While in the preceding case the total capital remained con- stant, owing to the conversion of constant capital into vari- able, or vice versa, there is in this case a tie-up of additional capital, if the variable capital is increased, and a release of previously employed capital, if the variable capital decreases.
In this case, the equation p' = s' -^ is changed into p/ = s' ^,. After eliminating the same factors on both sides,'] we have p/: p' = C: Ci. In other words, if the rates of surplus-value are the same and the variable capitals equal, the rates of profit are inversely proportioned to the total cap- itals.
Take it that we have three different capitals, or three dif- ferent conditions of the same capital, for instance Then we obtain the proportions: The general formula previously given for variations of ■^ when s' remained constant was p/ = s' g^. Now it be- comes p' = s' eT5- For since v remains unchanged, the fac- tor e, or v> becomes equal to 1.
Since s'v equals s, the mass of surplus-value, and since both s' and v remain constant, it follows that s is not affected by any variation of C. The mass of surplus-value is the same after the change that it was before.
If c were to fall to zero, p' would be equal to s', that is to j say, the rate of profit equal to the rate of surplus-value.
The alteration of c may be due either to a mere change in J the value of the material elements of constant capital, or | to a change in the technical composition of the total capital, 'The manuscript has the following note at this point: "Investigate later in what maimer this case is connected with ground-rent."
Relation of Profit to Surplus-Value. 75 that is to say a change in the productivity of labor in that line of industry. In the last named case, the increase in the productivity of social labor due to the development of in- dustry and agriculture on a large scale would bring about a transition, in the above illustration, from III to I and from I to II. A quantity of labor paid with 20 and pro- ducing a value of 40 would first work up means of produc- tion valued at 60. With a further increase in the produc- tivity, and the same value, the means of production would be worked up to the amount of 80, and later on of 100. A re- version of this succession would imply a decrease in produc- tivity. The same quantity of labor would work up a smaller quantity of means of production, the business would be cut down. This may occur in agriculture, mining, etc.
A saving in constant capital increases on the one hand the rate of profit, and on the other sets free some capital. It is, therefore, of great importance for the capitalist. We shall analyze this point later on, and likewise the influence of a change of prices of the elements of constant capital, particu- larly of raw materials.
We see once more, by this illustration, that a variation of the constant capital uniformly affects the rate of profit, no matter whether this variation is due to an increase or de- crease of the material elements of c, or merely to a change in their value.
In this case, the general formula indicated at the outset, namely p' = s' |^, remains in force. It follows from this, assuming the rate of surplus-value to remain the same, that a) the rate of profit falls, if E is greater than e, that is to say, if the constant capital increases to such an extent that the total capital grows at a faster rate than the variable cap- ital. If a capital of 80 c -f- 20 v + 20 s is transformed so that it becomes 170 c + 30 v + 30 s, then s' remains at 100%, but ^ falls from 100 to ^. in spite of the fact that both V and C have augmented, and the rate of profit falls corre- spondingly from 20% to 15%.
b) The rate of profit remains unchanged only in the case 76 Capitalist Production.
that e equals E, that is to say^ if the fraction -^ retain the same value even if the fraction is apparently changed, in other words, if its numerator and denominator are multi- plied or divided by the same number. It is evident that the capital 80c + 20vH-20s and the capital 160 c + 40 v + 40 s have the same rate of profit, namely 20%, because s' remains at 100% and -^ represents the same value, whether we write it y^^ or 2W.
c) The rate of profit arises, when e is greater than E, that is to say, when the variable capital grows at a faster rate than the total capital. If 80 c + 20 v + 20 s becomes 120 c -|- 40 V -|- 40 s, then the rate of profit rises from 20% to 25%, because s' has remained the same and -^ has risen from -^-Q to xW; or from ^ to i- If the variation of v and C follows the same direction, we may look upon this change of magnitude up to a certain de- gree as though both of them varied in the same proportion, so that -^ would be regarded as unchanged to that extent. Beyond this point only one of them would then vary, and by this means we should reduce this complicated case to one of the preceding simpler ones.
For instance, if 80 c + 20 v + 20 s becomes 100 c4- 30 v -|- 30 s, then the proportion of v to c, and also to C, remains the same up to the point of 100 c + 25v + 25s. Up to that point, the rate of profit remains likewise unchanged. We may then take our departure from 100 c + 25 v -|- 25 s. We find that later increased by 5 and became 30, so that C rose from 125 to 130. This is identical with 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 by this addition of 5 v to 23^^^%, always assum- ing the rate of surplus-value to remain the same.
