6The Marxist entanglement I
Values and prices

… the whole substance of the bread is changed into the whole substance of Christ’s body, and the whole substance of the wine into the whole substance of Christ’s blood. Hence … it can be called ‘transubstantiation.’

—Thomas Aquinas, Summa Theologica

As radical thinkers, we find it far more difficult to criticize Marx than the neoclassicists. So much of our thinking about capitalism originates from his writings. The very concept of the ‘capitalist system’; the view of capital as a political institution and of political critique as part of the class struggle; the emphasis on the ruling class and the socio-historical context in which it emerges; the dialectical development of history in general and of capital accumulation in particular; the imperative of empirical research; the universalizing tendencies of capital — these ideas and emphases are all due to Marx. It is hard to approach contemporary social phenomena — from globalization, to economic crisis, to militarization, imperialism, ecology, price movements, the modern corporation, cultural development, elite dynamics and technical change, to name a few — without feeling indebted to Marx and the controversies he opened up. His insights, along with the debates among his followers and critics, are deeply embedded in our current thinking.

But then it is precisely this crucial importance of Marx — along with his emphasis on dialectical thinking — that forces us to re-examine his underlying framework. Capitalism, he argued, is a system of commodities, driven by the accumulation of capital and denominated in prices. To decipher the secrets of this process is to look behind the front window of prices, and to do so we need a theory of value. This is the starting point, the ‘algorithm’ that Marx uses to develop much of his subsequent concepts and analysis. Marx chose to develop a value theory based on labour, and it is here that his analysis went wrong. Our purpose in this and the next chapter is to examine why. What are the inconsistencies in Marx’s logic, how has the development of capitalism undermined that logic, and most importantly, what can we learn from these theoretical and historical considerations as we seek to develop a radical alternative?

Content and form

Throughout Das Kapital there is no ‘analytical’ definition of capital, perhaps for a good reason. In contrast to his classical predecessors, Marx saw capital not as a ‘thing’, but as a comprehensive social relation whose description was intertwined with its explanation. The context of capital included the production process, the division of labour and technological progress, as well as the institutional and power arrangements shaping the collective consciousness. According to Erik Olin Wright (1977: 198), the notion that capital accumulation involves merely the tangible augmentation of machinery, buildings, raw materials and alike is alien to Marxist thinking. Instead, he maintains, ‘capital accumulation must be understood as the reproduction of capitalist social relations on an ever-expanding scale through the conversion of surplus value into new constant and variable capital’. Emphasizing this aspect of Marx’s writing, Anwar Shaikh (1990: 73) similarly reiterates that ‘capital is not a thing, but rather a definite set of social relations’, and that in order to understand it we must ‘decipher its character as a social relation’.

Marx started with three fundamental principles. The first was that human history is driven largely by a struggle over surplus. The second was that production and redistribution are inseparable: surplus presupposes a class society, and classes mean a struggle over how this surplus is created, who is going to get it and how it is to be used and abused. The third principle was that, regardless of its particular form, surplus is always generated through the labour process. The analysis of every class society therefore has to begin with the underlying process of production: ‘A distinct mode of production thus determines a specific mode of consumption, distribution, exchange and the specific relations of these different phases to one another’ (Marx 1859: 205). This latter conviction created the infamous ‘materialistic’ bias underlying Marx’s theory of accumulation.

The consequence of this bias was an over-preoccupation with content and less attention to form. The content of capitalism is the concrete technological fusion of workers and instruments through an ever-expanding social process of production and consumption. The form of capitalism is capitalist control; that is, the manipulation of human beings via the quantitative accumulation of universal ownership titles. As a historian of capitalism, Marx repeatedly emphasized the inherent interdependence of these two aspects. As a theoretician, though, he failed to integrate this interdependence into his analytical framework of accumulation. When it came to describing accumulation in abstract terms, his attention was focused almost solely on a relatively narrow understanding of production, leaving much of the power dynamics ignored. And so although Marx saw accumulation as an antagonistic social process, in the end his theorizing got entangled in the same ‘materialistic’ trap that would later confound the neoclassicists.

The labour theory of value

For the capitalist, accumulation is a simple process in which ‘money makes money’. The capitalist invests M dollars, ends up with M+∆M dollars, and the key challenge is how to make ∆M as big as possible. For Marx the question is different. He asks not so much how, but why: where does ∆M come from? And the answer, he argues, can be given only by looking over the capitalist’s shoulder, peering beyond the phenomenon and into the kernel.

What appears on the surface as the self-expansion of money, in fact, is a reflection of a social process. Money can ‘make’ money, Marx says, only through the exploitation of productive labour.

Conceptually, the process of capital accumulation can be represented by the following expression:

\[\begin{equation} M \longrightarrow c + v \longrightarrow Production \longrightarrow c + v + s \longrightarrow M + \Delta M \tag{1} \end{equation}\]

The capitalist uses money (M) to buy constant capital (c) and variable capital (v). The first of these capitals consists of used-up raw materials and semifinished goods, as well as machinery and structures that depreciate during production; the second form of capital comprises labour power. All commodities, including c and v, are assumed to be exchanged at prices proportionate to their value; that is, proportionate to the socially necessary abstract labour-time required for their reproduction (a concept which we define in the next section and examine more closely in Chapter 8).

Constant and variable capital nevertheless differ in that, when they go through production, c simply transfers its own value to the new products and in that sense remains ‘constant’, whereas v transfers its own value as well as generates new value, which is why it is called ‘variable’. Once the product is sold on the market, this new value, denoted by s for ‘surplus’ value, is realized by the capitalist in the form of money profit (∆M).

