is shown only because the surplus is calculated in two ways. In the first place it is calculated as a simple magnitude, as an excess of the selling price over the cost-price. In this form, the entire circulating capital enters into the cost-price, while of the fixed capital only the wear and tear enters into it. In the second place, the relation of this excess in value to the total value of the advanced capital is calculated. In. this case, the value of the fixed capital is taken into the cal- culation entirely, the same as that of the circulating capital. In other words, the circulating capital enters both times in the same way, while the fixed capital enters the first time in a different, the second time in the same way as the circulating capital. Under these circumstances, the difference between the fixed and circulating capital is the only one which ob- trudes itself.
The excess in value, then, if determined by the rate of profit, appears as a surplus generated annually, or during a 62 Capitalist Production.
definite period of circulation, by the total capital above its own value.
While the rate of profit differs numerically from the rate of surplus-value, the profit and the surplus-value are actually the same thing and numerically equal. However, the profit is a transformed kind of surplus-value, a form in which its origin and the secret of its nature are obscured and extin- guished. rJ*p©fii-ia,__therefoi'e, that disguise of surplus-value which must be removed before~l'he real nature of surplus- value can. be discovered. In the surplus-value, the relation between capital and labor is laid bare. But in the relation of capital and profit, that is to say, the relation between capital and that form of surplus-value which appears on one hand as an excess over the cost-price of commodities realized!^ in the process of circulation, and on the other hand as a sur- plus determined by its relation to the total capital, the capital appears as a relation to itself, a relation in which it, as the original amount of value, is distinguished from a new value generated by itself. It is dimly recog-nized, that capital gen- erates this new value by its movement in the processes of production and circulation. But the way in which this is done is surrounded by mystery, and thus surplus-value seems to be due to hidden qualities inherent in capital itself.
To the extent that we follow up the process of self-expan- sion of capital, the nature of the relation of surplus-value to capital becomes more and more mystified, and it becomes in- creasingly difficult to discover the secret of its internal or- ganism.
In this first part, we shall consider the rate of profit as- numerically different from the rate of surplus-value, while profit and surplus-value will be treated as the same numerical magnitude having only a different form. In the second part we shall see that the transformation continues and that profit presents itself as a magnitude differing also numerically from surplus-value.
Relation of Profit to Surplus-Value. 63, CHAPTEE III.
THE KELATION OF THE KATE OF PROFIT TO THE KATE OF SUKPLUS-VAEUE:.
We have stated at the conclusion of the preceding chapter, and repeat it here, that we consider in this entire first part the amount of profit made by a certain capital to be equal to the full amount of surplus-value produced by means of this capital during a certain period of circulation. In other words, we leave aside for the present the fact that this sur- plus-value is split up into various secondary forms, such as interest on capital, ground-rent, taxes, etc., and that surplus- value is not identical, as a rule, with profit as appropriated on the basis of an average rate of profit, which will be dis- cussed in part II.
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 the relations of simple numerical magnitudes given or ascertainable in every individual case. The analysis, therefore, is first carried on purely on the field of mathematics.
We retain the terms used in volumes I and II. The 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 ■—, is called the rate of surplus-value and designated by s'. Therefore -^ = s', and s = s'v. If this surplus-value is calculated on 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 ~, is called the rate of profit, p'. Accordingly, V—-c; = z^- ^ow, substituting for s its equivalent s'v, we find p' = s'-J=s'^. And this equation may be ex- pressed by the proportion p': s' ^ v: C, or in words, the 64 Relation of Profit to Surplus-Value.
rate of profit is proportioned to the rate of surplus- value as the variable capital is to the total capital.
This proportion shows that the rate of profit, p', is al- ways smaller than the rate of surplus-value, s', because the variable capital, v, is always smaller than the total capital, C, which is the sum of v -f- c, the variable plus the constant capital. The only exception to this rule is the practically impossible case, in which v = C, that is to say, in which n( i constant capital, no means of production, are advanced by the capitalist, but only wages.
However, our analysis must take into account a few other elements, which have a determining influence on the magni- tude of c, V, and s. We shall mention them briefly.
There is^ first, the value of money. We may assume this to be constant, throughout our analysis.
