Abstract
I thank Angelo Reati for a very kind and generous review of my book (Sinha 2010). Reati (2012), however, makes allusions to a couple of apparent mistakes in my book. Since these alleged mistakes are of a logical nature, I may be allowed to clarify the matter as they do not pertain to matters of differences in opinion or interpretations.
(1). Reati claims that:
This conclusion is not undermined by Sraffa’s reduction of prices to dated quantities of labor. As we know, such an exercise ends up with a series of weighted quantities of labor of several epochs, plus a “commodity residue,” residue that can be made as small as we wish provided we go sufficiently back in time. This means that, to understand the nature of the present economic system, we have to pursue our exercise sufficiently back to when the “commodity residue” becomes the products of nature that could be exploited directly by human activity. We would obtain, in such a case, an exact price-theory of value − since labor emerges as the sole genuine factor of production − while, if we stop our exercise at less distant epochs, our theory of value is only approximate.
What Reati forgets is that when commodity residue becomes negligible then the labor content going along with the residual commodity also becomes negligible, and if and when commodity residue becomes zero then the labor content must also become zero along with it. “Dated labor” does not change the technique of production. All the “previous dates,” no matter how backward in time we take our “dated labor” calculation to, use the same technique and if commodities are needed as means of production today then it logically follows that they must be needed for production at any backward “date” in the calculation. Sraffa’s “dated labor” calculation has nothing to do with the so-called “real” history and the metaphysical idea that the first historical man or woman must have produced something with his or her bare hands. The title of Sraffa’s book is designed to highlight this circular aspect of production and its consequences in a capitalist mode of production: there is no way out of the world of commodities, since commodities are produced by means of commodities. Once we understand this simple fact then we quickly realize that the measure of capital is not independent of the rate of profits (which is the message of the “dated labor” calculation as well as the “capital controversy”) and therefore it cannot be reduced to simple labor-values.
(2) Reati claims:
Now, the alert reader will notice immediately that such a conclusion is based on a serious misunderstanding of a technical aspect of the standard system. In fact, the equality of R* and R is always verified for the simple reason that the two maximum rates of profit derive from the input matrix of the system which, when there are only basic commodities, is exactly the same for the real and the standard system. More precisely, R* and R are a function of the maximum eigenvalue of such a matrix. The rates of profit of the different industries are only loosely related with R, in the sense that R represent the upper limit of the profit rates in question; within this boundary, the rates of profit could very well differ from one industry to another. Thus, contrary to Sinha’s efforts to show the opposite (323-330), Sraffa’s assumption of a uniform rate of profit brings to the fore the question of whether or not he was implicitly assuming competition and the gravitation process.
As a matter of fact, neither Sraffa nor I use matrix algebra to make our point since the point is simple and does not need any technicality of matrix algebra. In any case, it appears that Reati has completely missed my point. R and R* are respectively the average (or global) rates of profit of the real and the standard systems in my examples when wages are equal to zero. So, on the face of it, the argument that “The rates of profit of the different industries are only loosely related with R, in the sense that R represent [sic] the upper limit of the profit rates in question” makes no sense. Since R is the weighted average of the industrial rates of profits, it is clear that either all the industrial rates of profits must be equal to R or some industrial rates of profits must be above and some below the average R. If no industrial rates could be above R and they were not all equal to R either, then how could R be the average of the system? Since Reati grants me that R and R* must be equal then the same logic implies that it must be true for all the rescaled systems generated from the standard system. But what are the standard and its rescaled systems? They are systems of simultaneous equations made up of the exact same equations with the relative weights of individual equations (or industries) being different in different systems. Now, if all these systems have equal weighted average rate of profits, then it logically follows that they must all have an equal industrial rates of profits; otherwise unequal rates of industrial profits would ensure that all the averages are not equal because of the differential relative weights of industries in different systems. Once this is understood for the case of zero wages, it is a simple step to show that the same property must follow even when wages are positive as long as they are given or measured in terms of the standard commodity (for my latest statement on the proof of this proposition, see Sinha 2012).