three conditions of labour that have been mentioned.
Here we see precisely the special organic connection that the variable capital has with the movement of the capital as a whole and its valorization, as well as its distinction from the constant capital. The constant capital, in so far as the formation of value is concerned, is important only on account of the value that it has. It is quite immaterial here, as far as value formation is concerned, whether a constant capital of £1,500 represents 1,500 tons of iron at £1 a ton or 500 tons at £3. The quantity of actual material in which its value is expressed is completely unimportant for the formation of value and for the rate of profit, which varies in the opposite direction to the value of the constant capital, irrespective of what relationship the increase or decrease in this value has to the mass of material use-values that it represents.
The case of the variable capital is completely different. What matters above all here is not the value that it actually has, the amount of labour objectified in it, but rather this value as a mere index of the total labour that it sets in motion, which is not expressed in it. The difference between this total labour and the labour expressed and therefore paid for in the variable capital, i.e. the portion that forms surplus-value, is greater in proportion as the labour contained in the variable capital gets smaller. Say that a working day of 10 hours = 10 shillings. If the necessary labour, the labour that replaces wages, i.e. replaces the variable capital, is 5 hours, then the surplus-value is 5 shillings; if the necessary labour is 4 hours = 4 shillings, the surplus labour is 6 hours and the surplus-value 6 shillings.
Hence as soon as the value of the variable capital ceases to be an index of the mass of labour that it sets in motion, and the basis of this index itself changes, the rate of surplus-value changes in the opposite direction and in inverse proportion.
We can now move on to apply the above equation for the profit rate, p′ = s′ν/C, to the various possible cases. We shall let the individual factors of s′ν/C vary successively in value, and establish the effect of these changes on the rate of profit. We thus obtain various sets of cases which we can consider either as successive changes in circumstances for the action of one and the same capital, or, indeed, as different capitals, existing simultaneously alongside one another, and brought in for purposes of comparison, e.g. from different branches of industry or from different countries. If it therefore appears forced or practically impossible to interpret some of our examples as chronologically successive states of one and the same capital, this objection disappears as soon as they are viewed as the result of a comparison between separate capitals.
We shall therefore divide the product s′ν/C into its two factors s’ and s/C. First we shall take s’ as constant and investigate the effect of possible variations in s/C, then take the fraction s/C as constant and put s’ through its possible variations. Finally we shall take all the factors as variable, and in this way exhaust all the cases from which the laws governing the profit rate may be derived.
I. s’ constant, s/C variable
This case, which comprises a number of subordinate ones, can be covered by a general formula. If we have two capitals C and C1, with their variable components v and v1 respectively, a common rate of surplus-value s’ and rates of profit p′ and p′1, then:
p′ = s′ν/C; pν1 = s′ν1/C1.
C and C1 as well as v and v1 will then stand in certain definite ratios, and if c1/c = E, and ν1/ν = e, then C1 = EC and v1 = ev. By substituting these values into the above equation for p′1, we obtain:
p′ 1 = s′ eν/EC.
We can also obtain a second formula from the above two equations, if we transform them into the following proportionality:
p′:p′1 = s′ ν/C:s′ ν1/C1 = ν/C : ν1/C1.
Since the value of a fraction remains the same if numerator and denominator are both multiplied or divided by the same number, we can reduce s/C and ν1/C1 to percentages by taking both C and C1 as 100. We then have s/C = ν/100 and ν1/C1 = ν1/100. Multiplying the above proportionality by 100 to remove these denominators of 100, we get:
p′:p′1 = v:v1.
In other words, given any two capitals functioning with the same rate of surplus-value, the rates of profit stand in the same proportion as the variable components of the capitals, each calculated as a percentage of its total capital.
These two forms cover all cases of variation in s/C.
Before we investigate each of these particular cases, one further remark. Since C is the sum of c and v, the constant and the variable capital, and since the rate of surplus-value as well as the profit rate is customarily expressed as a percentage, it is generally convenient to take the sum c + v as also = 100, i.e. to express c and v in percentages too. It is not immaterial for determining the mass of profit, but it is so far as the rate of profit is concerned, whether we say that a capital of 15,000, of which 12,000 is constant capital and 3,000 variable, produces a surplus-value of 3,000 or whether we reduce the capital to percentages:
15,000 C = 12,000c + 3,000ν (+ 3,000s)
100 C = 80c + 20ν (+ 20s).
In both cases the rate of surplus-value s’ = 100 per cent and the rate of profit p′ = 20 per cent.