In the second place, there is the turn-over. We leave this element entirely out of consideration for the present, since its influence on the rate of profit will be treated later on in a special chapter. [We anticipate here only one point, namely that the formula p' = s''-J- is strictly correct only for one period of turn-over of the variable capital. But we may make it correct for an annual turn-over by substituting for s', the simple rate of surplus-value, the factor s'n, mean- ing the annual rate of surplus-value. The factor n in this term expresses the number of turn-overs of the variable capi- tal during one year. (See chapter XVI, I, volume II.) — In the third place, the productivity of labor must be con- sidered. Its influence on the rate of surplus-value has been thoroughly discussed in volume I, part V. The productivity of labor may also exert a direct influence on the rate of profit, at least of an individual capital. It has been demonstrated in volume I, chapter XII, that an individual capital may re- alize an extra profit, if it operates with a greater productivity than that of the social average and thereby produces its com- modities at a lower value than the social average value of the same commodities. However, this case will not be considered for the present, since our premise in this part of the work Relation of Profit to Surplus-Value. 65 is that the commodities are produced under normal social con- ditions and sold at their values. Hence Ave assume in each case that the productivity of labor remains constant. Under these circumstances the composition of the values of any capi- tal invested in any line of industry, in other words, the pro- portion between the variable and constant capital, expresses a definite degree in the productivity of labor. As soon as this proportion is altered by other means than a mere change in the value of the material elements of the constant capital, or a change in the value of wages, it follows that the pro- ductivity of labor must likewise undergo a corresponding change. We shall see frequently, for this reason, that altera- tions affecting the factors c, v^, and s imply also changes in the productivity of labor.
The same applies to the three remaining factors, namely the length of the working day, the intensity of labors and the wages. Their influence on the mass and rate of surplus- value has been discussed in detail in volume I. It will be understood, therefore, that notwithstanding our assumption that these three factors remain constant there may be changes in V and s which may imply changes in the magnitude of these determining elements. In this respect we have but to remember that wages influence the quantity of surplus-value and the degree of the rate of surplus-value inversely from the length of the working day and the intensity of labor; that an increase of wages reduces the surplus-value, while a prolongation of the working day and an increase in the in- tensity of labor add to it.
Take it that a capital of 100 produces with 20 laborers by a working day of 10 hours and a total weekly wage of 20 a surplus-value of 20. Then we have 80 c -|- 2(3 v -[- 20 s, which implies that s' equal 100% and p' 20%.
Now let the working day be prolonged to 15 hours without an increase of wages. The total value produced by the 20 laborers is thereby increased from 40 to 60, since 10: 15 = 40: 60. Seeing that v, the w^ages paid to the laborers, re- mains the same, the surplus-value rises from 20 to 40, and we have 80 c -j- 20 v + 40 s, implying that s' equals 200% 66 Capitalist Production.
and p' 40%. If, on the other hand, the working day re- mains unchanged at 10 hours, while wages fall from 20 to 12, the total value produced amounts to 40, but it is differently distributed. For v falls to 12, leaving a remainder of 28 for s. Then we have 80 c + 12 v + 28 s, whereby s' is raised to 233^%, while the rate of profit, p', is as 28 to 92, We see, then, that both a prolongation of the working day (or a corresponding increase in the intensity of labor) and a fall in wages increase the mass, and thus the rate, of sur- plus-value. On the other hand, a rise in wages, other circum- stances remaining the same, would lower the rate of surplus- value. Hence, if v rises through an increase of wages, it does not mean a greater, but only a dearer quantity of labor, and in that case s' and p' do not rise, ])ut fall.
This indicates that a change in the working day, in the intensity of labor, and in wages cannot take place without at the same time altering v and s and their proportion, and therefore also p', which expresses the proportion of s to the total capital c -(- v. And it is also evident that a change in the proportion of s to v implies a corresponding change in at least one of the three determining elements of labor.
