7 Transformation of values into prices of production

Competition between capitals in different sectors introduces an important shift in the level of analysis in Capital. This type of competition, and the possibility of capital migration, explains the distribution of capital and labour across the economy, and transforms the expression of value as price; the latter become prices of production. The transformation of values (or, more precisely, ‘value’, ‘simple’ or ‘direct’ prices, proportional to RSNLT; see section 5.4) into prices of production is due to the distribution of surplus value according to the size of each capital, regardless of origin.

The importance of the transformation for Marx’s work, and his seemingly counter-intuitive approach, have brought to this issue the attention of a vast array of writers of widely different persuasions.¹ It is often claimed that the transformation reveals fundamental flaws in Marx’s method, and shows that analyses based on his value theory are doomed.² These claims have been rejected by a vast literature, not necessarily Marxist, that argues that the problems in Marx’s transformation procedure can be rectified easily (although in different ways), or that Marx’s approach is cogent and needs to be understood properly rather than corrected.³ This chapter builds upon this tradition, but it approaches the transformation from another angle. Previous analyses usually if implicitly argue that the transformation is due to differences in the value composition of the advanced capitals. In contrast, it is well known that Marx attributes it to differences in their organic composition. These concepts were compared and contrasted in chapter 6, and their implications for the transformation are outlined below.⁴

This chapter has four sections. The first introduces the concepts of surplus value, profit, and rate of profit, and explores the role of OCC differences in the determination of profit. The second interprets Marx’s transformation procedure on the basis of differences in the OCCs of the advanced capitals. The third discusses the transformation of input values and the implications of the transformation for Marx’s analysis of the forms of value. Finally, the fourth section assesses the implications of this reading of Marx.

7.1 Surplus value, profit and the composition of capital

The third volume of Capital opens with the distinction between the concepts of surplus value (s) and profit. Surplus value is the difference between the newly produced value and the value of labour power, and profit is the difference between the value of the product and the value of the constant (c) and variable (v) capital (see section 4.1).

The rate of exploitation, e=s/v, measures the surplus value created per unit of variable capital. In contrast, the rate of profit (r) measures capital’s rate of growth, in which case the distinct role in production of the means of production and labour power is immaterial. The rate of profit is:⁵

where c/v is the value composition of capital.⁶

Marx subsequently considers the impact on the profit rate of changes in the quantity, quality and value of the inputs, and the implications of changes in the turnover time and the rate of surplus value. In chapter 8 of Capital 3, Marx points out that the same factors that affect the general rate of profit may also lead to differences between the profit rates of individual capitals in distinct sectors:

the rates of profit in different spheres of production that exist simultaneously alongside one another will differ if, other things remaining equal, either the turnover times of capitals invested differ, or the value relations between the organic components of these capitals in different branches of production. What we previously viewed as changes that the same capital underwent in succession, we now consider as simultaneous distinctions between capital investments that exist alongside one another in different spheres of production.⁷

This passage marks the shift in the level of analysis, or the introduction of competition between capitals in different sectors. This shift posits the need for the transformation. It may therefore come as a surprise that Marx does not immediately address this issue. Rather, in the following pages he analyses (differences between) the technical, organic and value compositions of capital (TCC, OCC and VCC; see chapter 6). It is only after this apparent detour that Marx looks into the transformation, in chapter 9 of Capital 3.

The profit rates of capitals invested in distinct sectors may be different because of their organic or value compositions. For example, two capitals producing steel and aluminium utensils (or cotton and wool clothing) with identical technologies have the same TCCs and OCCs. However, differences in the input values imply that their VCCs and profit rates, measured in direct prices, are different. This is how the literature has usually explained the need for the transformation. However, Marx was interested in another problem. Suppose, alternatively, that two identical capitals produce goods with distinct technologies, one employing relatively more machines and the other relatively more labour. In this case, regardless of the input costs (and the VCC), the capital employing more labour has a lower OCC, produces more value and surplus value and, all else constant, has a higher profit rate.