How is surplus value created? The answer is based on the distinction between labour power and labour. Labour power is the ability to work, which is what the worker sells. By contrast, labour is the actual time he or she ends up working for the capitalist. Since labour power is treated as a commodity, its price, like that of every commodity, is proportionate to the socially necessary cost of its own reproduction. In this case, it is proportionate to the average cost, counted in labour time, of having the worker replenish herself or himself for yet another day of labour.63

But this price of labour power, when measured in labour time, is, as a rule, smaller than the actual labour time the worker works for the capitalist. And here lies the crux of the matter: the secret of accumulation rests on the unique ability of labour power to create surplus value — a surplus which the institution of private property then allows the capitalists to appropriate.

Three challenges

This elegant exposition of both the social character of production and the conflictual–exploitative basis of accumulation enabled Marx to excite generations of followers and alter the course of history. And yet Marx’s conception of capital — particularly his Smithian emphasis on production as the engine of accumulation and his Ricardian belief that labour values reflect the inner quantitative code of the process — was far too restrictive and, in the final analysis, misleading.

Socially necessary abstract labour

The problem is threefold. The first difficulty concerns the underlying unit of measurement: socially necessary abstract labour time.64 Marx was appalled yet fascinated by the ‘mechanized’ order of capitalism, a social system that objectifies its human subjects and fetishizes their social interactions. His method reflected this double-sided sentiment. On the one hand, he subjected the transformations of capitalism to dialectical analysis. On the other hand, he viewed capitalist processes as obeying historical ‘laws of motion’ and therefore as amenable to scientific inquiry. This latter view was deeply influenced by the contemporary revolutions in physics and chemistry, and it drove Marx, just as it drove natural scientists, to search for basic units. He looked for the underlying building blocks, for the simplest elements with which the complex processes of capitalism are socially constructed and ideologically articulated.

The visible building block of capitalism, he argued, is the commodity. On the face of it, commodities are qualitatively different from each other and in that sense incommensurate: a meal in a restaurant is different from a barrel of oil, and both are unlike an automobile. And yet all commodities share a common denominator: their price. A meal may cost $50, a barrel of oil $100 and an automobile $20,000. Although incommensurate qualitatively, they nonetheless display a strict quantitative relationship, expressed by their price ratio of 1:2:400.

How is it possible for qualitatively different commodities to have quantitatively comparable prices? Marx isn’t puzzled. Commodities, he admits, indeed differ in their use value. But they nonetheless share one property in common: they are all products of human labour. And it is this human labour — understood as an undifferentiated universal quantum — that gives commodities their value and makes them commensurate. Marx defined this universal quantum as socially necessary abstract labour. This is the elementary particle of his system, the hidden entity that both underlies and embodies the entire architecture of the capitalist order.65

The significance of socially necessary abstract labour can hardly be overstated. Capitalism is a system organized through prices, and, according to Marx, socially necessary abstract labour time — mediated through the labour theory of value — provides the ultimate code of prices. It is the basic unit that gives commodities quantity and capital magnitude and, therefore, the common denominator with which all the important ratios of capitalism are expressed. It is crucial for understanding the profit rate of capitalists, the subsistence wage of workers, the distribution of income and the balance of class power. It is essential for explaining the historical development of capitalism, its short-term crises and long-term tendencies. It underlies the system’s eventual demise. Without this universal unit, it is doubtful that Marx’s grand theory can remain standing. Although Marx’s insights go beyond his labour theory of value, the hallmark of his system lies in its completeness: the claim that there is a single, universal logic that underlies the entire order of capitalism. And this latter claim depends crucially on abstract labour.

It turns out, though, that this elementary particle, the unit on which everything else stands, is deeply problematic. The key difficulty is that this particle — like God or the Ether — is forever beyond our reach. We can observe actual labour, but that still tells us nothing about socially necessary abstract labour. The latter term differs from the former on two counts. First, socially necessary labour time refers not to the specific time a given capitalist enterprise takes to produce the commodity, but to the average time society requires to produce this type of commodity. This is the ‘socially necessary’ aspect of the term. Second, socially necessary labour time is counted not in heterogeneous units of concrete labour, but in homogenous units that can be added up. This is the ‘abstract’ dimension of the concept. The problem is that both conversions — from actual to socially necessary and from concrete to abstract — are difficult if not impossible to perform. As noted, this is a make-or-break predicament — for, if we cannot perform these conversions, we don’t have a basic unit to work with and therefore no theory at all.


The second difficulty concerns the concept of ‘production’. Even if we can agree on what constitutes socially necessary abstract labour, there is still the issue of which labour is relevant and which is not. Although all values derive from the productive labour of workers, not all labour is productive. According to Marx, there are two types of workers: productive workers who create value and unproductive workers who do not. In order to render the labour theory of value meaningful, we need to count only the former and ignore the latter. Now, this selection assumes that we can distinguish between these two types of workers in the first place — and it is here that the theory runs into a second roadblock. It turns out that there is no objective basis, a priori or a posteriori, on which to decide that the labour of a Volvo engineer or Fluor crane operator is productive, while that of a government accountant or a stock broker is not.


And there is a third problem. Even if we could somehow identify and measure the socially necessary abstract labour time of productive workers, there is still the issue of ‘transforming’ the resulting labour values into money prices. The transformation has two steps. The first, analytical, step is to translate labour values into so-called production prices. The purpose here is to show how labour values determine equilibrium prices in a perfectly competitive capitalist economy. This step, though, takes us only half way. A real capitalist economy is neither perfectly competitive nor equilibrated, so we need an additional conversion to translate theoretical production prices into actual market prices. Attempts to achieve these transformations began with Marx himself, and the fact that they still continue today attests to their degree of success.

