Capital Vol. III Part I
The Conversion of Surplus-Value into Profit and of the Rate of Surplus-Value into the Rate of Profit

# Chapter 3. The Relation of the Rate of Profit to the Rate of Surplus-Value

Here, as at the close of the preceding chapter, and generally in this entire first part, we presume the amount of profit falling to a given capital to be equal to the total amount of surplus-value produced by means of this capital during a certain period of circulation. We thus leave aside for the present the fact that, on the one hand, this surplus-value may be broken up into various sub-forms, such as interest on capital, ground-rent, taxes, etc., and that, on the other, it is not, as a rule, identical with profit as appropriated by virtue of a general rate of profit, which will be discussed in the second part.

So far as the quantity of profit is assumed to be equal to that of surplus-value, its magnitude, and that of the rate of profit, is determined by ratios of simple figures given or ascertainable in every individual case. The analysis, therefore, first is carried on purely in the mathematical field.

We retain the designations used in Books I and II. Total capital C consists of constant capital c and variable capital v, and produces a surplus-value s. The ratio of this surplus-value to the advanced variable capital, or s/v, is called the rate of surplus-value and designated s'. Therefore s/v = s', and consequently s = s'v. If this surplus-value is related to the total capital instead of the variable capital, it is called profit, p, and the ratio of the surplus-value s to the total capital C, or s/C, is called the rate of profit, p'. Accordingly,

p' = s/C = s/(c + v)

Now, substituting for s its equivalent s'v, we find

p' = s' (v/C) = s' v/(c + v)

which equation may also be expressed by the proportion

p' : s' = v : C ;

the rate of profit is related to the rate of surplus-value as the variable capital is to the total capital.

It follows from this proportion that the rate of profit, p', is always smaller than s', the rate of surplus-value, because v, the variable capital, is always smaller than C, the sum of v + c, or the variable plus the constant capital; the only, practically impossible case excepted, in which v = C, that is, no constant capital at all, no means of production, but only wages are advanced by the capitalist.

However, our analysis also considers a number of other factors which have a determining influence on the magnitude of c, v, and s, and must therefore be briefly examined.

First, the value of money. We may assume this to be constant throughout.

Second, the turnover. We shall leave this factor entirely out of consideration for the present, since its influence on the rate of profit will be treated specially in a later chapter. [Here we anticipate just one point, that the formula p' = s' (v/C) is strictly correct only for one period of turnover of the variable capital. But we may correct it for an annual turnover by substituting for the simple rate of surplus-value, s', the annual rate of surplus-value, s'n. In this, n is the number of turnovers of the variable capital within one year. (Cf. Book II, Chapter XVI, 1) — F. E.]

Third, due consideration must be given to productivity of labour, whose influence on the rate of surplus-value has been thoroughly discussed in Book I (Abschnitt IV). [English edition: Part IV. — Ed.] Productivity of labour may also exert a direct influence on the rate of profit, at least of an individual capital, if, as has been demonstrated in Book I (Kap. X, S. 323/324 [ = MEW 23, S.335/336]) [English edition: Ch. XII, pp. 316-17. — Ed.] this individual capital operates with a higher than the average social productivity and produces commodities at a lower value than their average social value, thereby realising an extra profit. However, this case will not be considered for the present, since in this part of the work we also proceed from the premise that commodities are produced under normal social conditions and are sold at their values. Hence, we assume in each case that the productivity of labour remains constant. In effect, the value-composition of a capital invested in a branch of industry, that is, a certain proportion between the variable and constant capital, always expresses a definite degree of labour productivity. As soon, therefore, as this proportion is altered by means other than a mere change in the value of the material elements of the constant capital, or a change in wages, the productivity of labour must likewise undergo a corresponding change, and we shall often enough see, for this reason, that changes in the factors c, v, and s also imply changes in the productivity of labour.

The same applies to the three remaining factors — the length of the working-day, intensity of labour, and wages. Their influence on the quantity and rate of surplus-value has been exhaustively discussed in Book I [English edition: Vol. 1, pp. 519-30. — Ed.] It will be understood, therefore, that notwithstanding the assumption, which we make for the sake of simplicity, that these three factors remain constant, the changes that occur in v and s may nevertheless imply changes in the magnitude of these, their determining elements. In this respect we must briefly recall that the wage influences the quantity of surplus-value and the rate of surplus-value in inverse proportion to the length of the working-day and the intensity of labour; that an increase in wages reduces the surplus-value, while a lengthening of the working-day and an increase in the intensity of labour add to it.

Suppose a capital of 100 produces a surplus-value of 20 employing 20 labourers working a 10-hour day for a total weekly wage of 20. Then we have:

80c + 20v + 20s; s' = 100%, p' = 20%.