It is the same if we compare two capitals with one another, for example comparing the above capital with a second one:
12,000 C = 10,800c + 1,200ν, (+ 1,200s)
100 C = 90c + 10ν (+ 10s).
Here s’ = 100 per cent and p′ = 10 per cent, and the comparison with the previous capital is far easier to make in the percentage form.
If on the other hand we are dealing with changes taking place in one and the same capital, the percentage form can be used only rarely, as it almost always obliterates these changes. If a capital passes from the percentage form:
80c + 20ν + 20s
to the percentage form:
90c + 10ν, + 10s
we cannot tell whether the new percentage composition 90c + 10ν has come about by an absolute decline in v, or an absolute rise in c, or both. The absolute magnitudes must also be known here. And in our analysis of the following particular cases of variation, it is precisely how this change has come about that matters; whether the 80c + 20ν became 90c + 10ν because 12,000c + 3,000ν underwent a transformation, say, into 27,000c + 3,000ν (90c + 10ν in percentage terms), i.e. through an increase in the constant capital, the variable capital remaining the same; or whether it assumed this new shape through a reduction in the variable capital, the constant capital remaining the same, i.e. because it changed into 12,000c + 1,333 1/3ν (also 90c + 10ν in percentage terms); or finally through a change in both these quantities, resulting in 13,500c + 1,500ν (again 90c + 10ν in percentage terms). But we shall have to analyse all these cases in succession, thereby dispensing with the convenience of the percentage form, or only applying it as a supplement to the main argument.
1. s’ and C constant, v variable
If there is a change in the magnitude of v, C can remain unaltered only if its other component, the constant capital c, changes by the same amount as v, but in the opposite direction. If C was originally 80c + 20ν = 100 and v is then reduced to 10, C can remain at 100 only if c rises to 90; 90c. + 10ν = 100. In general, if v is changed to v ± d, to v increased or decreased by d, then c must be transformed to c ∓ d, varying by the same amount in the opposite direction, in order that the conditions of the present case may be satisfied.
In the same way, given an unaltered rate of surplus-value s’ but a changing variable capital, the mass of surplus-value must change, since s = s’v, and one of the factors of s’v, namely v, has been given another value.
The assumptions of the case at hand, together with the original equation
p′ = s′ ν/C,
give us the second equation:
p′ 1 = s′ ν1/C,
by variation of v. v has now been changed to v1, and we have to find p′1, the ensuing new rate of profit.
This is found by the appropriate proportionality:
p′ : p′1 = s′ ν/C : s′ ν1/C = ν:ν1.
Or, with the rate of surplus-value and the total capital both remaining the same, the original profit rate is related to the new profit rate arrived at by a change in the variable capital, as the original variable capital is to the new variable capital.
If the capital was originally, as above,
I. 15,000 C = 12,000c + 3,000ν (+ 3,000s); and it is now
II. 15,000 C = 13,000c + 2,000ν (+ 2,000s); then C = 15,000 and s’ = 100 per cent in both cases, and the rate of profit in case I, 20 per cent, is related to that in case II, 13 1/3, per cent, as the variable capital in case I, 3,000, is related to that in case II, 2,000; i.e. 20 per cent: 13 1/3 per cent = 3,000:2,000.
