For example, 1,000 kilos of cotton, with a unit value of £1 per kilo, is processed by 10 workers, in 10 hours, thereby adding £1000 in new value, divided £500 wages, £500 profit. The 1,000 kilos of yarn produced has a value of £1,000 cotton plus £1,000 new value produced by labour = £2,000. The price per kilo is then £2, the rate of profit is 33.3%.
If productivity doubles, the same amount of labour processes twice as much cotton. Suppose rising productivity also causes the value of cotton to fall to £0.75 per kilo. Now, 2000 kilos are processed with a total value of £1,500. The new value created by labour, remains £1,000, divided still £500 wages, and £500 profit. The 2,000 kilos of yarn now has a value of £1,500 (cotton) + £1,000 new value added by labour = £2,500, or £1.25 per kilo.
The material now constitutes 60% of this value, whereas previously it represented only 50%. The new value created by labour now falls to 40%, whereas previously it was 50%, and now wages and profit comprise only 20% each. The rate of profit, falls from 33.3% to 25%.
However, this rate of profit, or profit margin, is quite different to the annual rate of profit, which is the basis of the average or general rate of profit. The annual rate of profit is based not on the laid-out capital (c + v), which is also the cost of production, but on the advanced capital for one turnover period, or s/C.
For the same reason, that the mass of material processed rises, relative to the labour required to process it, i.e. a rise in social productivity, so the capital advanced to produce a given amount of surplus value, in a specific period of time, will fall, and similarly, the amount of surplus value produced in a year will rise relative to the capital advanced, in a turnover period.
So, for example, taking the above situation, if the industry originally turns over its capital once, during the year its annual rate of profit will be the same as the rate of profit. But, with the doubling of productivity, it produces the required amount of output in half the time. The required amount of output here, is that amount of output, which is determined as being required during a working period, prior to it being sent to market. Here 1000 kilos of yarn represented this quantity. Previously, it took a year before this quantity could be sent to market; now it takes only six months.
To produce this 1,000 kilos of yarn, it must buy 1,000 kilos of cotton, at a cost of £750. To process this yarn, it requires 10 workers, providing 5 hours of labour, or 5 workers providing 10 hours of labour, and so, with wages equal to £250, the situation is:-
c 750 + v 250 + s 250 = £1250.
But, now this output is sold, and the capital advanced, is thereby reproduced, and available to be advanced once more. No additional capital need be advanced, and so effectively, the surplus value produced in the following period, is produced at no capital cost.
Although the capital laid out for the year is then £2,000, the capital advanced during the year is only £750 for cotton, and £250 for wages = £1,000. A further £250 of profit is made in the second half of the year, giving a total profit for the year of £500, but only £1,000 has been advanced as capital to produce it, which gives an annual rate of profit of 50%, which is double the rate of profit, and 50% higher than the original rate of profit, prior to the rise in productivity.
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