Marx’s Capital, Volume 3, Chapter 10: A Critical Summary

Chapter 10 of volume 3 of Capital is called “Equalization of the General Rate of Profit through Competition. Market Prices and Market Values. Surplus Profit,” and it discusses the equalization of profit rate and the formation of prices of production.

Brewer (1984: 139) argues that the chapter in the manuscript used by Engels was in the form of a “a preliminary draft rather than a polished final version,” which is certainly evident when you read the chapter.

Marx begins by noting that some industries have a composition of capital equal to, or close to, the average composition of capital in the economy as a whole (the total social capital). In these industries, “the price of production of the produced commodities coincides exactly or approximately with their [sc. labour] values as expressed in money” (Marx 1909: 203).

Marx thinks all prices are driven towards their “prices of production” which can be expressed by this formula:

k + kpʹ
where k = cost price
and p = average rate of profit (Marx 1909: 204).

Marx also thinks that the “average rate of profit” is “nothing else but the percentage of profit in that sphere of average composition, in which the profit is identical with the surplus-value” (Marx 1909: 204). However, none of this follows unless prices do actually equal labour values in the sector with an average composition of capital. But Marx seems to miss that in that sphere cost prices of factor inputs will be “prices of production” as well, which means that the price of output commodities will deviate from labour values.

Marx now states two of his aggregate identities:

“Now, this average rate of profit is nothing else but the percentage of profit in that sphere of average composition, in which the profit is identical with the surplus-value. Hence the rate of profit is the same in all spheres of production, for it is apportioned according to that one of the average spheres of production in which the average composition of capitals prevails. Consequently the sum of the profits of all spheres of production must be equal to the sum of surplus-values, and the sum of the prices of production of the total social product equal to the sum of its values. But it is evident that the balance between the spheres of production of different composition must tend to equalise them with the spheres of average composition, no matter whether this average composition is exact or only approximate. Again, there are tendencies toward equalisation between the more or less similar spheres, and these tendencies seek to bring about the ideal average, which does not really exist, so that there is a trend toward crystallisation around the ideal. In this way the tendency necessarily prevails to make of the prices of production merely changed forms of value, or to make of profits but mere portions of surplus-value, which are assigned, however, not in proportion to the surplus-value produced in each special sphere of production, but in proportion to the mass of capital employed in each sphere of production, so that equal masses of capital, whatever may be their composition, receive equal aliquot shares of the total surplus-value produced by the total social capital” (Marx 1909: 204).

We must remember that in volume 3 of Capital, Marx argued that the “law of value” only ultimately and indirectly explains prices, and defended three aggregate equalities:

(1) the sum of surplus value = sum of profits;

(2) the sum of values = sum of prices, and

(3) the value rate of profit = the money rate of profit.

As I noted in the last post, Ladislaus von Bortkiewicz demonstrated that two of the three aggregate equalities above fail, and that the sum of surplus value = sum of profits quality cannot be defended unless under very special assumptions (see Bortkiewicz 1906; 1907a; 1907b; 1907c; English translations in Bortkiewicz 1949 and 1952; see also here).

Worse still, the idea that the value rate of profit equals the money rate of profit is impossible. If, as Ian Steedman has argued, commodity prices (including cost prices) do not equal labor value, then the formula S/(C + V) cannot explain the money rate of profit (Steedman 1977: 31).

To return to Chapter 10, Marx argues that competition moves social capital between branches of production, so that profit rates are equalized, as more commodities are produced in sectors with higher profit rates. Later on in the chapter Marx explains this process:

“Now, if the commodities are sold at their values, then, as we have shown, considerably different rates of profit arise in the various spheres of production, according to the different organic composition of the masses of capital invested in them. But capital withdraws from spheres with low rates of profit and invades others which yield a higher rate. By means of this incessant emigration and immigration, in one word, by its distribution among the various spheres in accord with a rise of the rate of profit here, and its fall there, it brings about such a proportion of supply to demand that the average profit in the various spheres of production becomes the same, so that values are converted into prices of production. This equilibration is accomplished by capital in a more or less perfect degree to the extent that capitalist development is advanced in a certain nation, in other words to the extent that conditions in the respective countries are adapted to the capitalist mode of production. As capitalist development proceeds, it develops also its own peculiar conditions and subjects to its specific character and its immanent laws all the social requirements on which the process of production is based.

