3. The Degree of Exploitation of Labour-power
Let us take a capital of, say, £250. The same is divided into two parts, a sum of money which is expended on the purchase of means of production, the constant capital c, which we will put at £205, and another sum of money which serves for the purchase of the necessary labour-power, the variable capital v, which is equal to £45. The constant capital itself is again divided into two parts: raw materials, etc., whose value reappears entirely in the product, and tools, etc., which only impart a portion of their value to the product in every production process. In the following investigation we shall leave this distinction out of account, as its observance would merely complicate the problem without altering anything in the result. For the sake of simplicity, we shall therefore assume here that the value of the whole of the capital employed reappear in the product.
The capitalist has bought means of production and labour-power, and employs them. At the end of the production process, the value of the capital advanced is augmented by the surplus-value s, which amounts to £45. Thus he now owns c + v + s = £205 + £45 + £45 = £295. Of this £205 are transferred value, and £45 + £45 newly-created value.
It is clear that the magnitude of value of the constant capital exercises no influence upon the magnitude of the surplus-value produced. Without means of production, nothing can, of course, be produced, and the longer the time that producing is to be carried on the more means of production are necessary. The production of a certain magnitude of surplus-value is therefore conditioned by the employment of a certain mass of the means of production, which depends upon the technical character of the labour-process. But the extent of the value of this mass has no influence upon the magnitude of the surplus-value.
If I employ 300 workers, and the daily value of each amounts to 3s., whilst the value which each creates in a day amounts to 6s.; these workers would create in a day a value of £90, of which £45 would be surplus-value, irrespective of whether the means of production which they utilised had a value of £100 or £200 or £400. The creation of value and the alteration of value are unaffected by the magnitude of value of the constant capital advanced. So far, therefore, as it is a question of merely regarding these two processes, we may leave constant capital out of account, and equate it with nil.
Consequently, we are here concerned only with the variable part, v, of the capital advanced; as to the value of the product only with the value newly created by labour, which is equal to the value of the variable capital employed, plus the surplus-value, v + s. The relation of the surplus-value to the variable capital advanced is in our case - £45 : £45 = 100 per cent.
This relative increase in the value of the variable capital or the relative magnitude of the surplus-value, Marx calls the rate of surplus-value. It should not be confused with the rate of profit, although this is often done. Profit is derived from, but is not identical with, surplus-value.
In order to produce during the working day a value equal to the value of his labour-power, equal to v, the worker is obliged to work a certain time; we have previously assumed this to be 6 hours. This labour-time is necessary for the maintenance of the worker. Marx calls it the necessary labour-time. The portion of the working-day in which the worker works beyond the limits of the necessary labour-time and creates, not value to replace his labour-power, but surplus-value for the capitalist, is called by Marx surplus labour-time, and the labour expended during that time, surplus labour. Surplus labour stands to necessary labour in the same relation as surplus-value to variable capital; we may express the rate of surplus-value in this wise
s or surplus labour / v necessary labour
Surplus-labour is represented by a quantity of products, which Marx calls surplus-produce. Its relation to variable capital must therefore be expressed in the relation of certain fractions of the product to each other. In contemplating this relation, which concerns not the newly-created value, but the finished product, we cannot, however, as before, leave out of account constant capital, which forma a part of the value of the commodity.
Let us assume that in a working day of 12 hours a worker produces 20lbs. of yarn of a value of 30s. The value of the cotton spun amounts to 20s. (20lbs. at 1s.). The wear and tear of the spindle, etc., is 4s., the value of the labour-power 3s. The rate of surplus-value is 100 per cent. Thus we have yarn-value 30s. = 24s. (c) + 3s. (v) + 3s. (s); this yarn-value exists in 20lbs. of yarn, and consequently the constant capital is contained in 16 lbs., the variable capital in 2lbs., and the surplus-value in 2lbs. of yarn.
The 20lbs. of yarn are produced in 12 hours, and therefore 12/3lbs. of yarn in each hour. The 16lbs. in which the value of the constant capital is embodied are produced in 9 hours 30 minutes; the 2lbs. in which the value of the variable capital is contained, in 1 hour 12 minutes, and likewise the 2 lbs. in which the surplus-value is embodied.
By calculating in this fashion, it would seem as if the surplus-value were not created in 8 hours, as supposed, but in 1 hour 12 minutes. And so reckon all the manufacturers, who prove to a nicety that their profit is created in the last working hours, and that if the labour-time should be shortened by only one hour, all profit would be made impossible, and industry would be ruined. In the year 1836, this mode of calculation was urged against any legal restriction of labour-time by the English manufacturers and their learned and unlearned advocates under the leadership of Senior. The same argument was revived in Germany and Austria against the normal working-day, although the actual experience of England had already demonstrated its fallacy. The working-day was legally curtailed, in various branches of labour in England without ruining industry, or even appreciably injuring the profits of the factory lords.
The whole argument is based on confusing use-value with value. The use-value of 2lbs. of yarn is created in the last hour, but not its value. The 2lbs. of yarn have not been spun out of the empty air. In the 2lbs. of yarn is contained not merely the spinner's labour of 1 hour 12 minutes, but also the value of 2lbs. of raw cotton, and according to our assumption (1 lb. of cotton = 1s., 1s = 2 working hours), 4 working hours are incorporated in 2lbs. of cotton. Moreover, as much value has been transferred from the spindle, etc., to the 2lbs. of yarn as would be created in 48 minutes of socially-necessary labour time. Therefore, 6 working hours have in reality been necessary for the production of the 2 lbs. of yarn that have been manufactured during 1 hour 12 minutes. If the worker in our example really created during 1 hour and 12 minutes the whole of the surplus-value, he ought to be able during a 12-hour working-day to create a value equivalent to 60 working hours! And nonsense of this sort was believed by the manufacturers.
As the argument still carries some weight in certain circles, yet another of its aspects may be elucidated. Let us calculate how high the rate of surplus-value would work out with a shortening of the working-day from 12 to 11 hours, under the conditions already assumed. 
We should then no longer have 24s. constant capital, but merely 22s., as less of its constituents would be utilised (181/3 lbs. cotton = 18s. 4d. wear and tear of spindle, etc., only 3s. 8d.), to which must be added a variable capital of 3s. (we assume that the wages for 11 hours remain the same as formerly for 12 hours) and a surplus-value of 2s. 6d. The rate of surplus-value would therefore amount to 82.33 per cent., instead of 100 per cent.
We have a total product of 181/3 lbs. yarn with a value of 27s. 6d.; the constant capital is embodied in 143lbs.; the variable in 2 lbs.; the surplus-value in 11 lbs. The 141 lbs. are produced in 8 hours 48 minutes; the 2 lbs. yarn in 1 hour 12 minutes; and the mass of yarn which contains the surplus-value in 1 hour. The time for the production of the surplus-produce which contains the surplus-value is therefore diminished, not by one hour, but only by 12 minutes, through the shortening of the labour-time by one hour.
The calculation of the manufacturer is based on the astonishing assumption that whilst one-twelfth less product is produced in 11 hours, as much of the means of production (raw material, etc.) is utilised as during 12 hours.
 In this connection we assume that a shortening of the labour-time from 12 to 11 hours is accomplished by a diminution of 1/12th in the output. In reality this is not necessarily the case; as a rule the shortening of working-time is accompanied by an increase in the strength, skill, endurance, care and intelligence, in short the labour-capacity of the worker, which sometimes goes so far that the worker produces in the shorter working-time more than formerly in the longer working-time.