Now the working-day is lengthened to 15 hours without raising the wages. The total value produced by the 20 labourers will thereby increase from 40 to 60 (10 : 15 = 40 : 60). Since v, the wages paid to the labourers, remains the same, the surplus-value rises from 20 to 40, and we have:

80c + 20v + 40s; s' = 200%, p' = 40%.

If, conversely, the ten-hour working-day remains unchanged, while wages fall from 20 to 12, the total value-product amounts to 40 as before, but is differently distributed; v falls to 12, leaving a remainder of 28 for s. Then we have:

80c + 12v + 28s; s' = 233⅓%, p' = 28/92 = 30 10/23 %.

Hence, we see that a prolonged working-day (or a corresponding increase in the intensity of labour) and a fall in wages both increase the amount, and thus the rate, of surplus-value. Conversely, a rise in wages, other things being equal, would lower the rate of surplus-value. Hence, if v rises through a rise in wages, it does not express a greater, but only a dearer quantity of labour, in which case s' and p' do not rise, but fall.

This indicates that changes in the working-day, intensity of labour and wages cannot take place without a simultaneous change in v and s and their ratio, and therefore also p', which is the ratio of s to the total capital c + v. And it is also evident that changes in the ratio of s to v also imply corresponding changes in at least one of the three above-mentioned labour conditions.

Precisely this reveals the specific organic relationship of variable capital to the movement of the total capital and to its self-expansion, and also its difference from constant capital. So far as generation of value is concerned, the constant capital is important only for the value it has. And it is immaterial to the generation of value whether a constant capital of £1,500 represents 1,500 tons of iron at, say, £1, or 500 tons of iron at £3. The quantity of actual material, in which the value of the constant capital is incorporated, is altogether irrelevant to the formation of value and the rate of profit, which varies inversely to this value no matter what the ratio of the increase or decrease of the value of constant capital to the mass of material use-value which it represents.

It is different with variable capital. It is not the value it has, not the labour incorporated in it, that matter at this point, but this value as a mere index of the total labour that it sets in motion and which is not expressed in it — the total labour, whose difference from the labour expressed in that value, hence the paid labour, i.e., that portion of the total labour which produces surplus-value, is all the greater, the less labour is contained in that value itself. Suppose, a ten-hour working-day is equal to ten shillings = ten marks. If the labour necessary to replace the wages, and thus the variable capital = 5 hours = 5 shillings, then the surplus-labour = 5 hours and the surplus-value = 5 shillings. Should the necessary labour = 4 hours = 4 shillings, then the surplus-labour = 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 quantity of labour set in motion by it, and, moreover, the measure of this index is altered, the rate of surplus-value will change in the opposite direction and inversely.

Let us now go on to apply the above-mentioned equation of the rate of profit, p' = s' (v/C), to the various possible cases. We shall successively change the value of the individual factors of s' (v/C) and determine the effect of these changes on the rate of profit. In this way we shall obtain different series of cases, which we may regard either as successive altered conditions of operation for one and the same capital, or as different capitals existing side by side and introduced for the sake of comparison, taken, as it were, from different branches of industry or different countries. In cases, therefore, where the conception of some of our examples as successive conditions for one and the same capital appears to be forced or impracticable, this objection falls away the moment they are regarded as comparisons of independent capitals.

Hence, we now separate the product s' (v/C) into its two factors s' and v/C. At first we shall treat s' as constant and analyse the effect of the possible variations of v/C. After that we shall treat the fraction v/C as constant and let s' pass through its possible variations. Finally we shall treat all factors as variable magnitudes and thereby exhaust all the cases from which laws concerning the rate of profit may be derived.

I. s' constant, v/C variable

This case, which embraces a number of subordinate cases, may be covered by a general formula. Take two capitals, C and C1, with their respective variable components, v and v1, with a common rate of surplus-value, s', and rates of profit p' and p'1. Then:

p' = s' (v/C) ; p'1 = s' (v1/C1)

Now let us make a proportion of C and C1, and of v and v1. For instance, let the value of the fraction C1/C = E, and that of v1/v = e. Then C1 = EC, and v1 = ev. Substituting in the above equation these values for p1, C1 and v1, we obtain

p'1 = s' ev/EC

Again, we may derive a second formula from the above two equations by transforming them into the proportion:

p' : p'1 = s' (v/C) : s' (v1/C1) = (v/C) : v1/C1 .

Since the value of a fraction is not changed if we multiply or divide its numerator and denominator by the same number, we may reduce v/C and v1/C1 to percentages, that is, we may make C and C1 both = 100. Then we have v/C = v/100 and v1/C1 = v1/100, and may then drop the denominators in the above proportion, obtaining:

p' : p'1 = v : v1', or:

Taking any two capitals operating with the same rate of surplus-value, the rates of profit are to each other as the variable portions of the capitals calculated as percentages of their respective total capitals.