The incessant equilibration of the continual differences is accomplished so much quicker, 1), the more movable capital is, the easier it can be shifted from one sphere and one place to another; 2) the quicker labor-power can be transferred from one sphere to another and from one local point of production to another. The first condition implies complete freedom of trade in the interior of society and the removal of all monopolies with the exception of those which naturally arise out of the capitalist mode of production. It implies, furthermore, the development of the credit-system, which concentrates the inorganic mass of the disposable social capital instead of leaving it in the hands of individual capitalists. Finally it implies a subordination of the various spheres of production to the control of capitalists. This last implication is of itself included in the assumption that it is a question of a transformation of values into prices of production in all capitalistically exploited spheres of production. But this equilibration meets great obstacles, whenever numerous and large spheres of production, which are not operated on a capitalistic basis (such as farming by small farmers), are interpolated between the capitalist spheres and interrelated with them. A great density of population is also a requirement.

The second condition implies the abolition of all laws which prevent the laborers from moving from one sphere of production to another and from one local center of production to another; an indifference of the laborer to the nature of his labor; the greatest possible reduction of labor in all spheres of production to simple labor; the elimination of all craft prejudices among laborers; and last, not least, a subjugation of the laborer under the capitalist mode of production.” (Marx 1909: 230–231).

In those industries with an average composition of capital, there exists a profit rate that is equal to the average rate of profit for prices of production (Marx 1909: 203–204). Surplus value is therefore redistributed between branches of production.

Marx now asks the question: “How is this equalization of profits into an average rate of profit brought about, seeing that it is evidently a result, not a point of departure?” (Marx 1909: 205). The estimates of value in money prices can only be made when commodities actually exchange (Marx 1909: 205). Marx’s theory predicts that, if commodities are sold at their real values, the “rates of profit in the various spheres of production would differ considerably” (Marx 1909: 205).

Marx now imagines a hypothetical scenario of simple commodity production where labourers own their means of production and exchange their goods with each other, without capitalists. The labourers’ incomes from exchange of commodities at their values would, according to Marx, include the value of their means of production and payment for the socially-necessary labour time required to produce them (Marx 1909: 207–208).

Marx then states:

“The exchange of commodities at their values, or approximately at their values, requires, therefore, a much lower stage than their exchange at their prices of production, which requires a relatively high development of capitalist production.

Whatever may be the way in which the prices of the various commodities are first fixed or mutually regulated, the law of value always dominates their movements. If the labor time required for the production of these commodities is reduced, prices fall; if it is increased, prices rise, other circumstances remaining the same.

Aside from the fact that prices and their movements are dominated by the law of value it is quite appropriate, under these circumstances, to regard the value of commodities not only theoretically, but also historically, as existing prior to the prices of production. This applies to conditions, in which the laborer owns his means of production, and this is the condition of the land-owning farmer and of the craftsman in the old world as well as the new. This agrees also with the view formerly expressed by me that the development of product into commodities arises through the exchange between different communes, not through that between the members of the same commune. It applies not only to this primitive condition, but also to subsequent conditions based on slavery or serfdom, and to the guild organisation of handicrafts, so long as the means of production installed in one line of production cannot be transferred to another line except under difficulties, so that the various lines of production maintain, to a certain degree, the same mutual relations as foreign countries or communistic groups.

In order that the prices at which commodities are exchanged with one another may correspond approximately to their values, no other conditions are required but the following: 1) The exchange of the various commodities must no longer be accidental or occasional, 2) So far as the direct exchange of commodities is concerned, these commodities must be produced on both sides in sufficient quantities to meet mutual requirements, a thing easily learned by experience in trading, and therefore a natural outgrowth of continued trading, 3) So far as selling is concerned, there must be no accidental or artificial monopoly which may enable either of the contracting sides to sell commodities above their value or compel others to sell below value. An accidental monopoly is one which a buyer or seller acquires by an accidental proportion of supply to demand.

