His mistake here is that he does not distinguish between concrete and abstract labour. There are indeed only 24 hours of any concrete labour in a day. For example, a joiner or a dentist can only work for 24 hours in a day, as an absolute maximum. But, value and surplus value is measured not in hours of concrete labour, but in hours of abstract labour. In terms of abstract labour hours, the labour of the dentist might equal twice that of the joiner. So even if the joiner's labour was equal to abstract labour, the dentist could work the equivalent not of 24, but of 48 hours of abstract labour in a day. So, the 24 hour day does not, in fact, act as an absolute limit for the amount of surplus value that can be extracted.
But, Marx makes a further and related error in discussing the rate of profit, in Capital III, Chapter 13. There he writes, discussing the situation comparing two different countries,
“Let a capital of 100 consist of 80 c + 20 v, and the latter = 20 labourers. Let the rate of surplus-value be 100%, i.e., the labourers work half the day for themselves and the other half for the capitalist. Now let the capital of 100 in a less developed country = 20 c + 80 v, and let the latter = 80 labourers. But these labourers require 2/3 of the day for themselves, and work only 1/3 for the capitalist. Everything else being equal, the labourers in the first case produce a value of 40, and in the second of 120. The first capital produces 80 c + 20 v+ 20 s= 120; rate of profit = 20%. The second capital, 20 c+ 80 v+ 40s= 140; rate of profit 40%. In the second case the rate of profit is, therefore, double the first, although the rate of surplus-value in the first = 100%, which is double that of the second, where it is only 50%. But then, a capital of the same magnitude appropriates the surplus-labour of only 20 labourers in the first case, and of 80 labourers in the second case.”
But, this is wrong, and at odds with what he says in Volume I. There, Marx sets out the way in which the introduction of machinery by particular firms, acts to make the labour of its workers the equivalent of complex labour in relation to that of the firm's competitors. In other words, say there are five firms in an industry, and they take on average 100 hours to produce 10,000 units of a commodity. Now, firm A introduces a machine, which means that its workers produce 20,000 units in 100 hours. The firm will continue to sell these units at the market value determined by the average for the industry. The consequence is that it is as if an hour of firm A's workers' labour produces twice as much value as an hour of labour by workers in all the other firms. Unlike actual complex labour, however, firm A's workers will only be paid the normal wage for the industry.
But, Marx points out in discussing international wages that this situation applies also to the different levels of productivity of different countries resulting from the different degrees of development of their productive forces. The consequence is, he says to create a modification of the Law of Value, so that in the same way as above, an hour of labour in one country produces more value than an hour of labour in some other country, where labour productivity is lower.
“In every country there is a certain average intensity of labour below which the labour for the production of a commodity requires more than the socially necessary time, and therefore does not reckon as labour of normal quality. Only a degree of intensity above the national average affects, in a given country, the measure of value by the mere duration of the working-time. This is not the case on the universal market, whose integral parts are the individual countries. The average intensity of labour changes from country to country; here it is greater, there less. These national averages form a scale, whose unit of measure is the average unit of universal labour. The more intense national labour, therefore, as compared with the less intense, produces in the same time more value, which expresses itself in more money.
But the law of value in its international application is yet more modified by the fact that on the world-market the more productive national labour reckons also as the more intense, so long as the more productive nation is not compelled by competition to lower the selling price of its commodities to the level of their value.
In proportion as capitalist production is developed in a country, in the same proportion do the national intensity and productivity of labour there rise above the international level. The different quantities of commodities of the same kind, produced in different countries in the same working-time, have, therefore, unequal international values, which are expressed in different prices, i.e., in sums of money varying according to international values.”
It is, in fact, as Marx points out there, the very fact that the more productive labour in one country acts as though it were complex labour, compared to the labour in the less productive country, that enables wages in the former to be higher than in the latter, and yet for the former to still be more competitive. The fact, that the labour is more productive in the former, does not mean, however, as Carey believed, that wages were proportionately higher or lower depending upon the level of productivity. Capitalists in the former country are able to pay higher wages, and provide a higher living standard for their workers, and yet still extract a larger volume of relative surplus value, precisely by not passing on the full benefit of the higher productivity to their workers. It was precisely on this basis that during much of the 20th. Century, Fordism acted to increase productivity, raise workers real wages, and yet still extract an every increasing amount of relative surplus-value.
If we proceed on the basis of what Marx says in Volume I, we arrive at a completely different conclusion to that he describes in Volume III.
He sets out that in the one case the capital is comprised 80 c + 20 v, and in the other 20 c + 80 v. In the former country a total of 40 hours of labour processes £80 of constant capital. In the latter, 120 hours of labour process just £20 of constant capital. On that basis 1 hour of labour in the first country processes 12 times as much constant capital as an hour of labour in the second. On a purely value basis then, labour in the first country is 12 times as productive as that in the latter. But, this underestimates the difference. As Marx repeatedly points out, as the technical composition of capital rises, the organic composition rises but not in the same proportion, because the constant capital becomes cheaper, it is used more efficiently, and fewer better machines replace a larger number of less efficient machines.
But, let us proceed on the basis that labour in the former country is just 12 times more productive than in the latter, and that, therefore, on the basis of what Marx sets out in Volume I, the value of an hour's labour in country 1 is equal to 12 hour's of labour in country 2. In that case what we would actually have is.
c 80 + v 20 + s 460 = 560, s' = 2300%, r' = 460%
c 20 + v 80 + s 40 = 140, s' = 50%, r' = 40%.
So, in other words, the workers in Country 1 undertake 40 hours of labour, but because the value of an hour's labour for country 1 is equal to 12 hour's of labour in country 2, this 40 hours creates a value equivalent to 480 hours of labour in Country 2.
If the workers in Country 1 were only paid the value of their labour-power they would be paid £20, which, as with the example Marx gives, of the firm that enjoys the advantage of being the first to introduce a machine, means that the capitalists in Country 1 would make an even greater rate of surplus value.
In fact, the consequence would likely be that workers in Country 1 would seek improvements in their real wages, which is why workers in these countries tend to have higher living standards.