I am writing this because of a discussion I got into yesterday about regulating profit rates. I had heard the term but had never pursued the argument down to its source. I was given a Chapter in Shaikh’s recent book as the source, and sought it out to read. My conclusion was that the notion as presented suffers from ambiguity and methodological weaknesses. I attempt to explain these here.

In Chapter 7 of his book on Capitalism, Anwar Shaikh introduced the notion of a regulating capital. He does this initially by means of a table showing several different firms in an industry thus

Shaikh’s Table 7.1 Competition within an Industry Equalizes Prices and Disequalizes Profit Rates

Note what he is assuming here – that there is a single price prevailing for all firms in the industry, and that this will result in a dispersion of profit rates in the industry.

He comments on this that :

In the situation depicted in table 7.1 conventional analysis says that method D will not be adopted because it offers a lower profit rate than method C at the “going” price of 100. This conclusion follows from the neoclassical assumption of perfect competition, in which all firms are assumed to be price-takers. But in the theory of real competition, price-setting and price-cutting behavior are fundamental. A firm with lower unit costs can always drive out its competitors by cutting price to the point where (p.263) their profit rates are lower than its own.

And then goes on to show that by reducing prices, firm D can produce the following situation:

Shaikh’s table 7.2 Effects of Universally Adopted Price Cuts on Relative Profit Rates Under this circumstance firm D has driven down both its own rate of profit and the rate of profit of its competitors. Shaikh implies that this ability to force down prices in order to gain market share will in fact be pursued by a firm in position D. He regards firms in this position as the regulators of the industry and calls them regulating capitals: At any moment of time within any given industry, there are a set of capitals representing the best generally reproducible condition of production in that industry. I have called these the regulating conditions of production—the ones with the lowest reproducible (quality-adjusted) costs in the industry.. Reproducibility is important because new investment must be able to replicate the conditions of these particular capitals. The profit rates of these regulating capitals will be the focus of new investment. When these profit rates are higher than those of regulating capitals in other industries, new investment into the industry will accelerate, and when their profit rates are lower, new investment will decelerate. There are a set of problems with this concept already. The first is in the assumption that a single price will prevail in the industry, and that it is as a consequence of the single price that that there will be a dispersion of profit rates. That there is a dispersion of profit rates, represents a shift by Shaikh from what had been the orthodox position among a prior generation of Marxian economists who had assumed profit rate equalisation as the rule determining price formation. The work of Farjoun and Machover on the Laws of Chaos, produced a gradual realisation that profit rate equalisation was not realistic. But Shaikh’s formulation in Chapter 7 is considerably weaker than that of Farjoun and Machover who treated prices themselves as random variables. Shaikh retains the old classical formalism of determininistic rather than stochastic prices. One may ask whether, if one allows for stochastic prices, the dispersion of profit rates in the face of varying techniques will be greater or less than Shaikh supposes. The next is in the assumption that the regulating firm will chose to reduce prices even if this means lower profits on its own part. This may sometimes happen, but how often, and how representative is this of the general operation of the economy?

Finally there is the assumption that capital outside of the industry is free to move into the industry and adopt the techniques of the regulating firm, that is to say of the best producing firm in that industry. The best producing firm may be in that position due to its ownership of patents, designs and other techniques that are not accessible to other firms. So the regulating firm may be able to prevent others from reproducing the same conditions of production. The argument seems to rely on a greater willingness on the part of the regulating firm to issue bonds to finance expansion. This may occur, but it is not self evident that the shareholders in such a firm will be willing to ramp up the gearing ratio, with the risks that such a course of action has associated with it. Shaikh has modified the traditional price of production theory in Marxian and Sraffian economics to one in which it is regulating rates of profit that equalise rather than the old belief that mean rates of profit in different industries tended towards the mean for all industries. But if we look at what he means by equalisation of regulating capitals, even this is hedged around with provisos: Hence, even regulating rates will be different in any given year, year by year. It is not their equality, but rather their “crossings,” which need to be considered. A corollary is that average profit rates are generally not equalized across industries, He then illustrates what he means by a diagram So equalisation in this context is indistinguishable from a random walk! Farjoun and Machover, who Shaikh fails to mention in this chapter, had said that there would be a stable statistical distribution of profit rates. How is what Shaikh presents any different? The matter becomes even more dubious when we look at his empirical tests of his theory. He attempts to measure the rate of return on regulating capital by the formula in his equation 7.3

When you see how he actually calculates the incremental profit it amounts to looking at the change in the total profit in a sector this year compared to what would have been expected had the existing capital invested in the sector continued to earn the previous year’s rate of profit. He adds in various correction terms to deal with changes in price levels from year to year, but that is the essence of what he measures. He then produces a pair of diagrams that he claims lend support to his theory of equalisation of the rate of profit on regulating capitals.

The top diagram showing the average rates of profit in several industries shows, as predicted by Farjoun and Machover a wide dispersion of profit rates with no tendency to equalise, and with some industries consistently earning higher rates of return than others. The lower diagram, which shows his incremental profit rates again shows a dispersion. First note that he has chosen to use very different scales on the two diagrams which tends to make the dispersion of the incremental rate look lower than the dispersion of the average rate. If we draw them to the same scale we get:

The idea that the incremental rate is less dispersed than the average rate does not survive honest graphical presentation.

But this is no surprise since his definition of the incremental profit comes down to the first derivative of the actual mass of profit divided by level of investment. Both of these are subject to random noise. If a stationary signal is subject to random noise, its derivative will be a random variable with zero mean, that is to say it will fluctuate between positive and negative values with a long term average of zero. If the variable has an underlying positive growth trend – as profit usually has in a growing economy – then the mean around which the fluctuations occur will be positive.

Here is a an entirely random pair of total profit graphs formed by rising trends with added Gaussian noise. Below are the first derivatives of these random series. As you can see the derivative series cross over in the way that Shaikh’s regulating profit rates do.

His data that he adduces in support of his regulating profit rate theory is no more than could be expected from taking the derivatives of random series. His suggestion that the incremental rate of profit corresponds to his theoretical regulating rate of profit would only be plausible if the profit earned on the previously invested capital was stable. In that case, and with various further caveats, one might assume that the incremental profits were entirely down to the new investment. But we have no reason to think this is true. Profits vary randomly from year to year for a multitude of causes associated with the business cycle, world events, changes in wages etc. If you take the derivative of profits you are just capturing this random noise. That you get cross overs in these series is not evidence for the equalisation of regulating profit rates, it is just an expected property of random series.