The road ahead

Together, these three problems make for a rather treacherous path. The value theorist is forced to begin with a highly ambiguous unit of abstract labour; to continue by applying this unit to a non-delineable sphere of production; and to conclude by converting the labour values that emerge from this procedure into prices, using a dubious if not circular calculation. Marxists have written thousands of learned books and articles to evade and bypass the hazards of this journey, with the effect of making Marx’s original value theory practically impenetrable to the laity.

This chapter and the following two explore this journey — in reverse. Our starting point is the observed phenomenon of actual prices. From there, we trace our way backwards to the underlying relationships and, eventually, to the elementary concepts of the theory. We begin in this chapter with the transformation of labour values into prices. We continue in Chapter 7 with the delineation of production. And we conclude in Chapter 8, which deals with the elementary particle of abstract labour, along with the elementary particle of the liberal universe — the util.

The second transformation

As noted, Marx’s labour theory of value requires a double transformation in which labour values are first converted into production prices, and then into market prices:

\[\begin{equation} labour~values~ ➊\longrightarrow production~prices~ ➋\longrightarrow market~prices \tag{2} \end{equation}\]

The first step is analytical. It implies a mathematical relationship between values and prices, one that ostensibly exists in a perfectly competitive capitalism. In this context, if we take two commodities — say a computer chip and a bag of potato chips — having a labour-value ratio of (lv1 / lv2), the ratio of their prices of production (pp1 / pp2) would be given by:

\[\begin{equation} \frac{pp_1}{pp_2} = \mu \frac{lv_1}{lv_2} \tag{3} \end{equation}\]

with µ representing a known coefficient reflecting differences in the ‘organic compositions’, or the c/v ratios, across the various sectors of the system.

This first step of converting production prices into market prices, although merely analytical, is far from trivial and — in the opinion of many Marxists — in fact impossible to make. However, we postpone these doubts for later in the chapter and assume, for the time being, that the first transformation is logically consistent and practically feasible. So if we know relative values, we also know relative production prices.66

This assumption, though, takes us only half way. We still have to take the second step and show that the production prices of a hypothetical perfectly competitive capitalism explain the market prices of an actually functioning capitalism. And here we run into a significant problem. As it stands, Marx’s labour theory of value does not even try — and indeed refuses — to take this step.

Why only labour?

This latter point was made early on by one of Marx’s fiercest critics, the Austrian economist Eugen von Böhm-Bawerk (1884; 1896). Marx wasn’t incorrect to search for the common property of commodities, Böhm-Bawerk conceded. But his insistence that this common property consists only of labour — to the exclusion of all other properties — was logically indefensible.

Commodities, argued Böhm-Bawerk, can also vary in other respects. They can differ in the degree of their ‘scarcity’ as expressed by supply and demand, in whether they are produced by people or gifted by nature, and in the extent to which their temporal production and consumption profile makes them sensitive to the discounting impact of interest rates.

Now, unlike the neoclassicists who translate all such factors into the language of utility, Marxists exclude them from their explanation on the ground that they are ‘subjective’, or otherwise external to the commodity itself. But since they also acknowledge that these factors do affect market prices, their theory becomes incomplete, by definition.

Excluding power

In fact, the theory is incomplete in ways that extend beyond Böhm-Bawerk’s utilitarian individualism. Note that the labour theory of value requires perfect competition. Firms and workers have to be ‘price takes’, unable to individually affect prices and wages — for otherwise, market prices could be set ‘arbitrarily’ without any necessary link to production prices. Moreover, capital and labour must be able to move freely between industries in order to equalize the rates of profit and exploitation across different sectors (for instance, Sweezy 1942: 270–74; and Howard and King 1992: 282).

And yet, these conditions of perfect competition do not — and, as we argue later in the book, cannot — exist in the capitalist reality. Instead of atomistic competition in the so-called economic sphere, the history of capitalism impresses on us a broader myriad of restrictive social institutions and power processes. These include, among others, big business, big bureaucracies and big armies, redistribution and restructuring by government, international struggles, segmented labour markets, core-periphery interactions, ideological persuasion, material cooptation and, last but not least, the extensive use of force and violence at every level of society.

The existence of these power institutions and processes makes labour values (and therefore prices of production) practically useless for the study of actual prices and accumulation. In fact, under such conditions, the value of labour power — the basic input in all production processes and the ultimate anchor of accumulation — is already contaminated by power relations (a point to which we return in Chapter 8).

Ironically, Marx was the first to predict these deviations from competition, particularly the centralization of capital and the growth of state power — yet he did not explore their detrimental implications for his own labour theory of value. Part of the reason was that these phenomena were only starting to emerge and therefore were still difficult to examine with some rigour. But there was a deeper cause.

Marx’s analytical framework, like that of the neoclassicists, was hostage to the mechanical worldview of static equilibrium. The neoclassicists, whose purpose was to eviscerate history from their positive economics and demonstrate the eternal harmony of capitalism, found mechanical equilibrium useful. But Marx tried to do the very opposite. He attempted to understand the transformative dynamics of social conflict — the very antithesis of mechanical equilibrium. The result was a lingering dissonance between his dialectical analyses of capitalist development and crisis, on the one hand, and his attempts to mimic physics and chemistry in his labour theory value, on the other. The former uses as its raw material the full plethora of power relations; the latter expunges power to retain the determinism of labour time.

