Prices, Profit and the Sraffian “One-Commodity” Corn Model

by Jehu

A drop in the rate of profit is attended by a rise in the minimum capital required by an individual capitalist for the productive employment of labour; required both for its exploitation generally, and for making the consumed labour-time suffice as the labour-time necessary for the production of the commodities, so that it does not exceed the average social labour-time required for the production of the commodities. Concentration increases simultaneously, because beyond certain limits a large capital with a small rate of profit accumulates faster than a small capital with a large rate of profit. At a certain high point this increasing concentration in its turn causes a new fall in the rate of profit. (Karl Marx, Capital, Volume 3, Chapter 15)

The problem of prices and profit and of the relation between the two, which has bedeviled the simpleton economist for two hundred years, has reared its ugly head again in a series of posts amounting to a food fight among bourgeois silverqueensimpletons. The question raised in the exchanges, which I have previously covered here, involves the question of the source of profits in the capitalist mode of production and the interrelation between profit and prices.

At stake is far more than is apparent in the obscure criticism raised by heterodox economists against the mainstream neoclassical school that the neoclassical school wants to determine profit by the marginal productivity of capital, and then calculate the quantity of capital in part by asking how profitable it is to own the capital goods. If prices and profit are dependent on each other in this way it calls into question the historical trajectory of the mode of production itself.

In the 1960s, two economists, Joan Robinson and Piero Sraffa essentially finished off the neoclassical argument in a debate where the neoclassical economists had to essentially concede their assumptions were unworkable. Much of the argument developed by Sraffa rested on the argument of the 19th century political-economist Ricardo and his variant of labor theory. In particular, Sraffa employed Ricardo’s so-called corn model to demolish the neoclassical school.

Interestingly enough, in the wake of their defeat, the neoclassical school joined forces with the Sraffians to declare that henceforth all talk of labor values could be ignored. The basis of this argument is that, with Sraffa, employment of the one-commodity corn model, value had been rendered redundant for explaining prices and profits. Prices, profits and the interrelation between the two could be discussed purely in terms of physical quantities of inputs and outputs.

According to Avi Cohen, in his paper, “Prices, capital, and the one-commodity model in neoclassical and classical theories”:

“There are two major price conceptions in the history of economic thought: the neoclassical conception of price as a scarcity index and the classical conception of price as an index of the difficulty of production. Each conception is associated with robust results that hold without exception within the respective one-commodity models that are the subject of this paper: Samuelson’s surrogate production function and the neo-Ricardian corn model.”

According to Cohen, the Ricardo/Sraffa corn model provides the simplest and most powerful description of prices, profits and the relation between prices and profits because it states the problem in terms of physical units of inputs and outputs:

“The simplest conception of the classical problem (as well as an implicit illustration of prices of production) is in the one-commodity corn model which Sraffa claims provides the “rational foundation” for Ricardo’s Essay on profits. Seed corn and labour produce more corn. The quantity of corn output is determined exogenously by the levels of population and accumulation, and the real wage is an exogenously determined quantity of corn. Inputs and outputs are measured in the same physical unit (corn) and profits are determined on marginal land as a residual: the surplus of output over inputs necessary for production.

Within the corn model these inverse (rent-rate of profits and wage-rate of profits) distributional relationships are clear and independent of changes in relative prices because there are no relative prices to change.”

The Sraffian one-commodity corn model is limited, however, because it appears to breakdown immediately once an attempt is made to include less restrictive assumptions:

“These one-commodity models are heuristically important because in a wide range of more general models, capital-related exceptions arise for each price conception. […] Modern descendents of classical political economy, the neo-Ricardians, face exceptions to the inverse wage-rate of profits relation.”

A number of labor theorists have accepted the argument made by the Sraffians that, within the simplified assumptions of the corn model, value is indeed made redundant in explaining prices. They blame the unnecessarily restricted assumptions of the model for this result, but never investigate the validity of the model on its own terms. For instance, Andrew Kliman, in his 2007 book, Reclaiming Marx’s Capital, argues the one-commodity corn model may render value redundant in the calculation of prices and profits, but this is only because it substitutes physical quantities of corn for prices:

“For instance, it is easy to show redundancy in the corn-model case. Since there is only one industry in this case, value cannot be transferred across industries, so the price of corn equals its value. Now imagine again that the capitalist farmers invest ten bushels of corn at the start of the year, to use as seed and to pay wages, while twelve bushels are harvested at year’s end. If we value the investment and the output simultaneously—that is, stipulate that they have the same value per bushel—then the twelve bushels of output must be worth exactly 20% more than the ten bushels initially invested. Profit must thus be equal to 20% of the sum of value invested. But profit as a percentage of investment is precisely what is meant by the rate of profit. So the rate of profit must equal 20%.”