These two formulas embrace all the possible variations of v/C.

One more remark before we analyse these various cases singly. Since C is the sum of c and v, of the constant and variable capitals, and since the rates of surplus-value, as of profit, are usually expressed in percentages, it is convenient to assume that the sum of c + v is also equal to 100, i.e., to express c and v in percentages. For the determination of the rate of profit, if not of the amount, it is immaterial whether we say that a capital of 15,000, of which 12,000 is constant and 3,000 is variable, produces a surplus-value of 3,000, or whether we reduce this capital to percentages:

15,000 C = 12,000c + 3,000v ( + 3,000s)

100 C = 80c + 20v ( + 20s).

In either case the rate of surplus-value s' = 100%, and the rate of profit = 20%.

The same is true when we compare two capitals, say, the foregoing capital with another, such as

12,000 C = 10,800c + 1,200v ( + 1,200s)

100 C = 90c + 10v ( + 10s).

in both of which s' = 100%, p' = 10%, and in which the comparison with the foregoing capital is clearer in percentage form.

On the other hand, if it is a matter of changes taking place in one and the same capital, the form of percentages is rarely to be used, because it almost always obscures these changes. If a capital expressed in the form of percentages:

80c + 20v + 20s

assumes the form of percentages:

90c + 10v + 10s,

we cannot tell whether the changed composition in percentages, 90v + 10c, is due to an absolute decrease of v or an absolute increase of c, or to both. We would need the absolute magnitudes in figures to ascertain this. In the analysis of the following individual cases of variation, however, everything depends on how these changes have come about; whether 80v + 20c changed into 90c + 10v through an increase of the constant capital without any change in the variable capital, for instance through 12,000c + 3,000v changing into 27,000c + 3,000v (corresponding to a percentage of 90c + 10v); or whether they took this form through a reduction of the variable capital, with the constant capital remaining unchanged, that is, through a change into 12,000c + 1,333⅓ v (also corresponding to a percentage of 90c + 10v); or, lastly, whether both of the terms changed into 13,500c + 1,500v (corresponding once more to a percentage of 90c + 10v). But it is precisely these cases which we shall have to successively analyse, and in so doing dispense with the convenient form of percentages, or at least employ these only as a secondary alternative.

1) s' and C constant, v variable.

If v changes in magnitude, C can remain unaltered only if c, the other component of C, that is, the constant capital, changes by the same amount as v, but in the opposite direction.

If C originally = 80c + 20v = 100, and if v is then reduced to 10, then C can = 100 only if c is increased to 90; 90c + 10v = 100. Generally speaking, if v is transformed into v ± d, into v increased or decreased by d, then c must be transformed into c ± d, into c varying by the same amount, but in the opposite direction, so that the conditions of the present case are satisfied.

Similarly, if the rate of surplus-value s' remains the same, while the variable capital v changes, the amount of surplus-value s must change, since s = s'v, and since one of the factors of s'v, namely v, is given another value.

The assumptions of the present case produce, alongside the original equation,

p' = s' (v/C) ,

still another equation through the variation of v:

p'1 = s' (v1/C)

in which v has become v1 and p'1, the resultant changed rate of profit, is to be found.

It is determined by the following proportion:

p' : p'1 = s' (v/C) : s' (v1/C) = v : v1

Or: with the rate of surplus-value and total capital remaining the same, the original rate of profit is to the new rate of profit produced by a change in the variable capital as the original variable capital is to the changed variable capital.

If the original capital was, as above:

I. 15,000 C = 12,000c + 3,000v ( + 3,000s), and if it is now:

II. 15,000 C = 13,000c + 2,000v ( + 2,000s), then C = 15,000 and s' = 100% in either case, and the rate of profit of I, 20%, is to that of II, 13⅓%, as the variable capital of I, 3,000, is to that of II, 2,000, i. e., 20% : 13⅓% = 3,000 : 2,000.

Now, the variable capital may either rise or fall. Let us first take an example in which it rises. Let a certain capital be originally constituted and employed as follows:

I. 100c + 20v + 10s; C = 120, s' = 50%, p' = 8⅓%.

Now let the variable capital rise to 30. In that case, according to our assumption, the constant capital must fall from 100 to 90 so that total capital remains unchanged at 120. The rate of surplus-value remaining constant at 50%, the surplus-value produced will then rise from 10 to 15. We shall then have:

II. 90c + 30v + 15s; C = 120, s' = 50%, p' = 12½%.

Let us first proceed from the assumption that wages remain unchanged. Then the other factors of the rate of surplus-value, i.e., the working-day and the intensity of labour, must also remain unchanged. In that event the rise of v (from 20 to 30) can signify only that another half as many labourers are employed. Then the total value produced also rises one-half, from 30 to 45, and is distributed, just as before, ⅔ for wages and ⅓ for surplus-value. But at the same time, with the increase in the number of labourers, the constant capital, the value of the means of production, has fallen from 100 to 90. We have, then, a case of decreasing productivity of labour combined with a simultaneous shrinkage of constant capital. Is such a case economically possible?