Omitting capitalization

Finally, as we shall see in Part III, labour values and production prices can tell us very little about what really matters to capitalists: the capitalization of their assets on the stock and bond markets. Marx, who didn’t know exactly what to do with these forward-looking assets, got himself off the hook by dubbing them ‘fictitious capital’. It was a choice of words for which his adherents were to pay dearly.

Following Marx’s death, the trajectory of financial markets has diverged from the underlying amassment of (what Marx considered) ‘real’ capital. As will be amply demonstrated in Chapter 10, nowadays the corporation’s market value commonly is much bigger than the price of its underlying plant and equipment (however estimated). Similarly, comparing any two corporations, we usually find the ratio of their market values to be markedly different from the price ratio of their plant and equipment (however measured).

As a result of these developments, those who have accepted Marx’s classification and exclude ‘financial’ capitalization from their ‘materialist’ labour theory of value now find themselves boxed into a corner. Being unable to explain the trajectory of financial markets with Marxist tools, they face the unpalatable choice of dismissing their movements as irrelevant, classifying them as ‘distortions’ or simply surrendering to the bourgeois theory of corporate finance and injecting its neoclassical econometrics into their Marxist dialectics.

What does the labour theory of value theorize?

The ambivalence of Marxists toward subjective considerations, power and ‘fictitious’ capital has had an important consequence: by excluding the role of these factors in principle while recognizing it in practice, they have made their labour theory of value logically ‘weightless’. As it stands, there is nothing in the theory itself to tell us whether labour values explain 1 per cent of prices, 99 per cent, or anything in between, and whether this explanatory power remains stable or changes over time.

This predicament hasn’t been lost on Marxists, and rather than fight a losing battle most have opted out. Marx’s labour theory of value, many now argue, is not a ‘price theory’ — at least not in the conventional liberal sense. Marx was primarily a critic of classical political economy, they say, and as such, he wasn’t concerned with the precise determination of price levels:

Whatever may be the way in which the prices of various commodities are first fixed or mutually regulated, the law of value always dominates their movement. 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.

(Marx 1909, Vol. 3: 208, emphases added)

Note the emphases: value does not determine but merely dominates market prices, and it affects not their level but their movement. More broadly, according to this view Marx was not really interested in the price of chewing gum or the day-to-day fluctuations of a particular sector. These were epiphenomenal:

Magnitude of value expresses a relation of social production, it expresses the connection that necessarily exists between a certain article and the portion of the total labour-time of society required to produce it. As soon as the magnitude of value is converted into price, the above necessary relation takes the shape of a more or less accidental exchange-ratio between a single commodity and another, the money-commodity.

(Marx 1909, Vol. 1: 114)

For Marx, then, the issue was not individual prices but the general tendencies of capitalism. And this broad emphasis shouldn’t be surprising. The period he was writing in had witnessed great strides in probability and statistics. The concept of least-squares deviations from mean, developed by both Gauss and Legendre in the late eighteenth century, was already widely used, while Galton’s reversion to mean was just around the corner. The notion of approximating the underlying truth from multiple imprecise measurements, first applied in the geodesic derivation of the standard metre, was gaining adherents in every science.67

In line with these developments, Marx, too, was searching for the longterm ‘fundamentals’, the mean equilibrium values around which prices oscillate and to which they ultimately revert:

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, Vol. 3: 210)

Now, here we have a possible re-entry point. Marx’s pronouncement was difficult to corroborate in his own time, but nowadays, with abundant statistics and cheap computing power, it shouldn’t be too hard to assess. All it takes is a simple chart. You plot the historical trajectories of labour values and prices of production; on these you superimpose the historical movement of actual prices; and then you look and see. The resulting pattern, mediated if need be by statistical paraphernalia, should be able to tell you both the extent to which the law of value governs prices — with short-term precision, in the long run only, or not at all — and how this pattern may have changed over time.

And, indeed, as we shall see in the next section, Marxists have taken on this task. Since the late 1970s, they have subjected the labour theory of value to rigorous testing — with results that seem to prove more than Marx could ever have hoped for. In general, the studies show that values govern prices not only in the long run, but also in the fairly immediate term, and that they do so very tightly and consistently across space and over time.

And so, in the end, everything falls into place. Although we do not live in a perfectly competitive capitalism, and although prices are subject to the impact of numerous factors other than labour time, none of this matters a great deal. In the final empirical analysis, Marx was right. Capitalism does seem to obey his law of value.

Or does it?

Testing the labour theory of value

The problem is surprisingly simple. The purpose of testing the labour theory of value is to show that market prices are positively correlated with labour values (or with their corresponding prices of production). Now, irrespective of how one approaches this task, two things must be known beforehand: prices and values. And yet it turns out that these seemingly trivial magnitudes are not so easy to ‘know’ and that, contrary to their explicit proclamation, the empirical studies do not appear to even try to correlate prices and values.

The price of what?

Begin with prices. Most people think of these as attributes of individual commodities — the price of a Toyota Corolla, the price of a bushel of wheat, the price of a United Airlines flight from New York to Tokyo. Price could also be an attribute of a group of commodities. The GDP deflator of the beverage industry, for instance, denotes the weighted average price of all newly produced commodities in that industry, while similar deflators express the weighted average price for entire sectors such as consumer and investment goods, or even the economy as a whole.

Marxist studies of price–value correlations, however, deal with neither of these concepts. Instead of looking at the price of a single commodity or the average price of a group of commodities, they focus on the price of total output — that is, on the unit price of the commodity multiplied by its quantity. Typically, the researcher divides an economy into a few dozen sectors as delineated by the national statistical service, estimates the price and value of total output in each of these sectors, and then correlates these two magnitudes across sectors for one or more years.

