Groucho Marxism

The so-called Fundamental Marxian Theorem (FMT) was first proven by the Japanese economist Nubuo Okishio in 1963 and was developed further by the Japanese economist Michio Morishima in 1973 and 1974. The theorem asserts that, in Miroshima’s words, “the exploitation of labourers by capitalists is necessary and sufficient for the existence of a price-wage set yielding positive profits or, in other words, for the possibility of conserving the capitalist economy.” On the other hand, the ‘New Interpretation’ of Marx, put forward by the French economist Gérard Duménil 1980 and developed further by the American economist Duncan Foley in 1982, approaches Marxian value theory from another perspective, emphasizing the direct link between labour time and price.

More recently, the issue of Marxian value theory was raised again by the development of the so-called ‘Temporal Single-System Interpretation’, first put forward by the American economist Andrew Kliman in 1999. There appears to be some controversy around which interpretation is the ‘correct’ one. In this blog post I will investigate these different interpretations of Marx. I’ve already devoted two blog posts to the original formulation of the FMT so I won’t go over that again here (see those blog posts for more info). In contrast to the original formulation, both the New Interpretation and Temporal Single-System Interpreration aim to connect price and labour time directly through the concept of the ‘monetary expression of labour time’, or MELT.

Let (A,L) be a Leontief economy, where A ≥ 0 is the nxn commodity input matrix, and L ≥ 0 is the 1xn row vector of labour inputs. Then the MELT associated with the 1xn price vector p and nx1 commodity output vector q is defined by m = p(I-A)q/Lq, where I is the nxn identity matrix. Further, the value of labour power is defined by v = w/m = wLq/p(I-A)q. The total surplus value is then given by the equation S = Lq(1-v) = p(I-A-L)q/m = P/m, where P is the total profit. The FMT says that S > 0 if and only if P > 0, so a necessary condition for the FMT hold is that m > 0. From the definition of m, this is equivalent to p(I-A)q > 0, as Lq > 0. This is a different condition than was used in the original formulation of the FMT.

Under the Temporal Single-System Interpretation, the value of labour power at the next time step, v’, is determined by the 1xn price vector at the previous time step, p, by v’ = pA+L; and the 1xn price vector at the next time step, p’, is given by p’ = pA+L+g, where g a 1xn vector with the property that gq = 0, where q is the nx1 commodity output vector. The real profit associated with the 1xn price vector p is defined by by P = p’q/(1+i)-C-V, where i is the rate of inflation, C = pAq is constant capital, and V = wLq is variable capital. Further, the rate of inflation is defined by i = (m’-m)/m, where m and m’ are the MELT at the current and next time step respectively. These are different to the definition of the MELT used in the New Interpretation and are instead defined recursively by m’ = mp’q/(pA+mL)q.

According to the Temporal Single-System Interpretation, the total value added by labour, Lq, must be equal to p’q/m’-C/m. Multiplying both quantities by m gives mLq = mp’q/m’-C, and substituting in the expression for i above and rearranging gives p’q/(1+i) = C+mLq. Substituting this into the formula for real profit above gives P = mLq-V, and therefore P = mS, where S = Lq(1-w/m) is surplus value. The possibility of a negative m disappears provided the initial value in the recursion m’ = mp’q/(pA+mL)q is positive, in which case the FMT holds automatically. However, this result is only possible due to the change in definition of the MELT, from a static definition to a recursive one. This redefinition is considered somewhat controversial and is not accepted by all Marxist economists.

Each of the three interpretations of Marxian value theory outlined in this blog posts starts with some assumption then shows that the FMT holds under this assumption. In the conventional interpretation, the FMT is proved under an assumption of ‘reproducibility’; in the New Interpretation, the FMT proved under the assumption of a positive MELT; and in the Temporal Single-System Interpretation, the FMT is proved under the assumption that the MELT satisfies a recursive equation. Which interpretation is considered to be ‘correct’ boils down to which assumption is most defensible. This is a question that can only be answered empirically, by looking at which assumption holds in actual capitalist economies.