In agriculture and the extractive industries, in which a decrease in labour productivity and, therefore, an increase in the number of employed labourers is quite comprehensible, this process is on the basis and within the scope of capitalist production attended by an increase, instead of a decrease, of constant capital. Even if the above fall of c were due merely to a fall in prices, an individual capital would be able to accomplish the transition from I to II only under very exceptional circumstances. But in the case of two independent capitals invested in different countries, or in different branches of agriculture or extractive industry, it would be nothing out of the ordinary if in one of the cases more labourers (and therefore more variable capital) were employed and worked with less valuable or scantier means of production than in the other case.

But let us drop the assumption that the wage remains the same, and let us explain the rise of the variable capital from 20 to 30 through a rise of wages by one-half. Then we shall have an entirely different case. The same number of labourers — say, twenty — continue to work with the same or only slightly reduced means of production. If the working-day remains unchanged — say, 10 hours — then the total value produced also remains unchanged. It was and remains = 30. But all of this 30 is now required to make good the advanced variable capital of 30; the surplus-value would disappear. We have assumed, however, that the rate of surplus-value should remain constant, that is, the same as in I, at 50%. This is possible only if the working-day is prolonged by one-half to 15 hours. Then the 20 labourers would produce a total value of 45 in 15 hours, and all conditions would be satisfied:

II. 90c + 30v + 15s; C = 120, s' = 50%, p' = 12½%.

In this case, the 20 labourers do not require any more means of labour, tools, machines, etc., than in case I. Only the raw materials or auxiliary materials would have to be increased by one-half. In the event of a fall in the prices of these materials, the transition from I to II might be more possible economically, even for an individual capital in keeping with our assumption. And the capitalist would be somewhat compensated by increased profits for any loss incurred through the depreciation of his constant capital.

Now let us assume that the variable capital falls, instead of rising. Then we have but to reverse our example, taking II as the original capital, and passing from II to I.

II. 90c + 30v + 15s, then changes into
I. 100c + 20v + 10s, and it is evident that this transposition does not in the least alter any of the conditions regulating the respective rates of profit and their mutual relation.

If v falls from 30 to 20 because ⅓ fewer labourers are employed with the growing constant capital, then we have before us the normal case of modern industry, namely, an increasing productivity of labour, and the operation of a larger quantity of means of production by fewer labourers. That this movement is necessarily connected with a simultaneous drop in the rate of profit will be developed in the third part of this book.

If, on the other hand, v falls from 30 to 20, because the same number of labourers is employed at lower wages, the total value produced would, with the working-day unchanged, as before = 30v + 15s = 45. Since v fell to 20, the surplus-value would rise to 25, the rate of surplus-value from 50% to 125%, which would be contrary to our assumption. To comply with the conditions of our case, the surplus-value, with its rate at 50%, must rather fall to 10, and the total value produced must, therefore, fall from 45 to 30, and this is possible only if the working-day is reduced by ⅓. Then, as before, we have:

100c + 20v + 10s; s' = 50%, p' = 8⅓%.

It need hardly be said that this reduction of the working-time, in the case of a fall in wages, would not occur in practice. But that is immaterial. The rate of profit is a function of several variable magnitudes, and if we wish to know how these variables influence the rate of profit, we must analyse the individual effect of each in turn, regardless of whether such an isolated effect is economically practicable with one and the same capital.

2) s' constant, v variable, C changes through the variation of v.

This case differs from the preceding one only in degree. Instead of decreasing or increasing by as much as v increases or decreases, c remains constant. Under present-day conditions in the major industries and agriculture the variable capital is only a relatively small part of the total capital. For this reason, its increase or decrease, so far as either is due to changes in the variable capital, are likewise relatively small.

Let us again proceed with a capital:

I. 100c + 20v + 10s; C = 120, s' = 50%, p' = 8⅓%.

which would then change, say, into:

II. 100c + 30v + 15s; C = 130, s' = 50%, p' = 11 7/13%.

The opposite case, in which the variable capital decreases, would again be illustrated by the reverse transition from II to I.

The economic conditions would be essentially the same as in the preceding case, and therefore they need not be discussed again. The transition from I to II implies a decrease in the productivity of labour by one-half; for II the utilisation of 100 requires an increase of labour by one-half over that of I. This case may occur in agriculture. 

