ABSTRACT
The transformation problem has produced a considerable literature with an array of solutions proposed. As a preliminary to considering such solutions it is useful to consider the original problem as formulated by Marx in Chapter 9 of the third volume of Capital. The rate of surplus-value is determined by the ratio of surplus-value to variable capital. Surplus-value comprises the profit, interest and rent produced and variable capital is that portion of total capital used to pay the wages of labour. Denoting the rate of surplus-value e, surplus-value s, and variable capital v, it follows that:2
e= s v
(4.1)
According to Marx the rate of profit for a particular commodity (ri), is the ratio of surplus-value to the total capital outlay, i.e. constant plus variable capital. Where c is constant capital (comprising fixed and circulating elements), wemaywrite the value rate of profit for particular commodities as:
ri= si
ci+vi (4.2)
Expanding (4.2) gives:
ri= si/vi
( civi +1) (4.3)
It is an implication of the assumption of atomistic competition that, where capital movements are unrestricted, capital will flow from sectors yielding a low rate of profit to sectors yielding a high rate of profit. This suggests that there will be the formation of an average rate of profit, r, and in the sphere of circulation there would be a redistribution of surplus-value such that profit realised by capitalists would be equalised in the sense that it will correspond to their capital outlay. To understand why this is necessary, consider the following: if we define civi as the
organic composition of capital, and the rate of surplus-value is assumed to be equal between industries, equalisation of the rate of profit between two industries, I and II, implies that:
rI = eI
+1 =
+1 =rII (4.4)
However, (4.4) will not generally hold given an equal rate of surplus-value and divergent organic compositions of capital. Explaining
Table 4.1 Value categories in Marx’s Capital Industry c v e=s/v s c+v+s ri I 80 20 100% 20 120 20% II 70 30 100% 30 130 30% III 60 40 100% 40 140 40% IV 85 15 100% 15 115 15% V 95 5 100% 5 105 5%
Source Marx 1981: 255
the formation of an equal profit rate, consistent with an equal rate of surplus value, is thus not simple. Further, the connection between value and price warrants explanation.
