Theories of Surplus Value, Part II, Chapter 15 - Part 19

Marx sets out a series of arguments and examples, here, that also form the basis of his explanation in Capital III of the transformation of exchange values, into prices of production, and of the effects of changes in wages on the rate of surplus value, rate of profit and price of production, in different sectors.

Marx starts from an assumption that the average industrial capital is comprised 80 c + 20 v, whilst the average agricultural capital is comprised 60 c + 40 v. The rate of surplus value is 50%, so the price of production of commodities is £110, and the rate of profit is then 10%. The value of agricultural output, however, is 60 c + 40 v + 20 s = £120, so that rent is £10, the difference between the price of production and the value of output. If the price of grain falls and wages fall by a quarter in industry, we have: 

c 80 + v 15 + s 15 = £110. 

as before, because the new value created by labour is unchanged at £30. However, instead of being divided £20 v + £10 s, it is now divided £15 v and £15 s, so the rate of surplus value has risen from 50% to 100%. Moreover, the rate of profit is now 15.79%. If there is £100 of capital, rather than £95 of capital, more c and v are employed, i.e. £84.21 c + £15.79 v, whilst the profit is £15.79, and the value of output is £115.79. 

Marx assumes that the agricultural capital is unchanged, but as set out earlier, this is not possible because the fall in grain prices was itself the result of a rise in agricultural efficiency, so that less c and v produced the previous quantity of output. Moreover, the fall in grain prices not only reduces industrial wages, but also agricultural wages, so that for £100 of capital in agriculture, more c and v can be employed, increasing output, and the value of output. Marx's assumption that the surplus agricultural profit falls, therefore, from £10 to £4.21, is false. 

The following examples illustrate the point.

C	V	S	Output Value	Output Quantity	Unit price	Price of Production	Rent
60.00	40.00	20.00	120.00	120	1.00	110.00	10.00
To reduce unit price to 0.75, assuming C remains constant, V+S must fall to 30. so
60.00	20.00	10.00	90.00	120	0.75	88.00	2.00
But, assuming 100 of capital is advanced in the same proportion
75.00	25.00	12.50	112.50	150	0.75	110.00	2.50
However, the fall in grain prices, also reduces agricultural wages by 25%, and raises rate of surplus value, and the industrial rate of profit rises to 15.79%, so
75.00	18.75	18.75	112.50	150	0.75	108.55	3.95
But this means that £100 of capital now employs more capital and labour, so
80.00	20.00	20.00	120.00	160	0.75	115.79	4.21
Now, assuming that the fall in the price of grain is a result of greater efficiency in both the use of capital and labour in agriculture, we might have c 50.That means V+S falls to 40.
50.00	26.66	13.33	90.00	120	0.75	84.33	5.67
Assuming 100 of capital is employed.
65.20	34.80	17.40	117.40	156.66	0.75	110.00	7.40
Taking into consideration the fall in wages by 25%, raises the rate of surplus value in agriculture
65.20	26.10	26.10	117.40	156.66	0.75	100.43	6.97
But this means that £100 of capital now employs more capital and labour, so
71.43	28.57	28.57	128.57	171.45	0.75	110.00	18.57
Finally, the rate of profit in industry has risen from 10% to 15.79%, with the consequent effect on the price of production of agricultural products and rent
71.43	28.57	28.57	128.57	171.45	0.75	115.79	12.78
On this basis, contrary to Marx's conclusion, the rent would rise from £10 to £12.78

Setting this correction of Marx to one side, and proceeding on the basis of his assumptions, we can agree that the overall rate of profit rises, and this means that, for a given amount of capital, a greater mass of constant and variable capital can be employed, resulting also in a greater value of output, though not a rise in the unit price of commodities, as the greater value of output is the consequence of a greater volume of production. 

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