But while the total capital remains constant in the preceding case, owing to the conversion of constant into variable capital, or vice versa, there is in this case a tie-up of additional capital if the variable capital increases, and a release of previously employed capital if the variable capital decreases.

3) s' and v constant, c and therefore C variable.

In this case the equation changes from:

p' = s' (v/C) into p' = s' (v/C1) ,

and after reducing the same factors on both sides, we have:

p'1 : p' = C : C1;

with the same rate of surplus-value and equal variable capitals, the rates of profit are inversely proportional to the total capitals.

Should we, for example, have three capitals, or three different conditions of the same capital:

I. 80c + 20v + 20s; C = 100, s' = 100%, p' = 20%;

II. 100c + 20v + 20s; C = 120, s' = 100%, p' = 16⅔%;

III. 60c + 20v + 20s; C = 80, s' = 100%, p' = 25%.

Then we obtain the proportions:

20% : 16⅔% = 120 : 100 and 20% : 25% = 80 : 100.

The previously given general formula for variations of v/C with a constant s' was:

p'1 = s' ev/EC ; now it becomes: p'1 = s' v/EC ,

since v does not change, the factor e = v1/v , becomes = 1.

Since s'v = s, the quantity of surplus-value, and since both s' and v remain constant, it follows that s, too, is not affected by any variation of C. The amount of surplus-value is the same after the change as it was before it.

If c were to fall to zero, p' would = s', i.e., the rate of profit would equal the rate of surplus-value.

The alteration of c may be due either to a mere change in the value of the material elements of constant capital, or to a change in the technical composition of the total capital, that is, a change in the productivity of labour in the given branch of industry. In the latter case, the productivity of social labour mounting due to the development of modern industry and large-scale agriculture would bring about a transition (in the above illustration) in the sequence from III to I and from I to II. A quantity of labour which is paid with 20 and produces a value of 40 would first utilise means of labour to a value of 60; if productivity mounted and the value remained the same, the used up means of labour would rise first to 80, and then to 100. An inversion of this sequence would imply a decrease in productivity. The same quantity of labour would put a smaller quantity of means of production into motion and the operation would be curtailed, as may occur in agriculture, mining, etc.

A saving in constant capital increases the rate of profit on the one hand, and, on the other, sets free capital, for which reason it is of importance to the capitalist. We shall make a closer study of this, and likewise of the influence of a change in the prices of the elements of constant capital, particularly of raw materials, at a later point. [Present edition: Ch. V, VI. — Ed.]

It is again evident here that a variation of the constant capital equally affects the rate of profit, regardless of whether this variation is due to an increase or decrease of the material elements of c, or merely to a change in their value.

4) s' constant, v, c and C all variable.

In this case, the general formula for the changed rate of profit, given at the outset, remains in force:

p'1 = s' ev/EC .

It follows from this that with the rate of surplus-value remaining the same:

a) The rate of profit falls if E is greater than e, that is, if the constant capital is augmented to such an extent that the total capital grows at a faster rate than the variable capital. If a capital of 80c + 20v + 20s changes into 170c + 30v + 30s, then s' remains = 100%, but v/C falls from 20/100 to 30/100, in spite of the fact that both v and C have grown, and the rate of profit falls correspondingly from 20% to 15%.

b) The rate of profit remains unchanged only if e = E, that is, if the fraction v/C retains the same value in spite of a seeming change, i.e., if its numerator and denominator are multiplied or divided by the same factor. The capitals 80c + 20v + 20s and 160c + 40v + 40s obviously have the same rate of profit of 20%, because s' remains = 100% and v/C = 20/100 = 40/200 represents the same value in both examples.

c) The rate of profit rises when e is greater than E, that is, when the variable capital grows at a faster rate than the total capital. If 80c + 20v + 20s turns into 120c + 40v + 40s, the rate of profit rises from 20% to 25%, because with an unchanged s' (v/C) = 20/100 rises to 40/160, or from 1/5 to 1/4.

If the changes of v and C are in the same direction, we may view this change of magnitude as though, to a certain extent, both of them varied in the same proportion, so that v/C remained unchanged up to that point. Beyond this point, only one of them would vary, and we shall have thereby reduced this complicated case to one of the preceding simpler ones.

Should, for instance, 80c + 20v + 20s become 100c + 30v + 30s, then the proportion of v to c, and also to C, remains the same in this variation up to : 100c + 25v + 25s. Up to that point, therefore, the rate of profit likewise remains unchanged. We may then take 100c + 25v + 25s as our point of departure; we find that v increased by 5 to become 30v, so that C rose from 125 to 130, thus giving us the second case, that of the simple variation of v and the consequent variation of C. The rate of profit, which was originally 20%, rises through this addition of 5v to 23 1/13 %, provided the rate of surplus-value remains the same.