This shift in focus has significant statistical implications. Correlations measured in this way reflect the co-variations not only of unit prices and values, but also of their associated quantities. Now, note that the unit value and unit price of each sector are multiplied by the same output. This fact means that, all other things being equal, the greater the size-variability of output across the different sectors, the tighter the correlation between their total price and total value.68 And since different sectors do vary in their output size, the common result is to make the overall correlation bigger than the underlying correlation between unit prices and values. The extent of this impact is revealed when sectors are controlled for their size: the value–price correlations usually drop sharply, often to insignificant levels.69

Absence of value

The other problem with empirical studies has to do with values — or rather the lack thereof. To our knowledge, all Marxist models that purport to correlate prices with values do no such thing. Instead of correlating prices with values, they in fact correlate prices with … prices!

The reason is simple enough. Recall that, according to Marx, the value of a commodity denotes the abstract labour time socially necessary for its production. Yet, as we already mentioned and elaborate further here and in Chapter 8, this quantum is impossible to measure. And so the researcher makes assumptions.

The most important of these assumptions are that the value of labour power is proportionate to the actual wage rate, that the ratio of variable capital to surplus value is given by the price ratio of wages to profit, and occasionally also that the value of the depreciated constant capital is equal to a fraction of the capital’s money price. In other words, the researcher assumes precisely what the labour theory of value is supposed to demonstrate.70

Duncan Foley tries to put on a brave face on this circularity by describing it as a matter of convenience:

… the choice of an embodied labor coefficients [sic] or a market price accounting system does not make much practical difference to estimates of Marxian categories like the rate of exploitation, or the ratio of unproductive to productive labor in real economies. Given the wide availability of market price accounting data in financial and government sources, and the expense, difficulty, and possible error involved in reconstructing embodied labor coefficients for many periods and economies from input/ output tables, most empirical work … will use market price data as a first approximation to an embodied labor coefficients system of accounts.

(Foley 2000: 35)

But this account is misleading. The issue isn’t convenience, it’s necessity. The imperative of this procedure was succinctly if opaquely stated in one of the first statistical studies:

In order to compute the rate of surplus value, input/output flows in market prices (hereafter prices) must be converted into input/output flows in labor time (hereafter values).

(Wolff 1975: 936, emphasis added)

In short, we have to pretend. Since values are forever unknown, we need to first convert prices into ‘values’ and then correlate the result with prices. It seems reasonable to expect the outcome to be positive and tight. After all, we are correlating prices with themselves. What remains unclear is why one would bother to show this correlation and, more puzzling still, how the whole excise relates to the labour theory of value.71


All in all, then, it seems that the second transformation does not take us very far, and that values and prices of production in fact tell us very little about actual prices. To summarize the difficulties: most Marxists concede that market prices are affected by an array of factors other than values; they nonetheless insist on excluding these factors from their theory and therefore make the theory logically incomplete to an unknown extent. Some researchers have tried to circumvent this problem statistically, by showing prices and values to be consistently and tightly correlated in practice. Their methodology, though, is highly questionable for two reasons. First, they usually focus not on individual commodities but on total output, and second, their ‘value’ data are in fact nothing but converted prices. The consequence is that the estimated correlations, no matter how tight, are irrelevant to the labour theory of value.

The first transformation

So far we have focused on moving from production prices to market prices, assuming that the former were merely transformed labour values. This assumption, though, isn’t trivial. In fact, most of Marx’s followers agree with his critics that this first step is impossible to take.

To explain the problem, begin with Marx’s value equation:

\[\begin{equation} lv = c + v + s, \tag{4} \end{equation}\]

where the commodity’s labour value is given by lv, the value of constant capital by c, the value of variable capital by v and surplus value by s.

Marx used these categories to spell out a definite relationship between three ratios across the political economy, a relationship that in turn bridges labour values with prices of production. The first is the rate of profit (π), given by the ratio of surplus value to the sum of constant and variable capital:

\[\begin{equation} \pi = \frac{s}{c + v} \tag{5} \end{equation}\]

The second is the rate of exploitation (ε), denoted by ratio of surplus value to variable capital:

\[\begin{equation} \varepsilon = \frac{s}{v} \tag{6} \end{equation}\]

And the third is the organic composition of capital (θ), defined as ratio of constant to variable capital:

\[\begin{equation} \theta = \frac{c}{v} \tag{7} \end{equation}\]

Dividing the numerator and denominator on the right-hand side of Equation (5) by v, and then substituting ε for s/v and θ for c/v, gives us the three-sided relationship between the rate of profit, the rate of exploitation and the organic composition of capital:

\[\begin{equation} \pi = \frac{s/v}{c/v + 1} = \frac{\varepsilon}{\theta + 1} \tag{8} \end{equation}\]

According to Marx, competition among capitalists pushes capital from low-profit to high-profit industries, creating a tendency for the rate of profit (π) to equalize across the economy. Similarly, competition between workers triggers labour mobility, causing a parallel equalization tendency of the rate of exploitation (ε). Now, if these two rates tend to equality across different industries, by definition so must the organic composition of capital (θ).

And yet, unlike the first two movements, the third one has no reason to happen.72 On the contrary: the ratio of constant to variable capital depends not on competition, but on the technical nature of production and therefore tends to differ across industries (the organic composition of capital in the computer industry, for instance, may be lower than in the steel industry, in dairy farming lower than in microchip production, in banking lower than in automobiles, and so on).

The only way to square the circle is to accept that prices of production and money profits in different industries are not proportionate to their respective labour values and surplus values. Specifically, industries with a higher-than-average organic composition of capital will have prices and profits that are higher than their respective labour values and surplus values, while in industries with a lower-than-average organic composition of capital the opposite will be the case.