These examples are significant, because they show that the OCC connects the rate of profit with the sphere of production, where living labour produces value and surplus value. In contrast, the VCC links the profit rate with the sphere of exchange, where commodities are traded and the growth of the advanced capital is measured by the newly established values (see chapters 5 and 6). Marx describes the impact of differences or changes in the OCC and the VCC on the profit rate as follows:

Fluctuations in the rate of profit that are independent of changes in either the capital’s organic components or its absolute magnitude are possible only if the value of the capital advanced … rises or falls … If the changed circumstances mean that twice as much time, or alternatively only half as much, is required for the same physical capital to be reproduced, then given an unchanged value of money … the profit is also expressed accordingly in twice or only half the monetary sum. But if it involves a change in the organic composition of the capital, the ratio between the variable and the constant part of the capital, then, if other circumstances remain the same, the profit rate will rise with a relatively rising share of variable capital and fall with a relatively falling share.⁸

If Marx were primarily interested on the impact on prices of differences in the value of the elements of the advanced capital, or the effect on the rate of profit of the distinct expenditure ratios in constant and variable capital, his transformation would pivot around the VCC. Most of the literature approaches the problem from this angle, but this is not Marx’s procedure. His emphasis on the OCC shows that Marx is primarily concerned with the effect on prices of the distinct (surplus) value-creating capacity of the advanced capitals, or the impact on prices of the different quantities of labour necessary to transform the means of production into the output, regardless of the value of the means of production.⁹ This approach is intuitively obvious for a labour theory of value; but let us discuss this issue in further detail.

It was shown in section 6.2 that the static comparison of the TCCs and OCCs nets out differences in the value of the labour power and means of production consumed, and that only differences in the conditions of production are influential. This leads Marx to a simple yet powerful conclusion; if we abstract from the input values, the capital with the lowest OCC employs relatively more workers and produces more surplus value, regardless of the commodity produced.¹⁰

This conclusion points to two reasons why the OCC is useful for the analysis of profit creation. First, because it pins the source of surplus value and profit firmly down to unpaid labour. This helps Marx to substantiate his claims that machines do not create value, that surplus value and profit are not due to unequal exchange, and that industrial profit, interest and rent are merely shares of the surplus value produced (see sections 3.2 and 4.1).¹¹ Second, it connects the concepts of profit rate, distribution of labour, surplus value and price of production with the sphere of production, rather than exchange. In the sequel, Marx illustrates how the general rate of profit is formed, and how prices of production are determined, through the comparison of five capitals with distinct OCCs.

7.2 From values to prices of production

In his well-known transformation tables in chapter 9 of Capital 3, Marx contrasts five capitals worth £100 (including fixed and circulating capital) and states that they have different profit rates because of their distinct OCCs. From their individual profit rates he calculates an average and, from this average, Marx derives the prices of production of the output (see Table 7.1).

In spite of their importance, the reason why Marx includes capitals with the same size, £100, and the reason why he determines the price of production of the entire output of each capital, rather the unit price, have escaped the literature. They have probably been attributed to convenience or ease of exposition. However, since Marx is interested in the OCC, this procedure is necessary. Let us start from the equal size of the advanced capitals:

the organic composition of capital … must be considered in percentage terms. We express the organic composition of a capital that consists of four-fifths constant and one-fifth variable capital by using the formula 80c + 20v.¹²

Marx uses the per cent form several times, in the transformation and elsewhere. He does this because this is the only way to assess the OCC in the static case, when it cannot be measured directly. If we assume, as Marx does, that the value-productivity of labour is the same in every firm and that the rate of surplus value is determined for the entire economy (see section 4.1), the per cent form (e.g., 60c+40v rather than 6c+4v or 180c+120v; and 80c+20v rather than 8c+2v or 2400c+600v) has striking consequences: variable capital becomes an index of the quantity of labour power purchased, labour performed, and value and surplus value produced.¹³ Moreover, there is a direct relationship between the quantity of labour put in motion, the value of the output and the rate of profit. This is what Marx wants to emphasise in the transformation. As these relations are established in production, they involve the organic (rather than value) composition of capital:

Table 7.1 Marx’s transformation

Capitals of the same size, or capitals of different magnitudes reduced to percentages, operating with the same working day and the same degree of exploitation, thus produce very different amounts of surplus-value and therefore profit, and this is because their variable portions differ according to the differing organic composition of capital in different spheres of production, which means that different quantities of living labour are set in motion, and hence also different quantities of surplus labour, of the substance of surplus-value and therefore of profit, are appropriated … At any given level of exploitation of labour, the mass of labour set in motion by a capital of 100, and thus also the surplus labour it appropriates, depends on the size of its variable component … Since capitals of equal size in different spheres of production, capitals of different size considered by percentage, are unequally divided into a constant and a variable element, set in motion unequal amounts of living labour and hence produce unequal amounts of surplus-value or profit, the rate of profit, which consists precisely of the surplus-value calculated as a percentage of the total capital, is different in each case.¹⁴

Use of the per cent form helps to illustrate the principle that profit is created in production, and that it depends primarily upon the quantity of labour power put in motion, rather than the value of the means of production. For Marx, this shows that profit is a ‘dividend’ drawn from the social surplus value.¹⁵ Finally, the per cent form shows clearly that total value equals total price of production, and that total surplus value equals total profit.

These aggregate equalities are essential for Marx. They should not be understood as two independent conditions or as ‘testable hypotheses’, as if Marx’s value theory would be falsified unless they are verified empirically. For Marx, these equalities are one and the same and they necessarily hold, but they are influential at distinct levels. Total price is equal to total value because price is merely a form of value, or because total profit is equal to total surplus value. Alternatively, individual prices differ from values because profits differ from surplus values, due to the redistribution of surplus value in the transformation. These equalities always hold because they express the development of the same concept, social labour, across distinct levels of analysis (see section 1.1).¹⁶

Marx’s abstraction from the transformation of the value of the inputs and the value of the money-commodity, which naturally follows from his analysis based upon the OCC, confirm that these equalities should be understood primarily conceptually. They express the relationship between value and surplus value with their own forms of appearance, price and profit. Prices of production are a relatively complex form of value, in which price-value differences redistribute surplus value across the economy until the average capital in each branch of industry has the same profit rate.¹⁷

Let us look at this relationship from another angle. Commodity values and prices can be analysed at distinct levels. At a very abstract level, value is a social relation of production or, in quantitative terms, the labour time socially necessary to reproduce each kind of commodity. It can also be seen as the monetary expression of this labour time as direct price, price of production, or market price (see chapter 5). These shifts are due to the refinement of these concepts through their reproduction at greater levels of complexity, which captures increasingly complex determinations of the price form and, therefore, of the value relation. Their detailed study comprises a large part of the body of Marx’s work, and of Marxian value theory more generally.¹⁸

We have seen above that the per cent form is convenient, because it highlights the effect on the profit rate of differences in the OCCs of the advanced capitals. However, because it equalises all capitals to £100 regardless of their actual size, the per cent form changes the average rate of profit and modifies the quantities produced by each original capital:

In our previous illustration of the formation of the general rate of profit, every capital in every sphere of production was taken as 100, and we did this in order to make clear the percentage differences in the rates of profit and hence also the differences in the values of the commodities that are produced by capitals of equal size. It should be understood, however, that the actual masses of surplus-value that are produced in each particular sphere of production depend on the magnitude of the capitals applied … [I]t is evident that the average profit per 100 units of social capital, and hence the average or general rate of profit, will vary greatly according to the respective magnitudes of the capitals invested in the various spheres.¹⁹

Since the values, surplus values, prices and profits calculated through the per cent form are different from their original magnitudes, it is impossible to calculate the price vector through Marx’s transformation procedure. As the per cent form is necessary to assess the OCC, and since its use precludes the calculation of prices, it cannot be argued that Marx’s main objective in the transformation is to devise a method for the calculation of the price vector. Although some may find this disappointing or worse, it is hardly surprising, for the transformation ‘problem’ is not primarily about the calculation of prices. It is essentially a qualitative problem: the demonstration that price of production is a more complex form of expression of social labour than value, because it reflects the distribution of labour and surplus value across the economy.²⁰ Analysis of the input values is irrelevant to this end, and their consideration may cloud, rather than illuminate, the essential problems at stake.