The assumption that the commodities of the various spheres of production are sold at their value implies, of course, only that their value is the center of gravity around which prices fluctuate, and around which their rise and fall tends to an equilibrium.” (Marx 1909: 208–210).

So here Marx is effectively admitting that the theory of value in the text of volume 1 – that commodities tend to exchange at their pure labour values which are anchors for the price system – was a historically contingent phenomenon existing in the “lower stage … of capitalist production” and before the emergence of a higher stage of capitalism where Ricardo’s prices of production are the anchors for the price system, though he had nowhere stated this in the introduction or text of volume 1, but left his readers with the impression that his “law of value” applied to real-world commodity exchange in 19th century capitalism.

This passage in Chapter 10 was seized on by Friedrich Engels in his “Supplement and Addendum to Volume 3 of Capital” (Engels 1991 [1895]), originally published in May 1895 for the Neue Zeit. In his supplement, Engels attempted to answer critics who charged that volume 3 of Capital contradicted the “law of value” in volume 1 (which was that reproducible commodities have prices that tend to equal their labour values). The whole point of Engels’ supplement is to explain the “law of value” as a theory of price determination in volume 1 of Capital and defend it from the charge that it was a wholly abstract concept (or “ideal or logical” concept as argued by Werner Sombart) or a “necessary fiction.”

Engels’ solution is to explain Part one of volume 1 of Capital as referring to the pre-modern word of commodity exchange:

“Proceeding from this determination of value by labour-time, commodity production as a whole, and with it the manifold relationships in which the different aspects of the law of value make themselves felt, now develops as presented in Part One of Capital Volume 1; ....

To sum up, Marx’s law of value applies universally, as much as any economic laws do apply, for the entire period of simple commodity production, i.e. up to the time at which this undergoes a modification by the onset of the capitalist form of production. Up till then, prices gravitate to the values determined by Marx’s law and oscillate around these values, so that the more completely simple commodity production develops, the more do average prices coincide with values for longer periods when not interrupted by external violent disturbances, and with the insignificant variations we mentioned earlier. Thus the Marxian law of value has a universal economic validity for an era lasting from the beginning of the exchange that transforms products into commodities down to the fifteenth century of our epoch. But commodity exchange dates from a time before any written history, going back to at least 3500 B.C. in Egypt, and 4000 B.C. or maybe even 6000 B.C. in Babylon; thus the law of value prevailed for a period of some five to seven millennia. We may now admire the profundity of Mr Loria in calling the value that was generally and directly prevalent throughout this time a value at which commodities never were sold nor could be sold, and which no economist will ever bother himself with if he has a glimmer of healthy common sense!” (Engels 1991 [1895]: 1036–1038).

Engels also stated that the “transition to metal money” – especially gold and silver flowing into the Old World but mined in far distant counties – began to obscure exchange at pure labour values (Engels 1991 [1895]: 1037).

But Engels’ explanation of volume 1 of Capital here is comical, since Marx, in volume 1, never makes any such qualifications or limitations to the law of value. In fact, in volume 1, Marx states that money prices depend on the labour value embodied in units of gold or silver, so that long-run prices are determined by abstract socially-necessary labour time needed to produce relevant units of the money commodity (Marx 1906: 108, 111). But Marx says nothing about the rise of commodity money overthrowing his law of value in modern capitalist production. At no point does Marx in volume 1 limit the “law of value” – that real-world reproducible commodities tend to exchange at their labour value – to the “beginning of the exchange that transforms products into commodities down to the fifteenth century of our epoch.”