The variable capital can either rise or fall. Let us first take an example in which it rises. Say that a capital is originally constituted, and functions, as follows:
I. 100c + 20ν + 10s; C = 120, s’ = 50 per cent, p′ = 8 1/3 per cent.
The variable capital now rises to 30. According to our assumption, the constant capital must fall from 100 to 90, so that the total capital remains the same at 120. The surplus-value produced must rise by 15, given the same rate of surplus-value of 50 per cent. We then have:
II. 90c + 30ν + 15s; C = 120, s’ = 50 per cent, p′ = 12 1/2 per cent.
Let us proceed first of all on the assumption that wages are unchanged. In that case the other factors involved in the rate of surplus-value, i.e. the working day and the intensity of labour, must also have remained the same. The increase in v (from 20 to 30) can only mean therefore that half as many workers again as before are employed. This means that the total value produced also rises by a half, from 30 to 45, while it is divided just as before, with two-thirds going to wages and a third to surplus-value. At the same time, however, as the increase in the number of workers, the constant capital, the value of the means of production, has fallen from 100 to 90. We have therefore a case of a decline in labour productivity combined with a simultaneous decline in constant capital. Is this case economically possible?
In agriculture and the extractive industries, where a decline in labour productivity and a consequent increase in the number of workers employed is easy to comprehend, this process – within the confines of capitalist production, and on its basis – is linked not with a decline in constant capital but with an increase. Even if the above decline in c were occasioned simply by a fall in price, an individual capital would be able to make the transition from I to II only under quite exceptional conditions. With two independent capitals, however, invested in different countries, or in different branches of agriculture or extractive industry, it would be by no means unusual if in one case more workers (hence a bigger variable capital) were employed and worked with less expensive or less plentiful means of production than in the other case.
Let us now drop the assumption that wages remain the same and explain the rise in variable capital from 20 to 30 in terms of an increase of a half in wages. We then have a completely different picture. The same number of workers – let us say 20 – carry on working with the same or only insignificantly reduced means of production. If the working day remains unaltered – at 10 hours for example – the total value produced remains similarly unaffected; it is still 30, just as before. But this 30 would now be fully employed in replacing the variable capital of 30 that was advanced; the surplus-value would have completely disappeared. We presupposed, however, that the rate of surplus-value remained constant at 50 per cent, as in I. This is possible only if the working day is also extended by half and increased to 15 hours. 20 workers would then produce in 15 hours a total value of 45, and all the conditions would be fulfilled:
II. 90c + 30ν + 15s; C = 120, s’ = 50 per cent, p′ = 12 1/2 per cent.
In this case, the 20 workers need no more means of labour, tools, machinery, etc. than in I. It is only the raw or ancillary materials that would have to be increased by half. If these materials fall in price, the transition from I to II would be much more possible as an economic phenomenon, given our assumptions, even for one and the same capital. And the capitalist would be compensated at least partially, by a bigger profit, for the loss that the devaluation of his constant capital would have caused him.
Let us now assume that the variable capital falls instead of rising. Then we need only reverse our above example, taking II as the original capital and moving from II to I.
II. 90c + 30ν + 15s is then transformed into
I. 100c + 20ν + 10s; and it is readily apparent that by this reversal, the rates of profit in the two cases and the conditions governing their mutual relationship are not changed in the slightest.
If v falls from 30 to 20, because one-third less labour is engaged with an increased constant capital, this is simply the normal case in modern industry: rising productivity of labour, the operation of greater quantities of means of production by fewer workers. And in Part Three of this volume we shall see how this movement is necessarily bound up with a simultaneous fall in the rate of profit.
But if the reason for the fall in v from 30 to 20 is that the same number of workers are employed at a lower wage rate, then, so long as the working day is unchanged, the total value product remains unaltered at 30ν + 15s = 45. Since v has fallen to 20, the surplus-value has risen to 25 and the rate of surplus-value from 50 per cent to 125 per cent, which would be against our assumption. In order to remain within the limits of our example, the surplus-value, at a rate of 50 per cent, must fall instead to 10, and thus the total value produced from 45 to 30, and this is possible only if the working day is cut by one-third. We then have, as above:
100c + 20ν + 10s; s′ = 50 per cent, p′ = 8 1/3 per cent.
We need hardly point out that a reduction in working hours of this kind combined with a fall in wages would not occur in practice. But this is beside the point. The rate of profit is a function of several variables, and if we want to know how these variables act on the profit rate we must investigate in turn the individual effect of each, irrespective of whether an isolated effect of this kind is economically possible or not in the case of one and the same capital.