The same reduction to a simpler case can also take place if v and C change their magnitudes in opposite directions. For instance, let us again start with 80c + 20v + 20s, and let this become: 110c + 10v + 10s. In that case, with the change going as far as 40c + 10v + 10s, the rate of profit would remain the same 20%. By adding 70c to this intermediate form, it will drop to 8⅓%. Thus, we have again reduced the case to an instance of change of one variable, namely of c.

Simultaneous variation of v, c, and C, does not, therefore, offer any new aspects and in the final analysis leads back to a case in which only one factor is a variable.

Even the sole remaining case has actually been exhausted, namely that in which v and C remain numerically the same, while their material elements undergo a change of value, so that v stands for a changed quantity of labour put in motion and c for a changed quantity of means of production put in motion.

In 80c + 20v + 20s, let 20v originally represent the wages of 20 labourers working 10 hours daily. Then let the wages of each rise from 1 to 1 ¼. In that case the 20v will pay only 16 labourers instead of 20. But if 20 labourers produce a value of 40 in 200 working-hours, 16 labourers working 10 hours daily will in 160 working-hours produce a value of only 32. After deducting 20v for wages, only 12 of the 32 would then remain for surplus-value. The rate of surplus-value would have fallen from 100% to 60%. But since we have assumed the rate of surplus-value to be constant, the working-day would have to be prolonged by one-quarter, from 10 to 12½ hours. If 20 labourers working 10 hours daily = 200 working-hours produce a value of 40, then 16 labourers working 12½ hours daily = 200 hours will produce the same value, and the capital of 80c + 20v would as before yield the same surplus-value of 20.

Conversely, if wages were to fall to such an extent that 20v would represent the wages of 30 labourers, then s would remain constant only if the working-day were reduced from 10 to 6⅔ hours. For 20 × 10 = 30 × 6⅔ = 200 working-hours.

We have already in the main discussed to what extent c may in these divergent examples remain unchanged in terms of value expressed in money and yet represent different quantities of means of production changed in accordance with changing conditions. In its pure form this case would be possible only by way of an exception.

As for a change in the value of the elements of c which increases or decreases their mass but leaves the sum of the value of c unchanged, it does not affect either the rate of profit or the rate of surplus-value, so long as it does not lead to a change in the magnitude of v.

We have herewith exhausted all the possible cases of variation of v, c, and C in our equation. We have seen that the rate of profit may fall, remain unchanged, or rise, while the rate of surplus-value remains the same, with the least change in the proportion of v to c or to C, being sufficient to change the rate of profit as well.

We have seen, furthermore, that in variations of v there is a certain limit everywhere beyond which it is economically impossible for s' to remain constant. Since every one-sided variation of c must also reach a certain limit where v can no longer remain unchanged, we find that there are limits for every possible variation of v/C, beyond which s' must likewise become variable. In the variations of s' which we shall now discuss, this interaction of the different variables of our equation will stand out still clearer.

II. s' variable

We obtain a general formula for the rates of profit with different rates of surplus-value, no matter whether v/C remains constant or not, by converting the equation:

p' = s' (v/C)

into

p'1 = s'1 (v1/C1) ,

in which p'1, s'1, v1 and C1 denote the changed values of p', s', v and C. Then we have:

p' : p'1 = s' (v/C) : s'1 (v1/C1) ,

and hence:

p'1 = (s'1/s') × v1/v × C/C1 × p'.

1) s' variable, v/C constant.

In this case we have the equations:

p' = s' (v/C); p'1 = s' (v/C) ,

in both of which v/C is equal. Therefore:

p' : p'1 = s' : s'1

The rates of profit of two capitals of the same composition are to each other as the two corresponding rates of surplus-value. Since in the fraction v/C it is not a question of the absolute magnitudes of v and C, but only of their ratio, this applies to all capitals of equal composition whatever their absolute magnitude.

80c + 20v + 20s; C = 100, s' = 100%, p' = 20%

160c + 40v + 20s; C = 200, s' = 50%, p' = 10%

100% : 50% = 20% : 10%.

If the absolute magnitudes of v and C are the same in both cases, the rates of profit are moreover also related to one another as the amounts of surplus-value:

p' : p'1 = s'v : s'1v = s : s1.

For instance:

80c + 20v + 20s; s' = 100%, p' = 20%

80c + 20v + 10s; s' = 50%, p' = 10%

20% : 10% = 100 × 20 : 50 × 20 = 20s : 10s.

It is now clear that with capitals of equal absolute or percentage composition the rate of surplus-value can differ only if either the wages, or the length of the working-day, or the intensity of labour, differ. In the following three cases:

I. 80c + 20v + 10s; s' = 50%, p' = 10%

II. 80c + 20v + 20s; s' = 100%, p' = 20%

III. 80c + 20v + 40s; s' = 200%, p' = 40%

the total value produced in I is 30 (20v + 10s); in II it is 40; in III it is 60. This may come about in three different ways.

