As Marx sets out, Proudhon's method of analysis is absurd, comparing percentages of different things, i.e. the percentage difference in speed with the percentage difference of profit, but he also fails to calculate consistently when comparing the position for the collective “person-society” and the individual, as well as failing to divide by 100 in calculating the percentages.
“We may even overlook the fact that M. Proudhon expresses a quadrupled speed as 400 per cent of the original speed; but that he should bring into relation the percentage of speed and the percentage of profit and establish a proportion between two relations which, although measured separately by percentages, are nevertheless incommensurate with each other, is to establish a proportion between the percentages without reference to denominations.” (p 87)
Its always possible to compare percentages, so as to say 400% is 40 times bigger than 10%, in the same way that 400 is 40 times bigger than 10, but what does it mean to say that the speed of a train is 4 times faster than that of road transport, and then compare this to a percentage of profit? That is like saying a cabbage is four times bigger than an apple, and then relating that to the sweetness of one to the other. As Marx notes, Proudhon arrives at this odd comparison, because he has a vague notion about labour being value, and measured in time, so that he then sees the reduction in time, resulting from the faster speed of the train meaning a reduction in value/labour. He says, indeed,
“Since in society time is value itself, the railway would, prices being equal, present an advantage of 400 per cent over road-transport. Yet this enormous advantage, very real for society, is far from being realised in the same proportion for the carrier, who, while bestowing upon society an extra value of 400 per cent, does not for his own part draw 10 per cent.” (p 86)
From this, Proudhon draws the conclusion that a profit of 10% is worth 40 times less than a quadrupled speed.
“This error arises from his recollecting vaguely that there is a connection between labour value and labour time, and he hastens to identify labour time with transport time; that is, he identifies the few firemen, drivers and others, whose labour time is actually transport time, with the whole of society.” (p 87)
Proudhon then fails to divide by 100, in his calculation, and treats the 400% as though it were an amount of 400. So, he turns speed into capital, and difference in speed into profit, and concludes that,
“A social profit equal to 400 represents for the individual, in a society of only a million men, four ten-thousandths.” (p 88)
But, even if it were rational to equate percentage differences in speed with differences in profit, which it isn't, Proudhon's calculation is still hopelessly wrong, because he has turned 400% into simply an amount of 400, and he then compounds it by dividing by 1 million to arrive at the profit, for each individual of just four ten-thousandths. But, if the labour-time of every one in the “person-society” was reduced by 400%, rather than just the labour-time of the handful of rail workers, Proudhon would have arrived at a wholly different conclusion.
“and a profit of 400 per cent represents for the individual 400 per cent, neither more nor less. Whatever be the capital, the dividends will always be in the ratio of 400 per cent.” (p 88)
To make the 10% profit of road transport, rail, Proudhon concludes, needs to charge 25 centimes, rather than 18 centimes, but can't do so, because it would lose its customers, and so, it suffers a loss of 35%. Proudhon does not seem to consider the fact that these customers might be prepared to pay 25 rather than 18 centimes, precisely because of getting their goods to market four times faster. But, even allowing for that, he, then, takes this 35% loss, and performs the same calculation in reverse to that above, again confusing percentages with amounts. He says,
“A loss of 33 per cent for the consumer would suppose a social deficit of 33 million.” (p 88)
And, so Marx responds,
“A loss of 33 per cent for the consumer remains a loss of 33 per cent for a million consumers. How then can M. Proudhon say pertinently that the social deficit in the case of a 33 per cent loss amounts to 33 million, when he knows neither the social capital nor even the capital of a single one of the persons concerned? Thus it was not enough for M. Proudhon to have confused capital with percentage; he surpasses himself by identifying the capital sunk in an enterprise with the number of interested parties.” (p 88)
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