The theory therefore isn’t true to the letter, but the damage is limited. Recall that Marx emphasizes the overall processes of capitalist development, and in that regard, argue his followers, his theory remains intact and, indeed, indispensable. The reason is that, although prices and profits differ from their respective labour values and surplus values in individual industries, their aggregates remain the same.

These aggregate equalities are crucial. Since, according to Marxists, the sum of all profits is equal to the sum of all surplus values, and since the sum of all prices is equal to the sum of all labour values, the rate of profit in price terms is equal to the rate of profit in value terms. It is through this determination of the rate of profit that the value system anchors the price system. Compared with this overall causality, price–value and profit–surplus inequalities across the individual industries are secondary. They represent a mere redistribution of the overall equalities, and ones that could be fully explained with value categories.

Inconsistency, redundancy, impossibility

The dual system

This understanding of ‘pulling and redistributing’ labour values was dominant among Western and Russian socialists until the Second World War. There were early challenges to this view, but Nazism and Stalinism helped keep them obscure. It was only in the 1940s, with the introduction to English readers of the work of German statistician Ladislaus von Bortkiewicz, that the problem with this view became widely recognized.73

Bortkiewicz (1907a; 1907b) demonstrated that Marx’s solution of pulling and redistributing is logically inconsistent. It turns out that, as we move from labour values to prices of production, the results do not ‘add up’: the outputs of the price system generally differ from its inputs.74 According to Bortkiewicz, the inconsistency occurs because Marx’s transformation is incomplete. It converts surplus value counted in labour time into profits counted in prices, but it does not do the same for constant and variable capital. The resulting price system therefore is half-baked — partly price denominated, partly value denominated.

Capitalists and workers, though, buy and sell commodities in prices rather than values, so it makes sense to specify two distinct systems — one denominated in values, the other in prices of production. And, indeed, with a dual-system specification, Bortkiewicz showed the transformation of values into prices of production to be mathematically consistent.

But there was a hefty price to pay for this consistency: the dual system no longer satisfies Marx’s aggregate conservation principle. With separate systems for prices and values, there is no longer a single µ that would satisfy Equation (3) for all commodities. The result is that total prices need not be equal to total labour values and total profit does not have to be the same as total surplus value. And given these inequalities, the rate of profit denominated in price terms is no longer the same as the rate of profit calculated from labour values.

This was no longer a secondary problem. Marx claimed his theory to be superior to the bourgeois alternatives, partly because it did something they couldn’t: it objectively derived the rate of profit from the material conditions of the labour process.75 Bortkiewicz turned this asset into a liability: he showed that Marx’s original framework was logically inconsistent and that it could be fixed only by making the rate of profit independent of the value system.

The complicating detour

Adding insult to injury, in 1957 Paul Samuelson demonstrated that, mathematically, the first transformation was a pointless ‘complicating detour’. Whether consistent or not, the theory was largely irrelevant. Marx stipulated a two-stage analytical process, moving from the conditions of production to labour values, and from labour values to prices of production. In fact, argued Samuelson, the process requires only one step — from the conditions of production to prices of production — without any intermediate resort to labour values. ‘Marxolaters, to use Shaw’s term’, he suggested triumphantly, ‘should heed the basic economic precept, valid in all societies, cut your losses’ and dump the labour theory of value (1957: 892).

Many Marxists, although silent on Samuelson’s mathematics, rejected his conclusion as typical bourgeois misunderstanding. The crux of value analysis, they argued, was never to explain prices per se, but to emphasize the underlying social essence of their formation — the class conflict in production, the social imperative of technical change and the workings of the capitalist mode of production as whole. According to Sweezy (1942: 129), value analysis, despite its many problems, is necessary in order to ‘look beneath the surface phenomena of money and commodities to the underlying relations between people and classes’.76

What remains unclear, though, is why only the analysis of labour time can do the job. Why should we assume that the logic of class conflict, technical change and the interaction between production, circulation and distribution must all be anchored in the quantitative combination of labour inputs — particularly when this combination is entangled in logical contradictions and sheer impossibilities? Surely, there could be other explanations — or are labour values necessary here, by definition?

Joint production

The picture was clouded further in the 1970s. Building on Sraffa’s Production of Commodities by Means of Commodities (1960), Ian Steedman (1975; 1977) and others claimed that the labour theory of value is not only inconsistent and redundant, but also impossible. The basic problem comes from ‘joint’ production processes, where multiple inputs jointly produce multiple outputs. Such jointness makes it difficult to identify which inputs are ‘responsible’ for which output, leading to strange mathematical results, with labour values becoming indeterminate, nil, or even negative!

This predicament, to which we return in Chapters 8 and 12, arises because, quantitatively, production is forever a black box. Even if we could identify its inputs and outputs (itself a questionable proposition), we could never examine the inner process by which the former quantitatively ‘generate’ the latter. The only way to attribute outputs to inputs is indirectly — first by finding a unique mathematical relationship between them, and then by assuming that this relationship represents the productive transformation occurring inside the black box. This superficial solution works well when there is only one output and therefore a single mathematical equation. But it tends to fail with joint production. The latter requires simultaneous equations, and there is nothing inherent in joint production to guarantee that these equations could be solved with unique and positive labour values.

The existence of joint production is potentially devastating for the labour theory of value. Since everything in that theory depends on labour values being positive, the possibility that they could be undefined, nil, or negative undermines Marx’s ‘laws of motion’ and, indeed, the very meaning of exploitation. These implications are all the more serious since joint production is the rule rather than the exception. In fact, even when there is only one sellable output, the process is still joint insofar as it also generates a (somewhat) depreciated constant capital.