First, if the wages are different, and 20v stands for a different number of labourers in every individual case. Suppose capital I employs 15 labourers 10 hours daily at a wage of £1⅓, who produce a value of £30, of which £20 replace the wages and £10 are surplus-value. If wages fall to £1, then 20 labourers may be employed for 10 hours; they will produce a value of £40, of which £20 will replace the wages and £20 will be surplus-value. Should wages fall still more, to £⅔, thirty labourers may be employed for 10 hours. They will produce a value of £60, of which £20 will be deducted for wages and £40 will represent surplus-value.

This case — a constant composition of capital in per cent, a constant working-day and constant intensity of labour, and the rate of surplus-value varying because of variation in wages — is the only one in which Ricardo's assumption is correct:

"Profit would be high or low, exactly in proportion as wages were low or high." (Principles, Ch. I, Sect. III, p. 18 of the Works of D. Ricardo, ed. by MacCulloch, 1852.)

Or second, if the intensity of labour varies. In that case, say, 20 labourers working 10 hours daily with the same means of production produce 30 pieces of a certain commodity in I, 40 in II, and 60 in III, of which every piece, aside from the value of the means of production incorporated in it, represents a new value of £1. Since every 20 pieces = £20 make good the wages, there remain 10 pieces = £10 for surplus-value in I, 20 pieces = £20 in II, and 40 pieces = £40 in III.

Or third, the working-day differs in length. If 20 labourers work with the same intensity for 9 hours in I, 12 hours in II, and 18 hours in III, their total products, 30 : 40 : 60 vary as 9 : 12 : 18. And since wages = 20 in every case, 10, 20, and 40 respectively again remain as surplus-value.

A rise or fall in wages, therefore, influences the rate of surplus-value inversely, and a rise or fall in the intensity of labour, and a lengthening or shortening of the working-day, act the same way on the rate of surplus-value and thereby, with v/C constant, on the rate of profit.

2) s' and v variable, C constant.

The following proportion applies in this case:

p' : p'1 = s' (v/C) : s' (v1/C) = s'v : s'1v1 = s : s1.

The rates of profit are related to one another as the respective amounts of surplus-value.

Changes in the rate of surplus-value with the variable capital remaining constant meant a change in the magnitude and distribution of the produced value. A simultaneous variation of v and s' also always implies a different distribution, but not always a change in the magnitude of the produced value. Three cases are possible:

a) Variation of v and s' takes place in opposite directions, but by the same amount; for instance:

80c + 20v + 10s; s' = 50%, p' = 10%

90c + 10v + 20s; s' = 200%, p' = 20%

The produced value is equal in both cases, hence also the quantity of labour performed; 20v + 10s = 10v + 20s = 30. The only difference is that in the first case 20 is paid out for wages and 10 remains as surplus-value, while in the second case wages are only 10 and surplus-value is therefore 20. This is the only case in which the number of labourers, the intensity of labour, and the length of the working-day remain unchanged, while v and s' vary simultaneously.

b) Variation of s' and v also takes place in opposite directions, but not by the same amount. In that case the variation of either v or s' outweighs the other.

I. 80c + 20v + 20s; s' = 100%, p' = 20%

II. 72c + 28v + 20s; s' = 71 3/7%, p' = 20%

III. 84c + 16v + 20s; s' = 125%, p' = 20%.

Capital I pays for produced value amounting to 40 with 20v, II a value of 48 with 28v, and III a value of 36 with 16v. Both the produced value and the wages have changed. But a change in the produced value means a change in the amount of labour performed, hence a change either in the number of labourers, the hours of labour, the intensity of labour, or in more than one of these.

c) Variation of s' and v takes place in the same direction. In that case the one intensifies the effect of the other.

90c + 10v + 10s; s' = 100%, p' = 10%

80c + 20v + 30s; s' = 150%, p' = 30%

92c + 8v + 6s; s' = 75%, p' = 6%.

Here too the three values produced are different, namely 20, 50, and 14. And this difference in the magnitude of the respective quantities of labour reduces itself once more to a difference in the number of labourers, the hours of labour, and the intensity of labour, or several or all of these factors.

3) s', v and C variable.

This case offers no new aspects and is solved by the general formula given under II, in which s' is variable.

The effect of a change in the magnitude of the rate of surplus-value on the rate of profit hence yields the following cases:

1) p' increases or decreases in the same proportion as s' if v/C remains constant.

80c + 20v + 20s; s' = 100%, p' = 20%

80c + 20v + 10s; s' = 50%, p' = 10%

100% : 50% = 20% : 10%.