The same reduction to a simpler case can take place, when- ever V and C change their magnitudes in opposite directions. For instance, let us start out once more from 80 c -j- 20 v + 20 s, and let this become 110 c + 10 v + 10 s. In that case, the rate of profit would have remained the same, if the I Relation of Profit to Surplus-Value. yy variation had proceeded to tlie point of 40 c + 10 v -f- 10 s. It would still have been 20%, By adding 70 c to this in- termediate form, the rate of profit is lowered to 85%. Thus we have reduced this case to a case of variation of one mag- nitude, namely of c.
Simultaneous variations of v, c, and C, do not, then, offer any new points of analysis. For they may be reduced in the last resort to cases in which only one factor is variable.
Even the only remaining case has actually been covered, namely that in which v and C are numerically unchanged, while their material elements experience a change of value, so that V stands for a changed quantity of assimilated labor and c for a changed quantity of assimilated means of pro- duction.
For instance, in the capital 80 c + 20 v -|- 20 s, let 20 v indicate originally the wages of 20 laborers working 10 hours daily. Then let the wages of each laborer increase from 1 to 1^. In that case 20 v pay only 16 laborers instead of 20. I^ow, if 20 laborers produce in 200 working hours a value of 40, then 16 laborers will produce in 160 working hours a value of only 32. After deducting 20 v for wages, only 12 would remain for surplus-value. The rate of sur- plus-value would have fallen from 100% to 60%. But since our assumption is that the rate of surplus-value shall remain constant, the working day would have to be prolonged by one- quarter, from 10 hours to 12^ hours. If 20 laborers, work- ing 10 hours daily, or 200 hours, produce a value of 40, then 16 laborers, working 12^ hours daily, or 200 hours, will pro- duce the same value, and the capital of 80 c -j- 20 v pro- duces the same surplus-value of 20.
Vice versa, if wages fall to such an extent that 20 v in- dicates the wages of 30 laborers, then s' can remain imchanged only in the case that the working day is reduced from 10 to 6| hours. For 20 X 10 = 30 X 6| = 200 working hours.
We have discussed previously in these diverging assump- tions, to what extent c may express the same value in money, and yet represent different quantities of means of production corresponding to different conditions. In reality this case 78 Capitalist Production.
will very rarely be practicable in its purely theoretical form.
As for the change of value of the elements of c, by which their mass is increased or decreased, it touches neither the rate of surplus-value nor the rate of profit, so long as it does; not imply a change of magnitude in v.. "m.
We have now exhausted all possible cases of variation of V, c, and C in our equation. We have seen that the rate of profit may fall, rise, or remain unchanged, while the rate of surplus-value remains the same, for the least variation in the proportion of v to c, or to C, is sufficient to change the rate of profit.
We have seen, furthermore, that there is everywhere a cer- tain limit in the variation of v where the constancy of s' becomes economically impossible. Since every one-sided varia- tion of c must also arrive at a certain limit where v can no longer remain unchanged, we find that every possible varia- tion of -g- has certain limits, beyond which s' must likewise become variable. In the variations of s', which we shall now discuss, this interaction of the different variable magnitudes of our equation will become still plainer.
II. s' variable.
We obtain a general formula for the rates of profit with variable rates of surplus-value, no matter whether -^ re- mains constant or not, by converting the equation p' = s' -^ into p/ = s/ ■^,. Here p/, s/, Ci, and Vi indicate the changed values of p', s', C, and v. Then we have p': pi' = s' "o": s/ ^, This may be manipulated into In this case we have the equations p' = s' -^ and p/ = s/ -5-. In both of them -^ is equal. Therefore p': pr = s': s/. That is to say, the rates of profit of two capitals of tliftcsame composition are proportioned as the corresponding two rates of surplus-value. Since it is not a question, in the fraction -g-, of the absolute magnitude of v and C, but only of their proportion to one another, this applies to all capitals Relation of Profit to Surplus-Value. 79 of equal composition, whatever may be their absolute magni- tude.
If the absolute magnitudes of v and C are the same in both cases, then the rates of profit are also proportioned to one an- other as the masses of surplus-value: p': p/ = s'v: s/v = s: Si. For instance: 80 c -I- 20 V -F 20 s; s' = 100%, p' = 20%. 80 c + 20 V + 10 s; s' = 50%, p' = 10%. 20%: 10% = 100 X 20: 50 X 20 = 20 s: 10 s. Now, it is evident that with capitals of equal absolute com- position, or equal percentages of composition, the rates of sur- plus-value can differ only when either the wages, or the length of the working day, or the intensity of labor are different. Take the following three cases: In the case of I, the total product in values is 30, namely 20 V -f- 10 s, in II it is 40, in III it is 60. This may come about in three different ways.