To return to Chapter 10, Marx proceeds to the distinction between the concepts of “market value” and “individual value”:

“We shall also have to note a market value, which must be distinguished from the individual value of the commodities produced by the various producers… The individual value of some of these commodities will be below the market-value, that is to say, they require less labor-time for their production than is expressed in the market-value, while that of others will be above the market-value. We shall have to regard the market-value on one side as the average value of the commodities produced in a certain sphere, and on the other side as the individual value of commodities produced under the average conditions of their respective sphere of production and constituting the bulk of the products of that sphere. It is only extraordinary combinations of circumstances under which commodities produced under the least or most favorable conditions regulate the market-value, which forms the center of fluctuation for the market-prices which are the same, however, for the same kind of commodities. If the ordinary demand is satisfied by the supply of commodities of average value, that is to say, of a value midway between the two extremes, then those commodities, whose individual value stands below the market value, realise an extra surplus-value, or surplus-profit, while those, whose individual value stands above the market-value cannot realise a portion of the surplus-value contained in them.

It does not do any good to say that the sale of the commodities produced under the most unfavorable conditions proves that they are required for keeping up the supply. If the price in the assumed case were higher than the average market-value, the demand would be greater. At a certain price, any kind of commodities may occupy so much room on the market. This room does not remain the same in the case of a change of prices, unless a higher price is accompanied by a smaller quantity of commodities, and a lower price by a larger quantity of commodities. But if the demand is so strong that it does not let up when the price is regulated by the value of the commodities produced under the most unfavorable conditions then these commodities determine the market-value. This is not possible unless the demand exceeds the ordinary, or the supply falls below it. Finally, if the mass of the produced commodities exceeds the quantity which is ordinarily disposed of at average market-values, then the commodities produced under the most favorable conditions regulate the market-value. These commodities may be sold exactly or approximately at their individual values, and in that case it may happen that the commodities produced under the least favorable conditions do not realise even their cost prices, while those produced under average conditions realise only a portion of the surplus-value contained in them. The statements referring to market-value apply also to the price of production, if it takes the place of market-value. The price of production is regulated in each sphere, and this regulation depends on special circumstances. And this price of production is in its turn the center of gravity around which the daily market-prices fluctuate and tend to balance one another within definite periods. (See Ricardo on the determination of the price of production by those who produce under the least favorable conditions.)” (Marx 1909: 210–211).

Here the “market-value” is not the price determined by supply and demand, but the value of commodities as determined by the average quantity of labour need to produce that commodity throughout the sector as a whole. Since different firms have different levels of productivity and technology, the “individual value” of any given commodity may differ from the average “market-value” owing to the different technical conditions of productivity in the individual firm that produces it.

Though Marx conducts a great deal of his following discussion in the rest of chapter in terms of “market value,” as we can see in the last quotation, it is clear Marx thinks that “prices of production” are the real-world anchors for the price system.

Marx now returns to how his “law of value” is still valid:

“No matter what may be the way in which prices are regulated, the result always is the following:

1) The law of value dominates the movements of prices, since a reduction or increase of the labor-time required for production causes the prices of production to fall or to rise. It is in this sense that Ricardo (who doubtless realised that his prices of production differed from the value of commodities) says that ‘the inquiry to which he wishes to draw the reader’s attention relates to the effect of the variations in the relative value of commodities, and not in their absolute value.’

2) The average profit which determines the prices of production must always be approximately equal to that quantity of surplus-value, which falls to the share of a certain individual capital in its capacity as an aliquot part of the total social capital.” (Marx 1909: 211).

Marx’s analysis of supply and demand in the remainder of the chapter is confusing and difficult to understand (Brewer 1984: 141–142).

Marx’s definition of the intersection of supply and demand is as follows:

“The real difficulty consists in determining what is meant by balancing supply and demand.

Demand and supply balance one another, when their mutual proportions are such that the mass of commodities of a definite line of production can be sold at their market-value, neither above nor below it. That is the first thing we hear.

The second is this: If the commodities are sold at their market-values, then supply and demand balance.