2) p' rises or falls at a faster rate than s' if v/C moves in the same direction as s', that is, if it increases or decreases when s' increases or decreases.

80c + 20v + 10s; s' = 50%, p' = 10%

70c + 30v + 20s; s' = 66⅔%, p' = 10%

50% : 66⅔% < 10% : 20%.

3) p' rises or falls at a slower rate than s' if v/C changes inversely to s', but at a slower rate.

80c + 20v + 10s; s' = 50%, p' = 10%

90c + 10v + 15s; s' = 150%, p' = 15%

50% : 150% > 10% : 15%.

4) p' rises while s' falls, or falls while s' rises if v/C changes inversely to, and at, a faster rate than, s'.

80c + 20v + 20s; s' = 100%, p' = 20%

90c + 10v + 15s; s' = 150%, p' = 15%.

s' has risen from 100% to 150%, p' has fallen from 20% to 15%.

5) Finally, p' remains constant whereas s' rises or falls, while v/C changes inversely to, but in exactly the same proportion as, s'.

It is only this last case which still requires some explanation. We have observed earlier in the variations of v/C that one and the same rate of surplus-value may be expressed in very much different rates of profit. Now we see that one and the same rate of profit may be based on very much different rates of surplus-value. But while any change in the proportion of v to C is sufficient to produce a difference in the rate of profit so long as s is constant, a change in the magnitude of s must lead to a corresponding inverse change of v/C in order that the rate of profit remains the same. In the case of one and the same capital, or in that of two capitals in one and the same country this is possible but in exceptional cases. Assume, for example, that we have a capital of

80c + 20v + 20s; C = 100, s' = 100%, p' = 20%;

and let us suppose that wages fall to such an extent that the same number of labourers is obtainable for 16v instead of 20v. Then, other things being equal, and 4v being released, we shall have:

80c + 16v + 24s; C = 96, s' = 150%, p' = 25%.

In order that p' may now = 20% as before, the total capital would have to increase to 120, the constant capital therefore rising to 104:

104c + 16v + 24s; C = 120, s' = 150%, p' = 20%.

This would only be possible if the fall in wages were attended simultaneously by a change in the productivity of labour which required such a change in the composition of capital. Or, if the value in money of the constant capital increased from 80 to 104. In short, it would require an accidental coincidence of conditions such as occurs in exceptional cases. In fact, a variation of s' that does not call for the simultaneous variation of v, and thus of v/C, is conceivable only under very definite conditions, namely in such branches of industry in which only fixed capital and labour are employed, while the materials of labour are supplied by Nature.

But this is not so when the rates of profit of two different countries are compared. For in that case the same rate of profit is, in effect, based largely on different rates of surplus-value.

It follows from all of these five cases, therefore, that a rising rate of profit may correspond to a falling or rising rate of surplus-value, a falling rate of profit to a rising or falling rate of surplus-value, and a constant rate of profit to a rising or falling rate of surplus-value. And we have seen in I that a rising, falling, or constant rate of profit may also accord with a constant rate of surplus-value.

The rate of profit, therefore, depends on two main factors — the rate of surplus-value and the value-composition of capital. The effects of these two factors may be briefly summed up as follows, by giving the composition in per cent, for it is immaterial which of the two portions of the capital causes the variation:

The rates of profit of two different capitals, or of one and the same capital in two successive different conditions,

are equal

1) if the per cent composition of the capitals is the same and their rates of surplus-value are equal;

2) if their per cent composition is not the same, and the rates of surplus-value are unequal, provided the products of the rates of surplus-value by the percentages of the variable portions of capitals (s' by v) are the same, i.e., if the masses of surplus-value (s = s'v) calculated in per cent of the total capital are equal; in other words, if the factors s' and v are inversely proportional to one another in both cases.

They are unequal

1) if the per cent composition is equal and the rates of surplus-value are unequal, in which case they are related as the rates of surplus-value;

2) if the rates of surplus-value are the same and the per cent composition is unequal, in which case they are related as the variable portions of the capitals;

3) if the rates of surplus-value are unequal and the per cent composition not the same, in which case they are related as the products s'v, i.e., as the quantities of surplus-value calculated in per cent of the total capital. 

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### Notes

9. The manuscript has the following note at this point: "Investigate later in what manner this case is connected with ground-rent." F. E.

10. The manuscript contains also very detailed calculations of the difference between the rate of surplus-value and the rate of profit (s'-p'), which has very interesting peculiarities, and whose movement indicates where the two rates draw apart or approach one another. These movements may also be represented by curves. I am not reproducing this material, because it is of less importance to the immediate purposes of this work, and because it is enough here to call attention to this fact for readers who wish to pursue this point further. — F.E.

Transcribed for the Internet by Hinrich Kuhls