Some Marxists have tried to minimize the significance of jointness by arguing that modified (i.e. depreciated) constant capital is not produced for the market and therefore should not be counted as a commodity (for instance, Fine and Harris 1979: 41–42).77 The basis of this claim, though, is difficult to comprehend. Entire firms are constantly bought and sold on the market for real dollars; indeed, some firms, particularly in research and development, are formed with the sole purpose of being sold to the highest bidder. And with that being the case, why should we consider second-hand machinery and structures as non-commodities? Alternatively, if we are to accept Fine and Harris’ position, should we not, just to be consistent, classify all intermediate products as non-commodities?

Another escape route is to argue that capitalist specialization tends to reduce jointness, so that eventually, if not immediately, theory will prevail over reality (ibid.). Specialization, however, is not the same thing as jointness. The former is about division, the latter about interaction, and more of one does not imply less of the other. To illustrate this point, consider the fact that General Electric has hundreds or thousands of different job descriptions, that its different corporate segments are formally associated with different types of output, and that these outputs are not the same as those of Ford and Exxon. These divisions attest the heightened specialization of contemporary capitalist production, but what do they reveal about the interaction of its different processes?

Do these divisions tell us what portion of the labour of a General Electric accountant, engineer, or driver goes into a GE pump? And when General Electric sells this pump to Ford, can we know — based on these divisions and without resorting to prices — how much of that labour is being ‘transferred’ to a typical Ford car? How will our answer differ if the plant using the pump jointly produces two types of automobiles rather than one? And what if the entire process were to be ‘internalized’ by Ford taking over GE’s pump division? Would such a takeover make the process less or more joint? Labour-value theorists cannot answer these questions; and as long as the issue of jointness hangs, the input–output structure stays unspecified and the theory remains stuck.

Capitalism sans values?

According to Cornelius Castoriadis (1988, Vol. 1: 20), Marx’s acceptance of wage inequality during a socialist transition to communism — ‘to each according to his work’ — shows how much he had bought into the ‘self-evident facts’ of bourgeois common sense; that is, into the presumption that we can somehow impute a product to its ‘producer’. As a 1958 AFL-CIO document on Automation and Technological Change puts it, this assumption can no longer be made, even in a socialist world: ‘Automation in its largest sense means, in effect, the end of measurement of work. . . . With automation, you can’t measure output of a single man’, and there is no longer ‘any reason at all to pay a man by the piece or pay him by the hour’ (cited in Tsuru 1993: 7, original emphasis).78

Paradoxically, Marx was remarkably prophetic in anticipating the demise of his own labour theory of value, and for this very reason. His insight is worth quoting at some length:

As large-scale industry advances, the creation of real wealth depends less on the labour time and quantity of labour expended than on the power of the instrumentalities set in motion during the labour time. . . . Human labour then no longer appears enclosed in the process of production — man rather relates himself to the process of production as supervisor and regulator. . . . He stands outside of the process of production instead of being the principal agent in the process of production. In this transformation, the great pillar of production and wealth is no longer the immediate labour performed by man himself, nor his labour time, but the appropriation of his own universal productivity, i.e. his knowledge and his mastery of nature through his societal existence — in one word, the development of the societal individual. . . . As soon as human labour, in its immediate form, has ceased to be the great source of wealth, labour time will cease, and must of necessity cease to be the measure of wealth, and the exchange value must of necessity cease to be the measure of use value. . . . The mode of production which rests on the exchange value thus collapses.

(Grundrisse der Kritik der politischen Oekonomie: 592f, translated from the German by Marcuse 1964: 35–36, emphases added)79

And, from there, …

with the abolition of the basis of private property, with the communistic regulation of production … the power of the relation of supply and demand is dissolved into nothing, and men get exchange, production, the mode of their mutual relation, under their own control again. . . .

(Marx and Engels 1970: 55)

This intriguing idea is typical of Marx’s search for inherent contradictions: the very development of the forces of production set against the relations of production is certain to undermine the quantitative logic of capitalism. In a complex socio-technological setting, he argues, the direct relationship between labour inputs and final prices is bound to break down. When that happens, price setting becomes increasingly arbitrary; capitalists lose their moral conviction and business compass; and with their sense of hegemony thus undermined, their system becomes vulnerable and eventually unsustainable.

Marx of course was proven wrong in believing that the demise of his own theory would bring capitalism down. Perhaps, contrary to his conviction, labour values are not a prerequisite for a functioning capitalism in the first place. However, his insight into the societal nature of production and into the insurmountable problems it creates for the theory of political economy was prescient.

The transformation so far

As our brief journey so far suggests, labour values cannot easily be transformed into prices. To recap, again, the transformation involves two parts: a first, logical step from labour values to prices of production and a second, logical/empirical step from prices of production to market prices. Beginning from the end and assuming that the first step is feasible, we saw that labour values still shed little light on the actual trajectory of capitalism. The reason is that the second step is inherently incomplete: Marxist value theorists readily agree that there is more to market prices than prices of production, yet deliberately refuse to theorize anything other than those prices. And since the theory itself gives no indication of how important these additional factors may be, its significance cannot be assessed.

Some Marxists have tried to settle the issue with statistical analysis. Their results seem very robust — but only because the dice in their tests are loaded and the tests themselves are circular. These studies tend to measure the value–price correlation not of individual commodities, but of total sectoral outputs. Worse still, given that labour values cannot be observed, the researchers commonly ‘derive’ them from market prices. The result is to have us go in a circle. We are shown that market prices (presented as values) are tightly correlated with market prices, but it isn’t clear how this revelation vindicates the labour theory of value.