First, if the wages are different, so that 20 v expresses in every individual case a different number of laborers. Take it that capital I employs 15 laborers for 10 hours per day at a wage of If p.st. and that these laborers produce a value of 30 p.st. of which 20 p.st. make good the wages and 10 p.st. are surplus-value. If wages fall to 1 p.st., then 20 laborers may be employed for 10 hours, and they will produce a value of 40 p.st., of which 20 p.st. make good wages and 20 p.st. are sur- plus-value. If wages fall still more, for instance to f p.st, then 30 laborers may be employed for 10 hours, and they w\U produce a value of 60 p.st., 40 p.st. of which will represt ^t surplus-value after deducting 20 p.st. for wages.
This case, in which the percentages of composition of the capital, the working day, the intensity of labor, are constant, while the rate of surplus-value varies on account of the varia- 8o Capitalist Production.
tion of wages, is the only one in which Ricardo's assumption is correct, to-wit, that " profits would be high or low, exactly in proportion as wages would be low or high," (Principles, chapter I, section III, page 18 of the " Works of D. Ri- cardo," edited by MacCulloch, 1852.)
Secondly, if the intensity of labor varies. In that case 20 laborers produce with the same means of production in 10 hours of daily labor 30 pieces of a certain commodity in I, 40 pieces in II, and 60 pieces in III. Every piece repre- sents, aside from the value of the means of production in- corporated in it, a new value of 1 p.st. Since every 20 pieces make good the wages of 20 p.st., there remain 10 pieces at 10 p.st. for surplus-value in I, 20 pieces at 20 p.st. in II, and 40 pieces at 40 p.st, in III.
Thirdly, the working day may vary in length. If 20 la- borers work with the same intensity for 9 hours in I, 12 hours in II, and 18 hours in III, then their total products, 30:40: GO vary in the proportions 9: 12: 18. And since wages are 20 in every case, the surplus-value is 10, or 20, or 40 re- spectively.
An increase or decrease in wages, then, influences the rate of surplus-value, and, since -J- was assumed as constant, also the rate of profit, inversely, while an increase or decrease in the intensity of labor, a lengthening or shortening of the work- ing day, influence them in the same direction.
The rates of profit are proportioned to one another as the corresponding masses of surplus-value.
A variation of the rate of surplus-value, while the variable capital remains constant, signifies a change in the magnitude and distribution of the product in values. A simultaneous variation of v and s' also implies always a change in the dis- tribution, but not always a change in the magnitude of the product in values. Three cases are possible.
a) The variation of v and s' takes place in opposite direc- tions, but by the same amount, for instance: Relation of Profit to Surplus-Value. 8i 90 c + 10 V + 20 s; s' = 200%, p' = 20%. The product in values is equal in both cases, hence the quan- tity of labor performed likewise: 20 v + 10 s = 10 v + 20 s = 30. The difference is only that in the first case 20 are paid for wages and 10 remain for surplus-value, v^^hile in the second case wages are 10 and surplus-value 20. This is the only case in which the number of laborers, the intensity of labor, and the length of the working day remain unchanged, while V and s' vary.
b) The variation of s' and v takes place in opposite direc- tions, but not by the same amount. In that case the varia- tion of either v or s'' is the greater.
I. 80 c + 20 V + 20 s; s' = 100 %, p' = 20%. II. 72c + 28v + 20s; s' = 71f%, p' = 20%. III. 84c+16v + 20s; s' = 125 %, p' = 20%. Capital I pays for a product in values amounting to 40 with 20 V, II a value of 48 witb 28, and III a value of 36 with 16. Both the product in values and the wages have changed. But a change in the product in values means a change in the amount of labor performed, and this implies a change either in the number of laborers, the hours of labor, or the intensity of labor, or in more than one of these.
c) The variation of s' and v takes place in the same di- rection. In that case it intensifies the effect of either.
90 c + 10 V + 10 s; s' = 100%, p' = 10%. 80 c + 20 V -f 30 s; s' = 150%, p' = 30%. 92 c+ 8v+ 6s; s' = 75%, p' = 6%. In these cases the three products in value are also different namely 20, 50, and 14. And this difference in the magni- tude of the respective quantities of labor reduces itself ouce more to a difference in the number of laborers, the hours of labor, and the intensity of labor, or of several or all of these factors.