It is precisely this fact which reveals the specific organic relationship of variable capital to the movement of the total capital and its self-expansion, and also its difference from the constant capital. So far as it is a cjuestion of the gen- eration of value, the constant capital is significant only f^r its value. It is immaterial for this question, whether a constant capital of, say, 1,500 p.st. represents 1,500 tons of iron at 1 p.st. each, or 500 tons of iron at 3 p.st. each. The quantity of the actual material, in which the value of the constant capital is incorporated, is immaterial for the ques- tion of the formation of value and the rate of profit. This rate varies inversely to the value of the constant capital, no matter what may be the proportion of the increase or de- crease of the value of constant capital to the mass of its ma''[ terial elements.
Relation of Profit to Surplus-Value. 67 It is different with the variable capital. Not its own value, not the labor incorporated in this capital, are of prime im- portance, but the fact that its own value implies the setting in motion of a grand total of labor whose quantity it does not express. This grand total of labor differs from the labor expressed in the value of the variable capital and paid by it in that it contains a certain amount of surplus-labor, which is so much greater, the smaller the value of the labor contained in the variable capital. Take it that a working day of 10 hours is equal to 10 shillings. If the necessary labor, which pays for the wages, or makes good the variable capital, is worth 5 shillings, then the surplus-labor amounts to 5 hours, or the surplus-value to 5 shillings. If the necessary labor amounts to 4 hours and is worth 4 shillings, then the surplus- labor 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 amount of labor actually set in motion by it, as soon as the measure of this index is altered, the rate of surplus-value will vary inversely and at an inverse ratio.
Now let us pass on and apply the previously found equa- tion of the rate of profit, p' = s' -^, to the various cases possible. We shall change the value of the individual factors of s' -^ one after another and ascertain the effect of these changes on the rate of profit. In this way we obtain a num- ber of different cases, which we may regard either as succes- sively altered determinants of one and the same capital, or as different capitals existing side by side and compared with one another, no matter whether they exist in different lines of industry or different countries. In cases where the concep- tion of some of our examples as successive conditions of the same capitals seems forced or impracticable, this objection is set aside by regarding them as illustrations of independent capitals.
We now separate the product s' -^ into its two factors s' and -^. In the first place, we treat s' as a constant factor and analyze the effects of the possible variations of -^. After that we treat the fraction -^ as constant and let s' go through i 68 Capitalist Production.
its possible variations. Finally we treat all factors as vari- able magnitudes and thereby exhaust all cases from which rules concerning the rate of profit may be derived.
We make a general formula for this case, which comprises a number of sub-cases. Take two capitals C and Cj, with their respective variable proportions v and Vj, with equal rates of surplus-value s', and the rates of profit p' and p/. Then ISTow^ let us make a proportion of C and C^, and v and Vj, for instance let the value of the fraction §i == E, and that of ^ = e. Then Cj = EC, and v^ = ev. Substituting in the above equation these values for p/, Cj and v^, we obtain p/ = s' g^. Again, we may deduct a second formula from the above tw^o equations, by transforming them into the equa- tion p': pi' = s' -J: s' c^ = "E": C^- Since the value of a fraction remains the same, if we multiply or divide its nu-, merator or denominator by the same number, we may reduce -^ and p-, to ^percentages, that is to say we may make both C and C^ equal to 100. Then we have -J = -j^ and ^ = ^. We may then drop the denominators in the above proportion and say that p': pi' =, v: v^. In other words, Avith any two capitals operating with the same rate of surplus-value the rates of profit are proportioned to one another as the variable capitals are to one another, calculated in percentages on their respective total capitals.
These two fonnulse comprise all cases of variation of -^.
Before we analyze these various cases, we make another remark. Since C is the sum of c plus v, of the constant and variable capital, and since the rates of surplus-value and of profit are generally expressed in percentages, it is convenient to assume that the sum of c plus v is also equal to 100, that is to say, to express c and v in percentages. It is immaterial for the determination, not of the mass, but of the rate of profit, whether we say that a capital of 15,000, composed of 12,000 of constant and 3,000 of variable capital, produces a surplus-value of 3,000, or whether we reduce this capital to per- centages. So we may say that 15,000 C = 12,000 c -f 3,000 Relation of Profit to Surplus-Value. 69 The same is true in the comj^arison of two capitals. For instance, if we compare the foregoing capital with another, such as 12,000 C =. 10,800 c + 1,200 v + (1,200 s), or 100 C = 90 c + 10 V + (10 s). In the last case, s' is 100% and p', 10%. And its comparison with the foregoing capital is easier by percentages.