2. s′ constant, v variable, C altered by the variation of v
This case is different from the previous one only in degree. Instead of decreasing or increasing by the same amount as v increases or decreases, c now remains constant. But under today’s conditions of large-scale industry and agriculture, variable capital is only a relatively small portion of the total capital and hence any reduction or growth in the total capital that is brought about by a change in the variable capital is also relatively slight. If we start once again with a capital such as:
I. 100c + 20ν + 10s; C = 120, s′ = 50 per cent, p′ = 8 1/3 Per cent,
this might perhaps be changed to something like:
II. 100c + 30ν + 15s; C = 130, s′ = 50 per cent, p′ = 11 7/13 per cent.
The opposite case of a decline in the variable capital would again be illustrated by the reverse transition from II to I.
Economic conditions here would be essentially the same as in the previous case, and hence need no further explanation. The transition from I to II involves a decline of a third* in the productivity of labour, or the operation of 100c requires half as much labour again in II as it does in I. This case is possible in agriculture.9
Whereas in the previous case the total capital was held constant by the conversion of constant capital into variable or vice versa, now the increase in the variable portion means that extra capital is tied up, while a decrease involves the release of capital that had previously been needed.
3. s′ and v constant, c and therefore also C variable
In this case the equation:
p′ = s′ ν/C
is changed to:
p′ 1 = s′ ν/C1,
and by cancelling out on both sides, we get the proportionality
p′1 : p′ = C : C1;
with the same rate of surplus-value and the same variable capital, the profit rate stands in inverse proportion to the total capital.
Say that we have three capitals or three different states of the same capital:
I. 80c + 20ν + 20s; C = 100, s′ = 100 per cent, p′ = 20 per cent;
II. 100c + 20c + 20s; C = 120, s′ = 100 per cent, p′ = 16⅔ per cent;
III. 60c + 20ν + 20s; C = 80, s′ = 100 per cent, p′ = 25 per cent;
then 20 per cent: 16⅔ per cent = 120 : 100; and 20 per cent: 25 per cent = 80 : 100.
The general formula given above for variations in ν/C, where s′ was constant, was:
p′ 1 = s′ eν/EC; it now becomes: p′ 1 = s′ ν/EC,
since v does not undergo any alteration, and the factor e = ν1/ν is therefore 1.
Since s′v = s, the mass of surplus-value, and since s′ and v both remain constant, s is also unaffected by any variation in C; the mass of surplus-value remains the same as before the change.
If c were to fall to zero, we would have p′ = s′, the rate of profit equal to the rate of surplus-value.
The alteration in c can come about either from a change merely in the value of the material elements of the constant capital, or from a changed technical composition of the total capital, i.e. a change in the productivity of labour in the branch of production in question. In the latter case, the productivity of social labour, which rises with the development of large-scale industry and agriculture, would successively move from III to I and from I to II in the above example. A quantity of labour that is paid 20 and produces a value of 40 would start by being used to operate a mass of means of labour to the value of 60; if its productivity rose, the means of labour put into operation would grow first to 80, and then to 100, if their value remained the same. The reverse sequence would indicate a decline in productivity; the same quantity of labour would set less means of production in motion, and the business would be cut back, as can well happen in agriculture, mining, etc.
A saving in constant capital both increases the rate of profit and releases capital as well, and this is important for the capitalist. We shall return to this point later, as well as investigating the effect of changes in the prices of the elements of constant capital, raw materials in particular.*
We see here again how a variation in constant capital has the same effect on the rate of profit, irrespective of whether this variation is brought about by an increase or decrease in the material components of c, or simply by a change in their value.
4. s′ constant, v, c and C all variable
In this case, the above general formula for changes in the profit rate, p′1 = s′ eν/EC, still applies. It results from this that, with the rate of surplus-value remaining the same:
(a) The rate of profit falls if E is greater than e, i.e. if the constant capital is increased in such a way that the total capital increases more sharply than the variable capital. If a capital of 80c + 20ν + 20s is changed to a composition of 170c + 30ν + 30s, then s′ remains at 100 per cent, but ν/C falls from 20/100 to 30/100, despite the fact that v has increased as well as C, and the rate of profit accordingly falls from 20 per cent to 15 per cent.