If demand and supply balance, then they cease to have any effect, and for this very reason commodities are sold at their market-values. If two forces exert themselves equally in opposite directions, they balance one another, they have no influence at all on the outside, and any phenomena taking place at the same time must be explained by other causes than the influence of these forces.” (Marx 1909: 223).

Brewer (1984: 141) argues that Marx thinks that “‘supply’ and ‘demand’ are defined as the quantities supplied and demanded when price equals market-value,” but also notes that Marx may have been inconsistent in his definitions of these concepts (a consequence presumably of the fact that large parts of volume 3 of Capital as published by Engels are from a draft of 1864–1865). According to Marx’s theory, the following is the case:

(1) Supply and demand do not determine “normal prices” (“prices of production”) but only the fluctuations around normal prices, and supply and demand do not determine what Marx calls the “market value.”

(2) if demand for a given commodity whose price is equal to the market value exceeds supply, then the price rises above the market value.

(3) if supply of a given commodity whose price is equal to the market value exceeds demand, then the price must fall below the market value. (Brewer 1984: 141–142).

Capitalist competition drives high prices caused by excess demand back to the market value.

At the end of the chapter, Marx states what he thinks is his original contribution to the subject:

“The price of production includes the average profit. We call it price of production. It is, as a matter of fact, the same thing which Adam Smith calls natural price, Ricardo price of production, or cost of production, and the physiocrats prix nécessaire, because it is in the long run a prerequisite of supply, of the reproduction of commodities in every individual sphere. But none of them has revealed the difference between price of production and value. We can well understand, then, why these same economists, who always resist a determination of the value of commodities by labor-time, by the quantity of labor contained in them, always speak of prices of production as centers, around which market-prices fluctuate. They can afford to do that, because the price of production is an utterly external and, at first glance, meaningless form of the value of commodities, a form as seen in competition and thus reflected in the mind of the vulgar capitalist, and consequently in that of the vulgar economists.

Our analysis resulted in the discovery that the market-value (and everything said concerning it applies with the necessary modifications to the price of production) implies a surplus profit for those who produce in any particular sphere of production under the most favorable conditions. With the exception of crises, and of over-production in general, this applies to all market-prices, no matter how much they may deviate from market-values or market-prices of production. For the market-price signifies that the same price is paid for commodities of the same kind, although they may have been produced under very different individual conditions and may have considerably different cost-prices.” (Marx 1909: 234).

Finally, Marx notes that certain capitalists can avoid the market competition which drives prices towards prices of production and so they can earn “surplus profit”, a profit above the average rate (Marx 1909: 234).

BIBLIOGRAPHY
Bortkiewicz, L. von. 1906. “Wertrechnung und Preisrechnung im Marxschen System I,” Archiv für Sozialwissenschaft und Sozialpolitik 23: 1–50.

Bortkiewicz, L. von. 1907a. “Wertrechnung und Preisrechnung im Marxschen System II,” Archiv für Sozialwissenschaft und Sozialpolitik 25: 10–51.

Bortkiewicz, L. von. 1907b. “Wertrechnung und Preisrechnung im Marxschen System III,” Archiv für Sozialwissenschaft und Sozialpolitik 25: 445–488.

Bortkiewicz, L. von. 1907c. “Zur Berichtigung der grundlegenden theoretischen Konstruktion von Marx im 3. Band des ‘Kapital,’” Jahrbücher für Nationalökonomie und Statistik 34: 319–335.

Bortkiewicz, L. von. 1949. “On the Correction of Marx’s Fundamental Theoretical Construction in the Third Volume of Capital,” in Paul. M. Sweezy (ed.), Karl Marx and the Close of His System and Böhm-Bawerk’s Criticism of Marx. August M. Kelley, New York. 197–221.
https://mises.org/library/karl-marx-and-close-his-system

Bortkiewicz, L. von. 1952. “Value and Price in the Marxian System,” International Economic Papers 2: 5–60.

Brewer, Anthony. 1984. A Guide to Marx’s Capital. Cambridge University Press, Cambridge.

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Steedman, Ian. 1977. Marx after Sraffa. NLB, London.