Monday, February 8, 2016

Alexander Gray on the Two Contradictions in Marx’s Theory of Surplus Value in Volume 1 of Capital

From Alexander Gray’s book The Development of Economic Doctrine: An Introductory Survey (1956):
“… the Marxian explanation suffers from two inner inherent contradictions (or two aspects of the same contradiction) from which it never escaped, and on which it finally made shipwreck in the third volume. In the first place, if all profit springs from variable capital and none from machinery, then it is the height of folly ever to introduce machinery, and it is a poor explanation to suggest that the capitalist does not know what he is doing. Marx realizes the difficulties of this ‘contradiction which is immanent’ in the application of machinery, but his observations leave it barking for solution in the minds of all readers. On the Marxian theory, with every progress of capital to a higher proportion of constant capital, there will be a diminution of profits, since profits come solely from labour, which admittedly represents a continually smaller proportion of total capital. With every step forward which the capitalist makes, he thus more deeply cuts his own throat. Surplus value calls for, and can only arise from, the existence of vast masses of workers; the Marxian analysis shows an increasing army of unemployed, displaced by machinery which can yield no profit.

The other flaw is a variant of this, and is in a sense even more fatal. If profit springs only from the labour employed, and in no wise from the constant capital, then the rate of profit in different industries will vary according as the proportion of variable capital is high or low. When there is much variable capital (i.e., in more primitive and undeveloped industries) the rate of profit will be high; in industries which have had extensive resort to machinery, the rate of profit will be low. Marx admitted with praiseworthy frankness that the observed facts were in glaring contradiction with the law so ascertained:
‘This law clearly contradicts all experience based on appearance. Everyone knows that a cotton spinner, who, reckoning the percentage on the whole of his applied capital, employs much constant and little variable capital, does not, on account of this, pocket less profit or surplus value than a baker, who relatively sets in motion much variable and little constant capital. For the solution of this apparent contradiction, many intermediate terms are as yet wanted, as from the standpoint of elementary algebra many intermediate terms are wanted to understand that 0/0 may represent an actual magnitude.’ [Marx 1906: 335].
The subsequent history of this conundrum furnishes one of the few comedies of economic literature. The promised solution did not appear in Volume II, but references to it figure largely in the preface written by Engels, above all in the form of a challenge addressed to the followers of Rodbertus. For if, as was claimed, Marx had plagiarized Rodbertus, now (and that right early, before the publication of Volume III) was the time for those who had championed Rodbertus to vindicate his claims by producing the correct solution of the riddle. The odd thing is that many socialists and economists did in fact respond, and took part in the competition to the extent of speculating as to what the Marxian solution was to be. But indeed it ought to have been clear a priori that there could be no solution, since irreconcilables cannot be reconciled, nor can harmony be established between two contradictory propositions—unless by the simple expedient of dropping one of them overboard. Contemplating the ‘Russian campaign of disaster’ organized by Engels, Loria, an enthusiastic admirer of Marx, even suggests that the procrastinations of Marx in getting on with Volumes II and III were due to a realization of the impending ruination of his life's work: ‘Is there any reason for surprise at Marx's hesitation to publish this so-called defence; need we wonder that his hand trembled, that his spirit quailed, before the inexorable act of destruction?’

The solution offered to the undiscerning in the third volume in explanation of the existence of a uniform rate of profit is embedded in a good deal of arithmetical illustration. Briefly, it amounts to this. Employers are not to be viewed in isolation. A group of enterprises, with different proportions of variable and constant capital, should be replaced by an imaginary enterprise, comprising the total of all the capitals of the members of the group. As this process of averaging cannot be limited, it means that all employers are to be regarded as one group, in which the surplus value gained by all is distributed among all. The possibility of a uniform rate of profit thus emerges; but it is on condition that some things sell above and some below their value. This uniform rate of profit is arrived at by competition, and capital everywhere looks for the average profit. Thus, there emerges a difference between value and price; and henceforth it will only be on rare occasions, indeed only by accident, that the surplus value really produced in any given branch of industry will correspond to the profit contained in the selling price of the commodity—the accidental case arising where the composition of the capital (as between constant and variable) is exactly the average of the sum total of all capitals. Elsewhere the products of industries, with a proportion of constant capital above the average, will sell at a price above their value, while in the contrary case they will sell below their value. Thus the desired uniform rate of profit is established, but at the cost of sacrificing the whole of the first volume of Capital; for the inspired doctrine of the first volume, that things exchange in accordance with the congealed labour they contain, is ignominiously tossed overboard. This is the ‘solemn mystification’ of which Loria speaks. In fact, Marx has replaced Volume I by a mere cost-of-production theory such as a vulgar economist like Adam Smith might have evolved in his most vulgar and least enlightened moments. Things exchange according to their cost of production (which includes a normal rate of profit). It is true that they still have a ‘value’ which differs in general from the price; but in a ‘value’ which is an abstract metaphysical conception, and which is uniformly ignored in the market-place, few of us have any lively interest.” (Gray 1956: 318–322).
And that is spot on.