(b) The rate of profit remains unchanged only if e = E, i.e. if the fraction ν/C retains the same value despite the apparent change, thus if both numerator and denominator are multiplied or divided by the same figure. 80c + 20ν + 20s and 160c + 40ν + 40s evidently have the same profit rate of 20 per cent, because s′ remains at 100 per cent and ν/c = 20/100 = 40/200 exhibits the same value in both examples.
(c) The rate of profit rises if e is greater than E, i.e. if the variable capital rises more sharply than the total capital. If 80c + 20ν + 20s becomes 120c + 40ν + 40s, then the rate of profit of 20 per cent rises to 25 per cent, because with s′ unaltered, ν/c = 20/100 has risen to 40/160, from 1/5 to 1/4.
Where v and C both change in the same direction, we can conceive this change in their magnitudes as if both vary to a certain extent in the same ratio, so that up to this point ν/C remains unaltered. Beyond this point, then, only one of them varies, and we can thereby reduce this more complicated case to one or other of the previous simpler ones.
If 80c + 20ν + 20s changes to 100c + 30ν + 30s, the ratio between v and c, and therefore also between v and C, remains unaltered up to the point 100c + 25ν + 25s. The rate of profit, therefore, is so far unaffected. We can now take this 100c + 25ν + 25s as our starting-point; we find that v rises by 5, to 30ν, and C thereby rises from 125 to 130, and we are thus faced with case 2, that of a variation simply in v and the variation in C that this occasions. The rate of profit, which was originally 20 per cent, is increased by this addition of 5ν to 23 1/13 per cent, given the same rate of surplus-value.
The same reduction to a simpler case can also take place even if v and C move in opposite directions. Let us proceed again from 80c + 20ν + 20s, and let this change to the form 110c + 10ν + 10s. A change to 40c + 10ν + 10s would have kept the profit rate the same as it was originally, i.e. 20 per cent. The addition of 70c to this intermediate form makes it fall to 8 1/3 per cent. We have again reduced the example to a variation in only one of the variables, i.e. c.
Thus the simultaneous variation of v, c and C does not offer any new aspects, and always leads back in the last analysis to a case in which only one factor is variable.
Even the sole case that still remains has really been dispensed with already, i.e. the case in which v and c remain numerically the same, but their material elements undergo a change in value – v represents a different quantity of labour set in motion, and c a different quantity of means of production.
In the capital of 80c + 20ν + 20s, the 20ν might originally represent the wages of 20 workers for a 10-hour working day. Say that the wage of each worker now rises from 1 to 1 1/4. In this case, 20ν only suffices to pay 16 workers instead of 20. But if the 20 workers produced a value of 40 in their 200 hours’ work, then the 16, in a 10-hour day that amounts to 160 hours’ work in all, will produce a value of only 32. After subtracting 20ν for wages, only 12 of the 32 is left for surplus-value; the rate of surplus-value would then have fallen from 100 per cent to 60 per cent. But since, according to our assumption, the rate of surplus-value has to remain constant, the working day must be extended by a quarter, from 10 hours to 12 1/2. If 20 workers produce a value of 80 in a working day of 10 hours, i.e. 200 hours’ work in all, 16 workers produce the same value in 12 1/2 hours per day, which also comes to 200 hours, so that the capital of 80c + 20ν still produces the same surplus-value of 20 as it did before.
Conversely, if wages fall in such a way that 20ν covers the wages of 30 workers, s′ can remain constant only if the working day is reduced from 10 hours to 6⅔. 20 × 10 = 30 × 6⅔ = 200 working hours.
We have already explained in essentials how c can retain the same value expression in money throughout all these conflicting assumptions, while representing the differing quantities of means of production which correspond to the changed conditions. This case would however be very exceptional in its pure form.
As far as a change in value of the elements of c is concerned, a change that increases or decreases certain elements while leaving their value sum c unaltered, this disturbs neither the rate of profit nor the rate of surplus-value, as long as it does not bring with it any alteration in the magnitude of v.