7.3 The transformation of input values

The first stage of the transformation, explained above, is the distribution of the surplus value newly produced by all capitals in order to equalise the profit rates across the economy. However, the transformation has another stage, in which the input values and the value money are transformed. This stage is analytically secondary, and it received little attention from Marx; however, this has been the source of most disputes about the meaning and significance of the transformation.

It is often argued that Marx ignores the transformation of the input values in his procedure. However, this statement is at best incomplete. Marx abstracts from the input values (within the limits discussed in section 6.2), for two reasons. First, the input values are irrelevant for his argument that prices are the form of appearance of values, and that profit is the form of appearance of surplus value. Second, the simultaneous transformation of input and output values would make undetectable the production and distribution of surplus value, which is the conceptual core of the transformation. If the inputs and outputs were transformed simultaneously, only two opposing and seemingly unrelated relative price systems would exist, one in values and the other in prices. Price and profit could not be assessed in the former, and value and surplus value would be absent in the latter. Their intrinsic relationship would be invisible. In contrast, if we follow Marx’s procedure and abstract from the value of the means of production, this dichotomy is avoided and the change in the level of abstraction can be ‘seen’ through the shift of surplus value across branches of industry.

Abstraction from the value of the means of production unveils the distribution of surplus value and the ensuing determination of prices of production, regardless of the systematic modification of the exchange ratios brought about by the transformation. Moreover, it nets out the impact of the transformation of the value of the money-commodity, that would complicate further the relationship between values and prices and obscure the concepts being introduced, especially if the VCC of the money-producing sector were distinct from the social average.²¹ In sum, there are three reasons why the price vector cannot be calculated from Marx’s transformation procedure: (a) Marx works with the price of production of the mass of commodities produced per £100 advanced, rather than their unit prices; (b) he abstracts from the transformation of the input values, and (c) he abstracts from the transformation of the value of the money-commodity.²²

In other words, the age-old objection that Marx’s transformation is wrong because he failed to transform the value of the inputs is beside the point. For, if the transformation pivots around the OCC, the value of the means of production is immaterial, and their transformation cannot affect the result. The same argument can be used to dismiss the critique that Marx ‘forgot’ to transform the value of the money-commodity (or was mathematically incompetent to handle this problem),²³ or that he ‘unwarrantedly’ failed to define the problem in terms of unit values and unit prices of production. Marx’s procedure is adequate for the derivation of the concept of price of production (although not immediately for its calculation), because it separates cause (the performance of labour in production and exploitation through the extraction of surplus value) from effect (the existence of a positive profit rate, and the forces leading to its equalisation across branches).²⁴

Having introduced the concept of price of production Marx’s analysis reaches a more complex level, and the second stage of the transformation may be considered. When the realm of the OCC is superseded and the prices of the means of production and labour power enter the picture, there are two reasons why commodity prices may diverge from their value:

1. because the average profit is added to the cost price of a commodity, instead of the surplus-value contained in it;
2. because the price of production of a commodity that diverges in this way from its value enters as an element into the cost price of other commodities, which means that a divergence from the value of the means of production consumed may already be contained in the cost price, quite apart from the divergence that may arise for average profit and surplus-value.²⁵

This change in the point of view, from the conceptual derivation of price to the study of the economy at the level of price, leads to the further determination of the concept of price of production and concludes Marx’s transformation procedure. Whilst the derivation of price departs from the distribution of surplus value abstracting from the value of the means of production and labour power, the calculation of the price vector involves, as is well known, the current technologies of production, the wage rate and the (price-) rate of profit.²⁶ In sum, as was shown in chapter 1, Marx’s method involves not only the progressive transformation of some concepts into others, but also gradual shifts in the meaning of each concept, whenever this is necessary to accommodate the evolution of the analysis.²⁷ Having done this, Marx can now claim that his prices of production are:

the same thing that Adam Smith calls ‘natural price’, Ricardo ‘price of production’ or ‘cost of production’, and the Physiocrats ‘prix nécessaire’, though none of these people explained the difference between price of production and value … We can also understand why those very economists who oppose the determination of commodity value by labour-time … always speak of prices of production as centres around which market prices fluctuate. They can allow themselves this because the price of production is already a completely externalized and prima facie irrational form of commodity value, a form that appears in competition and is therefore present in the consciousness of the vulgar capitalist and consequently also in that of the vulgar economist.²⁸