On the other hand, if it is a question of changes taking place in the same capital, the expression by percentages is rarely convenient, because these peculiar alterations are al- most always obliterated thereby. If a capital, expressed in percentages of 80 c + 20 v 4- 20 s assumes the percentages of 90 c -f- 10 V -|- 10 s, we cannot tell whether the change in the composition of percentages is due to an absolute decrease of v or an absolute increase of c, or to both. In order to as- certain this, we must have the absolute magnitudes in figures. But in the analysis of the following individual cases, every- thing depends on the question of the way in which the varia- tions have been accomplished. Has 80 c -|- 20 v been changed into 90 c -|- 10 V by an increase of the constant capital with- out any change in the variable capital, for instance by chang- ing 12,000 c + 3,000 V into 27,000 c + 3,000 v? Or has the same result been accomplished by leaving the constant capital untouched and reducing the variable capital, for in- stance by changing the above capital into 1^,000 c -|- 1,333^ v (corresponding to a percentage of 90 c -f- 10 v)? Or have both of the original capitals been changed into 13,500 c -|- 1,500 V (corresponding once more to percentages of 90 c -j- 10 v)? It is precisely these cases which we shall have to an- alyze, and in so doing we must dispense with percentages, or at least employ them only in a minor degree.
If v changes its magnitude, then C can remain unaltered only by a change in the opposite direction of c, the other com- ponent of C. If C consists originally of 80 c + 20 v, and if v is reduced to 10, then C can remain 100 only by an increase 70 Capitalist Production.
of c to 90; for 90 c + 10 v = 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 decreased or increased by the same amount, into c varying in the opposite direction from v, in order that the conditions of the present case be fulfilled.
Again, if the rate of surplus-value, s', remains the same, while the variable capital, v, changes, then the mass of sur- plus-value must change, since s = s'v, and since one of the factors of s'v, namely v, is invested with a different value.
The assumptions of the present case produce, aside from the original equation p' = s' -^, still another equation by the variation of v, namely p/ = s' ■^', in which v has become Vi and p/, the corresponding rate of profit, is to be sought.
It is found by the corresponding proportion: p': p/ = s' "c: s' -^ = v: Vi. That is to say, if the rate of surplus-value and the total capi- tal remain the same, then the original rate of profit is propor- tioned 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 I) 15,000 C = 12,000 c -|- 3,000 v -F (3,000 s), and if it is now II) 15,000 C = 13,000 c + 2,000 V + (2,000 s), then C is 15,000 and the rate of surplus-value 100% in either case, and the rate of profit of I), 20%, is proportioned to that of II), 13^%, as the variable capital of I), 3,000, is to the variable capital of II), 2,000, that is to say 20%: 13^% = 3,000: 2,000.
Now, the variable capital may either increase or decrease. Take first an example in which it increases. Let a certain capital be constituted and operated as follows: I) 100 c -|- 20 V + 10 s. Then C equals 120, s' equals 50%, and p' equals 8|%. Now let the variable capital increase to 30. In that case the constant capital must fall to 90, according to our assumption, which requires that the total should re- main unchanged at 120. The amount of surplus-value pro- duced will then rise from 10 to 15, the rate of surplus-value Relation of Profit to Surplus-Value. 71 remaining constant at 50%. Our capital then is constituted as follows: Now let us start out with the assumption that the wages remain unchanged. Then the other factors of the rate of surplus-value, namely the working day and the intensity of labor, must also be unchanged. Therefore the increase of v from 20 to 30 can signify only that more laborers are em- ployed. In that case the total product in values also increases by one-half, from 30 to 45, and is distributed, the same as before, to f for wages and \ for surplus-value. Simulta- neously with the increase in the number of laborers the con- stant capital, the value of the means of production has fallen from 100 to 90. We have before us then, a case of de- creasing productivity of labor combined with a simultaneous decrease of constant capital. Is such a case economically possible?