In this way we have dealt with all possible cases of variation of v, c and C in our equation. We have seen how the profit rate can fall, rise or remain the same, with the rate of surplus-value constant throughout, in so far as the slightest alteration in the ratio between v and c or C is sufficient to alter the profit rate as well.
It has also become evident that there is always a limit to the variation of v beyond which it is economically impossible for s′ to remain constant. Since any unilateral variation of c must similarly reach a limit at which v can no longer remain constant, it is clear that limits are placed on all possible variations of ν/C beyond which s′ must also vary. In the case of these variations in s′, which we shall now turn to investigate, the mutual interaction of the various different variables in our equation appears even more clearly.
II. s′ variable
We can obtain a general formula for the rates of profit corresponding to different rates of surplus-value, irrespective of whether ν/C remains constant or also varies, if we convert the equation: p′ = s′ ν/C into the equation: p′1 = s′1 ν1/c1, in which p′, s′1, v1 and C1 stand for the new values of p′ s′, v and C.
We then get: p′: p′1 = s′ ν/C: s′1 ν1/C1, and therefore:
p′1 = s′ 1/s′ × ν1/ν × C/C1 ×p′.
1. s′ variable, ν/C constant
In this case we have equations:
p′ = s′ ν/C and p′ 1 = s′ ν/C,
such that ν/C has the same value in both cases. It follows therefore that p′:p′1 = s′:s′1.
The rates of profit for two capitals of the same composition are in direct proportion to their respective rates of surplus-value. Since the absolute magnitudes of v and C do not come into play in the fraction ν/C, but simply the ratio between the two, this holds for all capitals of the same composition, whatever their absolute magnitude may be.
80c + 20ν + 20s; C = 100, s′ = 100 per cent, p′ = 20 per cent
160c + 40ν; + 40s; C = 200, s′ = 50 per cent, p′ = 10 per cent
100 per cent: 50 per cent = 20 per cent: 10 per cent.
If the absolute magnitudes of v and C are the same in both cases, the profit rates also stand in the same ratio as the masses of surplus-value:
p′:p′1 = s′v: s′1v = s:s1
80c + 20ν + 20s; s′ = 100 per cent, p′ = 20 per cent
80c + 20ν + 10s; s’ = 50 per cent, p′ = 10 per cent
20 per cent: 10 per cent = 100 × 20 : 50 × 20 = 20s : 10s.
It is evident now that given capitals of the same composition either absolutely or relatively, the rate of surplus-value can vary only if either wages, or the length of the working day, or again the intensity of labour, also vary. In the following three cases:
I. 80c + 20ν + 10s; s′ = 50 per cent, p′ = 10 per cent
II. 80c + 20ν + 20s; s′ = 100 per cent, p′ = 20 per cent
III. 80c + 20ν + 40s; s’ = 200 per cent, p′ = 40 per cent,
the total value produced is 30 in I (20ν + 10s), 40 in II and 60 in III. This can happen in three different ways.
Firstly, if wages vary, so that 20ν represents a different number of workers in each individual case. Let us assume that, in case I, 15 workers are employed for 10 hours at a wage of £1⅔, to produce the value of £30, of which £20 replaces wages and £10 remains for surplus-value. If wages fall to £1, then 20 workers are employed for 10 hours and produce a value of £40, of which £20 is wages and £20 surplus-value. If wages fall yet further to £⅔, then 30 workers are employed for 10 hours and produce a value of £60, of which £40 remains for surplus-value after subtracting the £20 for wages.
This case, that of a constant percentage composition of capital, constant working day, constant intensity of labour, with changes in the rate of surplus-value brought about by changes in wages, is the only one that meets Ricardo’s assumption:
‘Profits would be high or low, exactly in proportion as wages would be low or high’ (Principles, Chapter I, section iii, p. 18 in the Works of D. Ricardo, ed. MacCulloch, 1852).*
Secondly, it can happen if the intensity of labour varies. In this case, for example, 20 workers might make 30 items of a certain commodity in case I, 40 in case II and 60 in case III, working with the same means of labour for 10 hours a day, with each item representing a new value of £1 over and above the value of the means of production consumed in it. Since 20 items, = £20, are always needed to replace wages, there remains for surplus-value in case I 10 items, = £10, in case II 20 items, = £20, and in case III 40 items, = £40.
