To illustrate Proudhon's confusion, here, Marx reworks the example, and uses an actual amount of capital. If there are 1 million people, each with F1 of capital, so that there is a total social capital of F1 million, then a social profit of 400% is equal to F4 million, and each individual would obtain a profit of F4.
“Likewise a loss of 33 per cent for each of the participants represents a social deficit of 330,000 francs and not of 33 million (100:33 = 1,000,000:330,000).” (p 88)
So, Marx says, if we compared this F330,000 loss for society, with the F4 million profit for society, it would, in fact, leave a F3,670,000 net profit for society!
“This accurate calculation proves precisely the contrary of what M. Proudhon wanted to prove: namely, that the profits and losses of society are not in inverse ratio to the profits and losses of individuals.” (p 88)
Having corrected the basic mathematical errors, Marx then turns to the legitimacy of comparing speed and profits/capital.
“Let us suppose that a transport four times as rapid costs four times as much; this transport would not yield less profit than cartage, which is four times slower and costs a quarter the amount. Thus, if cartage takes 18 centimes, rail transport could take 72 centimes. This would be, according to “the rigour of mathematics,” the consequence of M. Proudhon's suppositions – always minus his mistakes in calculation. But here he is all of a sudden telling us that if, instead of 72 centimes, rail transport takes only 25, it would instantly lose all its consignments.” (p 89)
To put this in another context, take the spinning of yarn. A spinning machine might cost £10, as against a spinning wheel costing £1, but, if the spinning machine is ten times faster, then, relatively, its cost per kilo of yarn spun is the same as that of the spinning wheel. In fact, as Marx demonstrates, no such inventions are introduced unless their cost is such that they are cheaper, So, for example, the spinning machine might cost £5, five times more than the spinning wheel, but, because it is ten times more productive, its relative cost is half that of the wheel.
“Let us return to the fiction of the person-society, a fiction which has no other aim than that of proving this simple truth – that a new invention which enables a given amount of labour to produce a greater number of commodities, lowers the marketable value of the product. Society, then, makes a profit, not by obtaining more exchange values, but by obtaining more commodities for the same value.” (p 89)
In other words, the fundamental role of The Law of Value, in driving forward increased social productivity, by technological innovation. As Marx sets out, in Capital I, for the individual inventor or applicant of such technology, they obtain a first-mover advantage, and higher rate of profit, due to relative surplus value. If 10 firms employ 100 workers each, and each firm produces 10,000 units of a given commodity, per day, with a market value of £100, or £0.01 per unit, and one of these firms introduces a new machine, which enables its workers to produce 20,000 units, the individual value of these units falls to £0.005, but it continues to sell them at the market value of £0.01 per unit, so that it obtains £200 for its output (material costs and wear and tear are not included, here)
If wages are £50, then the average rate of surplus value is 100%, but, in this one firm, the rate of surplus value is 150:50 = 300%. It is as though its workers labour is complex, compared to the labour in the other firms, and produces, for it, a kind of relative surplus value. Its what appears to orthodox economics as additional value created by the machine. In practice, the firm would sell its output at a slightly lower price than the market value (unless demand was such as to absorb the additional 10,000 units at the existing market price), so as to sell all its output, and this also acts to expand the market.
The supply of the commodity increases as the other firms seek to introduce the same machine to compete. The result is that the market value of the commodity is itself driven down to this individual value, at which point, the relative surplus value enjoyed disappears. The market value of all units drops to £0.005, and output of 20,000 units produces £100, with wages of £50, so that the rate of surplus value is once again 100%.
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