This case offers no new points of view and is solved by the general formula given under II, in which s' is variable.
82 Capitalist Production.
The effect of a change in the magnitude of the rate of sur- plus-value on the rate of profit is summed up, according to the foregoing, by the following cases: 1) p' increases or decreases in the same proportion as s', if -^ remains constant.
2) p' rises or falls at a greater rate than s', if -^ moves in the same direction as s', that is to say, if -^ increases or decreases when s' increases or decreases.
3) p' rises or falls at a smaller rate than s', if -^ changes in the opposite direction from s', but at a smaller rate.
4) p' rises, while s' falls, or falls while s' rises, if -^ changes in the opposite direction and at a greater rate than s'.
s' has risen from 100%o to 150%o, p' has fallen from 20%, 5) Finally, p' remains constant, while s' rises or falls, if ■^ changes in the opposite direction, but at exactly the same rate, as s'.
It is only this last case which requires some further expla- nation. We observed in the variations of -^ that the same rate of surplus-value may be an expression of different rates of profit. We see now that the same rate of profit may be based on different rates of surplus-value. So long as s' is constant, any change in the proportion of v to C is sufficient to call forth a difference in the rate of profit. But if s' varies in magnitude, it requires a corresponding inverse change of -^ in order that the rate of profit may remain the same. This happens but exceptionally in the case of one and the same Relation of Profit to Surplus-Value. 83 capital, or of two capitals in one and the same country. Take it that we have a capital 80 c + 20 v + 20 s; C = 100, s' = 100%, p' = 20%. And let us assume that wages fall to such an extent that the same number of laborers may be bought for 16 V instead of 20 v. Then we have released 4 v, and other circumstances remaining the same, our capital will have the composition 80 c + 16 v + 24 s; C = 96, s' = 150%,, p' = 25%. In order that p' may be 20%, as before, the total cap- ital would have to increase to 120, the constant capital, there- fore, to 104, thus, 104 c -f 16 V + 24 s; C = 120, s' = This would be possible only if the fall in wages were ac- companied by a change in the productivity of labor, which would require such a change in the composition of capital. Or, it might be that the money value of the constant capital would increase from 80 to 104. In short, it would require an accidental coincidence of conditions such as occurs very rarely. In fact, a variation of s' which does not imply a simultaneous variation of v, and thus of -^ is practicable only under very definite conditions. It may happen in lines of industry in which only fixed capital and labor are employed, while the materials of labor are supplied by nature.
But this is not so in the comparison of the rates of profit of two different countries. For in that case the same rate of profit is based as a rule on different rates of surplus-value.
It follows from all of these five cases that a rising rate of profit may be the companion of a falling or rising rate of sur- plus-value; a falling rate of profit go hand in hand with a ris- ing or falling rate of surplus- value; a constant rate of profit ex- ist by the side of a rising or falling rate of surplus-value. And we have seen under No. 1 that a rising, falling, or constant rate of profit may be based on a constant rate of surplus- value.
The rate of profit, then, is determined by two main factors, namely the rate of surplus-value and the composition of the value of capital. The effects of these two factors may be briefly summed up in the manner stated hereafter. We may, in this summing up, express the composition of capital in per- 84 Capitalist Production.
centages, for it is immaterial for this point which one of the two portions of capital is the canse of variation.
The rates of profits of two different capitals, or of one and the same capital in two different successive conditions, are equal 1) If the percentages of composition of capital are the same and the rates of surplus-value equal.
2) If the percentages of composition are not the same, and the rates of surplus-value unequal, provided that the products of the multiplication of the rates of surplus-value by the per- centages of the variable portions of capital (s' and v) are the same, that is to saj, the masses of surplus-value (s = s'v) calculated in percentages on the total capital; in other words, if the factors s' and v are inversely proportioned to one an- other in both cases.
Tliey are unequal 1) If the percentages of composition are equal and the rates of surplus-value unequal, in which case the rates of profit are proportioned as the rates of surplus-value.
2 ) If the rates of surplus value are the same and the per- centages of composition unequal, in which case the rates of profit are proportioned as the variable portions of capital.
3) If the rates of surplus value are unequal and the per- centages of composition not the same, in which case the rates of profit are proportioned as the products s'v, that is to say, as the masses of surplus-value calculated in percentages on the total capital. 1^ '" The manuscript contains also very detailed calculations of the difference be- tween the rate of surplus-value and the rate of profit (s' — p'); these show very interesting peculiarities and their movement indicates the cases in which the two rates draw apart or approach one another. These movements may be represented by curves. I do not reproduce this material, because it is of less importance for the immediate purposes of this work. It is enough to call the attention of those readers to this fact who wish to follow up this line of inquiry. — F. E.