The third possibility is that the working day varies in length. If 20 workers work with the same intensity for 9 hours in case I, 12 hours in case II, and 18 hours in case III, their total products will stand in the ratio of 9 : 12 : 18, i.e. 30 : 40 : 60, and since wages are 20 each time, there again remains 10, 20 or 40 left over for surplus-value.
A rise or fall in wages thus effects an opposite change in the rate of surplus-value, while a rise or fall in the intensity of labour, or an extension or reduction of the working day, both effect a change in the same direction, and with ν/C constant, the rate of profit is therefore similarly affected.
2. s′ and v variable, C constant
In this case, we have the proportionality:
p′ : p′ 1 = s′ ν/C: s′1 ν1/C = s′ν: s′1ν 1 = s: s1.
The rates of profit stand in the same ratio as the respective masses of surplus-value.
Variation in the rate of surplus-value, with variable capital remaining the same, means a change in the size and distribution of the value product. Simultaneous variation in v and s′ similarly entails a different distribution, but not always a change in the magnitude of the value product. Three cases are possible:
(a) The variations in v and s′ take place in opposite directions, but by the same amount.* For example,
Given that v + s = v1 + s1, then substituting vs′ for s, we get:
ν + νs′ = ν1 + νs′ 1, or:
s′ 1 = ν/ν1 (1 + s′) − 1
On the basis of this formula, case (b) below can similarly be reduced to an inequality.
80c + 20ν + 10s; s′ = 50 per cent, p′ = 10 per cent
90c + 10ν + 20s; s′ = 200 per cent, p′ = 20 per cent.
Here the value product is the same in both cases, and so too, therefore, is the quantity of labour that is performed. 20ν + 10s = 10ν + 20s = 30. The distinction is simply that in the first case 20 is paid for wages and 10 for surplus-value, while in the second case wages amount only to 10, and surplus-value is therefore 20. This is the only case in which a simultaneous variation in v and s′ leaves the number of workers, the labour intensity and the length of the working day unaffected.
(b) The variations in s′ and v still occur in opposite directions, but not to the same extent in each case. Either the variation in v must predominate, or that in s′.
I. 80c + 20ν + 20s; s′ = 100 per cent, p′ = 20 per cent
II. 72c + 28ν + 20s; s′ = 71 3/7 per cent, p′ = 20 per cent
III. 84c + 16ν + 20s; s′ = 125 per cent, p′ = 20 per cent.
In case I a value product of 40 involves a payment of 20ν, in case II a product of 48 a payment of 28ν, and in case III one of 36 a payment of 16ν. Both the value product and the wages have altered; but an alteration in the value product means an alteration in the quantity of labour performed, and therefore either in the number of workers, the duration of labour, or its intensity, if not more than one of these three.
(c) s′ and v both vary in the same direction; in this case the effect of one reinforces that of the other.
90c + 10ν + 10s; s’ = 100 per cent, p′ = 10 per cent
80c + 20ν + 30s; s′ = 150 per cent, p′ = 30 per cent
92c + 8ν + 6s; s′ = 75 per cent, p′ = 6 per cent.
Here, too, the three value products are different, i.e. 20, 50 and 14; and this difference in the quantity of labour in each case can again be reduced to a difference in the number of workers, the duration or intensity of labour, or any combination of these factors.
3. s′, v and C all variable
This case offers no new aspects and is settled by the general formula given under heading II, s’ variable [p. 156].
*
The impact of a change in the rate of surplus-value on the profit rate can thus be covered by the following cases:
1. p′ is increased or diminished in the same ratio as s′, if ν/C remains constant.
80c + 20ν + 20s; s′ = 100 per cent, p′ = 20 per cent
80c + 20ν + 10s; s′ = 50 per cent, p′ = 10 per cent
100 per cent: 50 per cent = 20 per cent: 10 per cent.
2. p′ rises or falls in a higher ratio than s′ if ν/C moves in the same direction as s′, i.e. increases or decreases according to whether s′ increases or decreases.