At this stage,

The value of commodities appears directly only in the influence of the changing productivity of labour on the rise and fall of prices of production; on their movement, not on their final limits. Profit now appears as determined only secondarily by the direct exploitation of labour, in so far as … it permits the capitalist to realize a profit departing from the average.²⁹

Marx’s price theory is two-fold: on the one hand, it is a production cost theory similar to the classical. On the other hand, Marx’s theory is distinctive because he explains the price form through the social division of labour in capitalism, analysed at increasing levels of complexity. The transformation has a four-fold impact upon the structure of Capital. First, it explains why market exchanges are not directly regulated by the labour time socially necessary to reproduce each commodity. Second, it shows that price is a relatively complex form of social labour. Third, it allows a more complex understanding of Marx’s analysis of the forms of value (see below). Fourth, it explains the distribution of labour across the economy.³⁰ Even though it was left incomplete, Marx’s procedure is important because it develops further his reconstruction of the capitalist economy, and substantiates the claim that living labour alone, and not the dead labour represented by the means of production, creates value and surplus value.

In contrast, approaches that argue that the input values should be taken into account from the start, and that they should be transformed together with the output values, often conflate the roles of living and dead labour in the production of value, and can hardly distinguish between workers and machines in production. The ‘non-transformation of the inputs’ cannot be considered a defect. Rather, it is a feature of Marx’s method. By abstracting from (changes in) the value of the inputs and the money-commodity, Marx locates the source of profit in the performance of labour in production, and carefully builds the conditions in which circulation may be brought into the analysis and add positively to its development.

7.4 Conclusion

This chapter has shown that Marx’s transformation of values into prices of production includes two stages. In the first, he abstracts from (differences in) the value of the means of production, in order to highlight the principle that value is produced by labour alone or, alternatively, that the greater the quantity of living labour put in motion, the more surplus value is produced. Distribution of the surplus value according to the size of each capital forms prices different from values. In the second stage, the economy is analysed at the level of prices of production; all commodities are sold at their prices, and the input prices are taken into account. The role of transformation is to allow a greater determination in the form of social labour, and to explain the distribution of labour and surplus value across the economy.

The use of the organic composition of capital is essential in order to distinguish these stages, because it helps to identify the cause of the transformation and to explain the relationship between prices and values. Moreover, it shows that Marx’s interest lies in the conceptual relationship between labour, price and profit, rather than the algebraic calculation of prices or the rate of profit. Finally, it indicates that equilibrium (or simple reproduction) assumptions are unwarranted in this case. This reading of the transformation shows that the presentation in Capital 3 is consistent with Marx’s method, and is part of his reconstruction of the main categories of the capitalist economy.

Most of the literature has investigated the transformation through the VCC. Whilst this is not in itself wrong, and may lead to important theoretical developments, this approach has no bearing upon Marx’s problem. The various solutions to which this approach leads can be distinguished from each other by the structures that they contemplate, the processes at the forefront, and the treatment which is given to them (in other words, the nature of the normalisation condition, the use of interactions or simultaneous equations, and so on). Most transformation procedures found in the literature are alternative to Marx’s. They cannot claim to ‘correct’ the latter, because they address different issues and include a conception of the price-value relationship at odds with Marx’s. Inadequate understanding of Marx’s transformation has often led to the complaint that he unwarrantedly omitted the specification of the technologies of production or, more often, that he did not transform the value of the inputs.³¹ This chapter has demonstrated that these objections are misplaced, because they emphasise issues that are not the primary object of Marx’s concern in the transformation, and may obscure, rather than help to reveal, the subject of his inquiry.