Eftect of Turn-Over on Rate of Profit.
CHAPTER IV, THE EFFECT OF THE TUKN'OVER ON THE KATE OF PROFIT.
The effect of the turn-over on tlie production of surplus- value, and consequently of profit, has been discussed in vol- ume IT. It mav be briefly summarized in the statement that the entire capital cannot be employed all at once in produc- tion, because the turn-over requires a certain lapse of time; for this reason a portion of the capital is always lying fallow, either in the form of money-capital, of a supply of raw ma- terials, of finished but still unsold commodity-capital, or of outstanding bills not yet due; hence the capital active in the production and appropriation of surplus-value is always short by this amount, and the production and appropriation of sur- plus-value is curtailed to that extent. The shorter the period of turn-over, the smaller is the fallow portion of capital as compared Avith the whole, and the larger will be the appro- priated surplus-value, other conditions remaining the same.
It has been shown explicitly in the second volume to what extent the mass of the produced surplus-value is augmented by the reduction of the period of turn-over, or of one of its two sections, the time of production and the time of circula- tion. But it is evident that any such reduction increases the rate of profit, since this rate expresses but the mass of surplus- value produced in proportion to the total capital employed in production. Whatever has been said in the second part of the second volume in regard to surplus-value, applies just as well to profit and the rate of profit, and requires no repetition at this place. We shall touch only upon a few of the principal points.
A reduction of the time of production is mainly due to an increase in the productivity of labor, a thing commonly called the progress of industry. If this does not require at once a 86 Capitalist Production.
considerable extra-outlay of capital for expensive machin- ery, etc., and thus a reduction of the rate of profit, which is calculated on the total capital, this rate must rise. And this is decidedly the case with many of the latest improvements in metallurgy and chemical industry. The recently discov- ered methods of making iron and steel, such as the processes of Bessemer, Siemens, Gilchrist-Thomas, etc., shorten for- merly tedious processes to a minimum with relatively small expense. The making of alizarin, a red coloring substance extracted from coal-tar, produces in a few weeks, by the help of already existing installations for the manufacture of coal- tar colors, the same results which formerly required years. It took at least one year to mature the plants from which this coloring matter was formerly extracted, and it was customary to let them grow a few years before the roots were used for the purpose of making color.
The time of circulation is reduced principally by improved means of communication. In this respect the last fifty years have brought about a revolution, which can be compared only with the industrial revolution of the last half of the eighteenth century. On land the macademized road has been displaced by the railroad, on sea the slow and irregular sailing vessel by the rapid and regular steamboat line, and the entire globe has been circled by telegraph wires. The Suez Canal has fully opened Eastern Asia and Australia for steamer traffic. The time of circulation of a shipment of commodities to East- ern Asia was at least twelve months as late as 1847, and it has now been reduced to almost as many weeks. The two large centers of commercial crises, 1825-1857, America and India, have been brought from 70 to 90 per cent, nearer to Europe by this revolution of the means of communication, and have thereby lost a good deal of their explosive nature. The period of turn-over of the world's commerce has been re- duced to the same extent, and the productive capacity of the capital engaged in it has been doubled or trebled. It goes without sajnng that this has not been without effect on the rate of profit.
In order to view the effect of the turn-over of the total Effect of Turn-Over on Rate of Profit. 87 capital on the rate of profit in its purest form, it is necessary to assume all other conditions of two compared capitals as equal. Aside from the rate of surplus-value and the working day it is especially the percentages of composition which we assume to be the same. Now let us select a capital A com- posed of 80 c -F 20 V = 100 C. Let this have a rate of sur- plus-value of 100%, and let it be turned over twice per year.
The annual product is then 160 c -f 40 v + 40 s. But for the purpose of ascertaining the rate of profit we do not cal- culate the 40 s on the turned-over capital-value of 200. We calculate it on the advanced capital of 100, and we obtain thus a rate of profit of 40%.
Now let us compare this with a capital B composed of 160 c + 40 V = 200 C, which has the same rate of surplus- value, 100%, but which is turned over only once a year.
The annual product of this capital is the same as that of A, namely 160 c + 40 v -|- 40 s. But the 40 s in this case are to be calculated on an advance of capital amounting to 200, so that the rate of profit of B is only 20%, or one-half that of A.