80c + 20ν + 10s; s′ = 50 per cent, p′ = 10 per cent
70c + 30ν + 20s; s′ = 66⅔ per cent, p′ = 20 per cent
50 per cent: 66⅔ per cent < 10 per cent: 20 per cent.
3. p′ rises or falls in a lower ratio than s′, if ν/C changes in the opposite direction to s′, but in a lower ratio.
80c + 20ν + 10s; s′ = 50 per cent, p′ = 10 per cent
90c + 10ν + 15s; s′ = 150 per cent, p′ = 15 per cent
50 per cent: 150 per cent > 10 per cent: 15 per cent.
4. p′ rises, even though s′ falls, or falls, even though s′ rises, if ν/C changes in the opposite direction to s′, and in a higher ratio.
80c + 20ν + 20s; s′ = 100 per cent, p′ = 20 per cent
90c + 10ν + 15s; s′ = 150 per cent, p′ = 15 per cent.
Here s′ has risen from 100 per cent to 150 per cent, while p′ has fallen from 20 per cent to 15 per cent.
5. Finally, p′ remains constant even though s′ rises or falls, if ν/C changes in the opposite direction to s′, but in exactly the same ratio.
It is only this last case that still requires some further discussion. 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. But while with s′ constant, any change whatsoever in the ratio of v to C is sufficient to induce a variation in the rate of profit, a change in s′ must involve an exactly corresponding, but opposite, change in ν/C, if the profit rate is to remain the same. This is possible only very exceptionally in the case of one and the same capital, or with two capitals in the same country.
Let us take for example a capital
80c + 20ν + 20s; C = 100, s′ = 100 per cent, p′ = 20 per cent,
and assume that wages fall in such a way that the same number of workers can be had for 16ν as previously with 20ν. With conditions remaining otherwise unchanged, we would then have 4ν set free, giving
80c + 16ν + 24s; C = 96, s′ = 150 per cent, p′ = 25 per cent.
If p′ is still to be 20 per cent, as before, the total capital has to increase to 120, and the constant capital therefore to 104:
104c + 16ν + 24s; C = 120, s′ = 150 per cent, p′ = 20 per cent.
This would be possible only if a change in the productivity of labour took place simultaneously with the fall in wages, and required this changed composition of capital; or alternatively, if the money value of the constant capital rose from 80 to 104 – in other words, a chance combination of conditions that only comes about in exceptional circumstances. In actual fact a change in s′ which is not simultaneously a change in v, thus also giving rise to a change in ν/C, is conceivable only under quite special conditions, i.e. in those branches of industry in which only fixed capital and labour are applied, and the object of labour is provided by nature.
The position is different when comparing rates of profit in two countries. Here the same rate of profit expresses in most cases different rates of surplus-value.
It results from all these five cases, therefore, that a rising profit rate can correspond to a falling or a rising rate of surplus-value, a falling profit rate can correspond to a rising or a falling rate of surplus-value, and a rate of profit that remains the same can also correspond to a rising or a falling rate of surplus-value. We have already shown under heading I [s′ constant, ν/C variable] that a rising, falling or unchanged rate of profit can also correspond to a rate of surplus-value that remains the same.
*
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.
The rates of profit of two different capitals, or of one and the same capital in two successive and different states,
are equal:
(1) given the same percentage composition and the same rate of surplus-value;
(2) given unequal percentage compositions and unequal rates of surplus-value, if the [mathematical] product of the rate of surplus-value and the percentage of the variable part of capital (s′ and v) is the same in each case, i.e. the mass of surplus-value reckoned as a percentage of the total capital (s = s′v); in other words, when the factors s′ and v stand in inverse proportion to one another in the two cases.
They are unequal:
(1) given the same percentage composition, if the rates of surplus-value are unequal, in which case they stand in the same ratio as these rates of surplus-value;
(2) given the same rate of surplus-value and different percentage compositions, in which case they stand in the same ratio as the variable portions of the capitals;
(3) given different rates of surplus-value and different percentage compositions, in which case they stand in the same proportion as the products s′v, i.e. as the masses of surplus-value reckoned as a percentage of the total capital.10