In debates about Marx’ value theory, we tend to get bogged down in the question of whether Marx’ formulation for the transformation of values into production prices was consistent, incorrect, or redundant, with the so-called “transformation problem” being the major tool of attack from Bohm Bawerk to Samuelson to many bourgeois economists today. I’m not going to talk about the transformation problem in great detail, probably the simplest introduction can be found here, which I think you should read before approaching this piece. I will however discuss the issue of profit rate equalization and the book Laws of Chaos by Emmanuel Farjoun and Moshe Machover, which is central to the transformation problem.
Do Profit Rates Equalise?
While it would be satisfying, throwing up a graph of profit rates and proclaiming that they don’t equalize is not exactly the best means by which we can understand the issue. Despite this, it is fair to look at data that already exists and begin to question the assumptions made by deterministic economic models.
Why Don’t Profit Rates Equalise?
For us to answer this question, we need to bring up the book Laws of Chaos. During the debates over Marx’s value theory and the controversy surrounding the “transformation problem”, Emmanuel Farjoun and Moshe Machover began to question the fundamental assumptions made by Marx and the classical political economists which led to such controversy ever occurring.
In 1983 they published the book Laws of Chaos in which they dissolve the assumption of a uniform rate of profit and thus the existence of a transformation problem by question the deterministic models of economics at the time. They argued, instead, that while production may be organized and deterministic, the sphere of exchange is chaotic. They draw from this the hypothesis that the sphere of exchange, profit, price, wages .etc are similar to molecules in a gas, in which their interactions are random and stochastic. They draw from this that like measuring the various qualities of molecules in a gas, one must use statistical methods in order to successfully analyze the nature of the capitalist economy. With this hypothesis, a uniform rate of profit cannot exist since the rate of profit, too must act as a random variable.
We discuss, under certain broad assumptions, the general form of the probability distribution function of the rate of profit. In fact, theoretical and empirical evidence suggests that the rate of profit has a so-called gamma distribution. We draw some interesting consequences from this conjecture.
Farjoun and Machover go on to justify why there would not exist a general rate of profit beyond declaring the rate of profit to be a random variable. They do this by positing a thought experiment:
The first thought experiment is concerned with a pendulum. Suppose that the pendulum is pinned down, by an external constraint, to its vertical position. Then imagine that the constraint is removed and the pendulum is left to its own devices, free from the intervention of external forces. What will happen? Clearly, the pendulum will persist at rest in its vertical position. The persistence of this state is guaranteed by its being a state of equilibrium.
Now consider an analogous thought experiment with a perfectly competitive capitalist economy. Suppose that, due to the intervention of some all-powerful planning authority, rates of profit are forced to be absolutely uniform throughout the economy for a couple of years; suppose also that other conditions which are traditionally thought to characterize a state of equilibrium are enforced. Then imagine that the external constraint is removed, and the economy is left to its own devices, shielded from external intervention. Perfect competition will then resume its unfettered operation. Will rates of profit then remain uniform for any length of time, or will the uniformity be rapidly scrambled by competition itself? Clearly, the latter; but then it follows that the initially enforced state could not possibly have been a state of equilibrium!
To expect competition to preserve an initial parity in rates of profit is as unreasonable as expecting all horses in a race to finish together just because they started together.
If the very competition and anarchy in production forces profit away from ever being in a state of equilibrium, the fundamental assumption that competition forces the economy towards an equilibrium cannot be supported both logically or mathematically.
Farjoun and Machover later go on to argue that the forces of competition on the grounds of profit are not the only things that drive capital into various sectors.
For one thing, even if rates of profit were to start from an initial uniform level, this would not prevent the flow of new investment capital from one branch of production to another. This flow is motivated not only by past differences in rates of profit in different branches, but at least as much by conjectures about future demand for various products.
For example, firms in the coffin-making business may decide to invest their profits in another branch, say in furniture-making, rather than expand the manufacture of coffins, not because that other branch is at present more profitable, but because they do not anticipate a growing demand for coffins.
[Another] example, a large motorcar manufacturing firm, wishing to maximize its profits in the long run, may actually price its products down in order to encourage demand, or in order to drive its competitors into bankruptcy. Such a price war may, in the short term, reduce rates of profit in this branch of production well below the general average. Nor can technical innovations be left out of account; after all, their introduction is motivated by competition. But such innovations, taking place at an uneven and uncoordinated pace, would clearly tend to scramble any putative uniformity in the rate of profit. The general point to be grasped is the following: competition, by its very essence, is a disorderly process-and the freer it is, the more disorderly. Because of this, it would tend to destroy rather than preserve a uniformity in the rate of profit if such uniformity were ever imposed on the system
What implications does this have for the transformation problem? They lay it here simply:
In other words, the generally rejected model of the first volume of Capital, happens to point to the same results, concerning the specific price of non-labour commodities,’ for which we have argued in chapter V. So, from the point of view of our own theory, the model leads, in this particular but important case, to a broadly correct conclusion.
Thus, even if the transformation problem could be solved mathematically, the resulting model would not only rest on the fallacious assumption of the uniformity of the rate of profit, but would actually be inferior to the original unmodified model in respect of prices.
While Marx may have been operating on a level of simplicity and abstraction, deterministic economic models should be seen with great skepticism. If we accept the idea that capitalism is anarchic and chaotic, we thus cannot analyze it as if it were orderly. As Farjoun and Machover point out in their book, the use of statistical mechanics are both more reflective of the reality of the capitalist economy as well as proving Marx’s value theory correct (They discuss this at length in the book). With this in mind, we can trash the debates over the transformation problem as a faulty assumption Marx had made when writing Capital Volume 3.