I'm reading on this blog that the rate of profit can decline while the rate of surplus value rises. Is this true? If so, how?
The rate of surplus value is the rate of surplus labour, that is to say that portion of the working day that is free to the capitalist after the workers have reproduced the value of their own labor power, which is the necessary labor. If the working day is 8 hours, but the workers reproduce the value of their wages in 4 hours, then the rate of surplus value is s/v or 100%. If the necessary labor time drops to 2 hours, then the rate of surplus value is, s/v again, 6/2, or 300%
So if the portion of the working day necessary for reproducing the wage is reduced, the proportion of surplus labour, manifested as surplus value rises as a fraction of the total working day.
The rate of profit is derived from the surplus value in relation to the total capital advanced by the capitalists-- that is the constant capital made up of the means of production, raw materials, etc. plus the wage. The relation is s/c+v. Using our previous example as a baseline, let's say the value of the constant capital was 12. The rate of profit in the base conditions was 4/(12 + 4)= 25%.
Now if we alter production so that v declines to 2, and in so doing c increases to 28, we have a new rate of profit that is 6/(28+2)= 20%.
Suppose the rate of surplus value is improved further so that the wage is reproduced in only 1 hour. Now we have a surplus value (surplus labor) of 7. And we have a rate of profit of 7/(28 +1) =24.13%
Why then would capitalists invest in C? First, more capital is regenerated; value has expanded from 12 + 4 +4= 20, to 28+2+6= 36, and capitalists have (almost) no choice. Value has the shelf-life of dead fish in the summer sun. It exists only in its reproduction, its accumulation.
In addition the application of greater quantities of C, and the expulsion of proportionately greater amounts of v, pushes greater masses of surplus value into the markets where the profits are then allocated, apportioned, according to the size of the capitals and their relative efficiencies.
The increased applications of technology, and science, to production are refracted through lower costs of production which allow the more efficient capitals, through the prices of production, or the "average price" or the price reflecting the socially necessary labor time, to claim the portions of surplus value thrown into the exchange process by all other capitals, thus offsetting, a bit, the reduced rate of profit of the more efficient capitals.