So here is my problem with this assertion by Cohen, Kliman and the Sraffians:

The criticism to be directed at the one-commodity corn model is not that it simplifies the capitalist mode of production in an unrealistic manner by assuming only physical quantities of a single commodity, but that even on this basis it runs into the very same problems posed by more sophisticated models — a problem which shows that even in its simplest form the mode of production has profound irresolvable contradictions.

Simply put, the so-called one-commodity corn model is not really a one-commodity model at all. While Cohen, the Sraffians and even labor theorists agree the one commodity model contains only one commodity, corn; in the model this corn is paid out to the worker in the form of wages. Which is to say. there are not one, but two commodities in the so-called one-commodity corn model. I believe labor theorists make a serious error here by accepting the assertion by the Sraffians that the corn model only has one commodity and that by limiting itself to a single commodity it makes value redundant in explaining prices.

Simply stated, it is impossible to have capitalist production without labor power.  Since Kliman knows he is dealing with a case of capitalist production, there is no reason for this error. The problem here is not that Sraffians have retreated to some sort of “physicalism”, but simply that they don’t even grasp their own model.

In the corn model, we are essentially dealing with silver, i.e., a commodity functioning in the role of money, not just silver queen corn.

The employment of corn as wages is a tip-off the Sraffians are terribly wrong in their assessment of their own model. The corn wage means corn is being employed within the model for the purchase/sale of another commodity, labor power. As a commodity, the corn is the means to purchase labor power; in turn, the value of the labor power is expressed in so many units of corn. This suggests that corn in this model is not simply another commodity, but a commodity money in whose material form is expressed the value of labor power.

Thus it is not true as Cohen asserts, following the Sraffians, that the corn model contains no true relative prices. In fact, in the corn model, as in Capital, the price of the commodity labor power is assumed to be its actual value. The value of labor power may in this case be expressed in the physical material of corn, but this is not at all extraordinary: in Capital the price of labor power is also expressed in the physical material of another commodity, gold.

By reducing the whole of the product of production to a single commodity, corn, in the corn model, Ricardo and Sraffa  did no more than is already accomplished in reality when, as a matter of course, the capitalists reduce the whole of their inputs and output of production to some quantity of dollars or euros.

Moreover, introducing heterogeneous inputs and output into this problem adds nothing to understanding a problem that is already present with the sale of labor power.  Replacing corn in the model, as the sole form of capital, with corn, plus tractors, fertilizer, irrigation infrastructure, etc. does not change the problem. We still have capital, on the one hand, and labor power, on the other. Even if we introduced heterogeneity into the wage good, so that in place of corn we now have potatoes, beef, shoes, trousers, a house, etc., in addition to corn, there is still no change.

The contradiction within capitalist prices arises out of the exchange of wages for labor power itself. The corn model, despite its simplicity, already contains all the contradictions inherent in price within the capitalist mode of production.

That problem can be stated this way: The price of labor power, wages, is determined both by the labor time required to produce the means of consumption and, at the same time, by the ability of labor power to produce surplus value. There are, in fact, two contradictory determinants of the value of labor power (and therefore all capitalistically produced commodities) already given even in the simplest model of capital. As one labor theorist wrote, that the price of a commodity is inherently overdetermined in the capitalist mode of production.

Bourgeois simpletons and labor theorists alike constantly try to expunge this “contradiction” in price determination, however, the contradiction is real and can only be resolved if socially necessary labor time falls to zero; or the rate of profit falls to zero.

The error in the analysis of the Ricardian corn model, however, is only part of a greater error: bourgeois simpletons and labor theorists alike have sought to prove there is no contradiction at the heart of capitalist prices. Somehow Bohm-Bawerk got it into his head that a contradiction in capitalist prices that was identified by classical political-economy implied a contradiction in the labor theory of value. It never occurred to him that the contradiction within capitalist prices according to labor theory is a real, not theoretical, contradiction.

The problem with the Marxist ‘critique’ of Sraffa and his followers like Steedman is that Marxists accept the argument of the Sraffians that we are dealing only with physical quantities of output. This is no more true than the idea we are only dealing with physical quantities when a day’s labor is purchased with ten gold coins. The value of labor power can be represented alternately as ten gold coins, as a money name of one hundred dollars or as a duration of four hours of socially necessary labor. We are simply saying each of these expressions are identical with the others.

If asked, Kliman would think nothing of representing the value of a day’s labor power by reference to a physical unit of the material of another commodity — a gold coin — so representing this value in the corm of so many bushels of corn does not in any way suggest physicalism.

Thus, contrary to the Sraffians and to Cohen, the contradiction inherent in capitalist prices is already given in the exchange of labor power for wages paid in corn. This contradiction is expressed in the fact that the value of labor power is determined by the socially necessary labor time required for production of the wage, but it is also determined by the fact the workers cannot sell her labor power unless the capitalist makes a profit. Unless both of these conditions are met, the labor power of the worker has no exchange value — which is to say, it cannot be sold no matter its price.