Gray, Alexander. 1956. The Development of Economic Doctrine: An Introductory Survey. Longmans, Green and Co., London.

Marx, Karl. 1906. Capital. A Critique of Political Economy (vol. 1; rev. trans. by Ernest Untermann from 4th German edn.). The Modern Library, New York.


  1. First off, congratulations on finding a third voice to agree with you. Still not a Marxist, of course; instead, someone whose work only appears on and is claimed by Rothbard as his "favorite" historian of economics.

    Isn't it funny how social democrats will always side with the far right over the far left?

    First off, Gray gives a much clearer summary than you've yet managed, and should be applauded for that. But for one reason or another -- likely a mix of irrealism and ideology -- he takes an issue that has been no trouble for the overwhelming majority of readers of Marx, and renders it scandal by refusing to accept the man's own solution -- not because there's any problem with the math, not because it doesn't make sense, but because he seeks something mystical where only materialism lurks.

    "There must be more," Gray seems to insist. But no, it's really that simple. Some of the people responding to Engels's challenge were even able to figure it out in advance. One would think this would give pause to someone reading the abstraction as somehow "irreconcilable." But ideology is a hell of a drug.

    Case in point:

    1. (1) "First off, congratulations on finding a third voice to agree with you."

      The laughable statement of a liar and a troll.

      Let's just run through the list of people who agree that there is a fundamental contradiction between vol. 1 of Capital and volume 3:

      (1) Joan Robinson (Robinson 1950: 359), probably one of the most respected Post Keynesians.

      (2) Gerald F. Shove (Shove 1944: 48–49), a Marshallian neoclassical.

      (3) Werner Sombart (1894), a German Historical School economist who early on was sympathetic to Marx's theories.

      (4) Achille Loria (1895; English trans. Loria 1920) am Italian socialist sympathetic to Marx, and

      (5) Eugen von Böhm-Bawerk (1949 [1896]), a Austrian.
      Gray is no. 6, and we could find numerous other people too, e.g., probably Benedetto Croce and Eugen Dühring.

      And already the people listed above are a broad spread of people from different schools.

      Furthermore, your pathetic attempt to dismiss Gray's statements here only because he was an Austrian reeks of the ad hominem fallacy. That is NOT rational grounds for dismissing what he says. E.g., Rothbard opposed the US war in Vietnam.

      Was opposing the US war in Vietnam therefore wrong because Rothbard was an Austrian? You, Hedlund, are an idiot.

  2. Yet more evidence: the many critics who pointed to the contradictions between vol. 1 and vol. 3 were noted **quite casually** even by early Marxists.

    E.g., Georgi Plekhanov in a review of Benedetto Croce's Historical Materialism and the Economics of Karl Marx:

    “Indeed, the offspring of that remarkable specimen of human nature are most numerous. They include all those ‘critics’ of Marx who believe in the existence of a contradiction between Volumes One and Three of Capital. In a review of Mr. Frank’s book Marx’s Theory of Value and Its Significance …, we showed that, in reality, there is no contradiction between the two volumes, ….

    For Rodbertus, the entire law of value consisted in the exchange relations of commodities being determined by the amount of labour spent on the production of each of them. In other words, Rodbertus confused the operation of the law with one of the modes (“forms”) of its operation determined in each particular period by society’s economic structure. The same error is repeated by all who think that in Volume Three of Capital Marx discarded his theory of value.”

    Plekhanov, Georgi. 1901. “On Croce’s Book,”

    So right there Plekhanov refers to “all those” or “all those critics” who think this: it is clear there are many, not few.

    Plekhanov even refers to another one: Simeon Frank’s Teoriya tsennosti Marksa i yeyo znachenie [Marx’s Theory of Value and its Significance] (1900). Frank was another early Marxist in the 1890s who noticed this contradiction and abandoned Marxism.

    So at this point your absurd claim that only a few people have thought vol. 1 contradicts vol. 3 is totally refuted -- by the evidence of early Marxists themselves.

    How do you feel now, chump? Like the halfwit you are?