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.
Country 1
c 80 + v 20 + s 460 = 560, s' = 2300%, r' = 460%
Country 2
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.
This does not invalidate Marx’s explication of the Law, per se. It only shows that this example, across economies, is wrong. It would only invalidate the explication of the law as such, if it could be shown that “the past is another country”, so that it could be shown that the labour employed at historical point t+1, stands as complex labour in relation to the labour employed at historical point t, as a result of the technological differences between the two periods. I don't think that can be done as a general rule, because the products of the past are not in general being compared, in the market, with the products of the present, except in the case of fixed capital. In that case, it is precisely this kind of comparison which means that the old products are devalued compared to the new via moral depreciation.
However, as stated previously, it quite clearly is the case that in particular industries, i.e. in relation to particular concrete labours, it is true that some modern labour stands in relation to past labour as complex labour stands to simple labour, and that is due to technological changes, for example, the computer programmer. But, this is more a factor of the spread of different types of industry, and different types of labour employed in these different historical periods.
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