In agriculture and industries engaged in the extraction of substances, where a decrease in the productivity of labor and, therefore, an increase in the number of laborers are readily understood, this process is accompanied on the basis and within the scope of capitalist production, by an increase of constant capital, not by a decrease. Even if our assumed decrease of c were due merely to a fall in prices, an indi- vidual 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 lines of agriculture or extractive industry, it would not be strange if more laborers (and therefore more variable capital) were employed on less valu- able or fewer means of production in the case of one than in the other.
But let us have done with the assumption that the wages remain the same, and let us explain the rise of the variable capital from 20 to 30 by a rise of wages by one-half. Then we have another case. The same number of laborers con- tinue to work with the same or slightly reduced means of 72 Capitalist Prodnctioru production. If the working day remains unchanged, say at 10 hours, then the total product also remains unchanged. It was and remains 30. But this amount of 30 is now required to make good the consumed variable capital. The surplus- value would have disappeared. But we had assumed that the rate of surplus-value should remain constant at 50%, the same as in I). This is possible only if the working day is prolonged by one-half, increased to 15 hours. In that case 20 laborers produce in 15 hours a total value of 45, and all conditions would be fulfilled. We should have Under these circumstances the 20 laborers do not require any more instruments, tools, machines, etc., than in the case of I). Only the raw materials or auxiliary substances would have to be increased by one-half. If there were a fall in the prices of these materials, then the transition from I) to II) under the conditions of our assumed case might very well be accomplished even by an individual capital. And the capi- talist 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 were to be re- duced instead of increased. Then we have but to reverse our example. We have but to assume that II) is the orig- inal capital and to pass from II) to I). Then II), or 90 c -f 30 V + 15 s changes into I), or 100 c -f 20 v -f 10 s, and it is evident that this transposition does not alter any of the conditions which regulate the respective rates of profit and their mutual relations.
If V falls from 30 to 20 because the number of laborers is reduced by one-third while the constant capital increases, then we have before us the normal case of modem industry, namely an increasing productivity of labor, an operation of a larger mass of means of production by fewer laborers. That this process is necessarily connected with a simultaneous fall of the rate of profit, Avill be demonstrated in the third part of this volume.
Relation of Profit to Surplus-Value. 73 On the other hand, if v falls from 30 to 20 because the same number of laborers are employed at lower wages, while the working day remains the same, then the total product in values would remain 30 v -|- 15 s, or 45. Since wages have fallen to 20, the surplus-value would rise to 25, the rate of surplus-value from 50% to 125%, contrary to our assump- tion. In order to comply with the conditions of our case, the surplus-value, with its rate at 50%, must fall to 10. The total product must, therefore, fall from 45 to 30, and this is possible only by a reduction of the working day by one-third. Then we have, the same as before, 100 c + 20 v -f-10 s. C It need hardly be mentioned that this reduction of the working time with a fall in wages would not occur in practice. But this is immaterial. The rate of profit is a function of several variable magnitudes, and if we wish to know in what manner these variable magnitudes influence the rate of profit, we must analyze the individual effect of each seriatim, re- gardless of whether such an isolated effect is practicable with one and the same capital or not.
2) ^ constant, v variable, C changed by the variation' of v.
This case differs from the preceding one only in degree. Instead of c decreasing or increasing by as much as v in- creases or decreases, c remains constant. Under the modern conditions of great industry and agriculture the variable cap- ital is but a relatively small part of the total capital. For this reason, the increase or decrease of the total capital, so far as either is due to variations of the variable capital, are like- wise relatively small.
Let us start out again with a capital I) of 100 c -|- 20 v -f- 10 s. C equals 120, s' 50%, and p' 8^%,. This will then be transformed into II) 100 c + 30 v + 15 s, with C at 130, s' at 50%, and p' at 11-t^%. The opposite case, in which the variable capital would decrease, would be symbolized by the transition from II) to I).
The economic conditions would be essentially the same as m the preceding case, and therefore require no reiteration. The transition from I) to II) implies a decrease in the pro- 74 Capitalist Production, ductivity of labor by one-half. The assimilation of 100 c requires an increase of labor in II) by one-half over that of I). This case may occur in agriculture.®