The problem, however, begins much earlier, with the logical conversion from labour values to prices of production. First, this conversion is logically inconsistent — and can be made consistent only at the cost of casting out many of Marx’s key conclusions. Second, even if perfectly consistent, the conversion is mathematically redundant in that it adds little to what we know to start with. And finally, once we enter the realm of joint production, it becomes difficult if not impossible to even specify the labour values to be converted.

New solutions, new interpretations

Value theorists have responded to these challenges with a voluminous literature of new solutions. Most have accepted that Marx’s own transformation was problematic and that the subsequent critiques needed to be addressed. But they’ve also insisted that the difficulties can be overcome — by modifying one or more of Marx’s assumptions.

Changing the assumptions

Michio Morishima, for example, examined the so-called Fundamental Marxian Theorem, according to which a positive rate of profit both implies and is implied by a positive rate of exploitation. He argued that the Theorem is valid — but only if we valuate commodities differently than Marx. Whereas for Marx value is based on average labour time, Morishima claimed that the Theorem would hold only if value is counted in minimum labour time (Morishima 1973; Morishima and Catephores 1978). Another approach was offered by David Laibman (1973–74). Laibman correctly observed that the class struggle rages not over the rate of profit, but over the distribution of income; and he therefore concluded that it is the rate of exploitation rather than the rate of profit that tends to equalize across industries.

A very different and highly original solution was developed and empirically examined by Emannuel Farjoun and Moshé Machover (1983). Conventional Marxist models, they argued, specify their variables as discrete, equilibrium magnitudes. But the competitive capitalist reality is inherently stochastic. Competition, they noted, tends to disperse rates of profit as well as equalize them. Of these two processes, the former is stronger, both within and across industries, and rates of profit, as a result, do not converge to equality but rather spread across a range. This tendency means that we should not expect the correspondence between market prices and labour values to be deterministic but probabilistic. And with determinism gone, the logical consistency of the system obviously is no longer an issue.


Over time, the proliferation of different solutions, the restrictive nature of their assumptions and the heightened disagreements among their advocates have served to complicate and fracture Marx’s original framework. Most value theorists, though, have remained unmoved by this increasing complexity.

According to Marx, the deviation of prices from values is inherent in the price-form itself. ‘This is no defect’, he insists, ‘but, on the contrary, admirably adapts the price-form to a mode of production whose inherent laws impose themselves only as the mean of apparently lawless irregularity that compensate one another’ (Marx 1909, Vol. 1: 115). From this viewpoint, the transformation problem undermines neither the value principle nor the insight it offers into capitalist relations. ‘On the contrary’, argues Laibman (2000: 314), the complicated process of converting values into the prices ‘is a further development of a core insight: capitalist market relations mystify and obscure — and thereby enable — the class exploitation at the heart of the system’ (original emphasis). Indeed, in this sense, says Laibman, the rejection of Marx’s pulling and redistributing process merely serves to show that ‘exploitation, far from taking place in mutually isolated sectors, is systemic and inseparable from the entire web of interconnections in the structure of production and exchange’ (ibid.).

The problem with this approach is twofold. First, it is hard to evaluate a theory whose purpose is both to explain and obscure reality (since a weaker explication implies greater mystification — and vice versa). Market prices may indeed seem chaotic and bourgeois theory certainly serves to mystify them. But it is doubtful that Marx wanted his own value theory to serve the same end. Second, all things being equal, tells us Occam’s razor, the best solution is the simplest. Complicated explanations tend be intellectually unattractive and politically ineffective — a suicidal combination for a theory whose ultimate purpose is praxis.

Changing the definitions

And so there has emerged since the 1980s a different approach altogether, one that offers not new solutions, but new interpretations.80 According to the new interpretationists, the theory that Marxists have laboured to fix for over a century is indeed logically inconsistent and plagued by insoluble problems — but that theory isn’t Marx’s. Interpreted correctly, they argue, Marx’s texts yield a very different labour theory of value — one that is both internally consistent and fully congruent with all of his theoretical results.81

The new-interpretation literature has different variants, all sharing one thing in common: they redefine the meaning of labour value. In what follows, we focus on the version that departs most radically from received Marxism — the Temporal Single-System Interpretation, or TSSI.82 According to the TSSI, Marx’s ‘true’ value theory differs from the conventional interpretation on two main counts, which we consider in turn.

Recounting costs

First, the system is not simultaneous but temporal. To illustrate the difference, consider the production of a personal computer by Dell. The company purchases inputs, such as motherboards from Intel, hard drives from Toshiba, sound cards from Creative Labs, etc.; it assembles these components with its own workers; and then, three weeks later, when the process is complete, it sells the computer to the final consumer. According to the standard, simultaneous approach, the value of these inputs should be recorded at current rates. They should be measured based on what they would have taken to produce now, at the end of the process, regardless of what they actually took to produce earlier in the process. This assumption guarantees that commodities that act both as inputs and outputs have a single value.

The TSSI disagrees. This logic makes no business sense, and certainly it isn’t Marx’s. The dollar costs are recorded when Dell purchases its inputs, not when it sells its output. To be consistent, argue TSSI advocates, the same temporal sequence must also hold for labour values. We need to record them when the inputs enter the process, not when the output leaves.

There is really no way to decide which of these two methods is ‘valid’. According to Michael Perelman (1990), Marx himself left the issue open. He used antecedent (past) labour at the micro level of the firm and coexisting (current) labour at the macro level of capitalism as a whole — though without indicating why. Conventional accounting practices make a similar distinction between the LIFO and FIFO methods — and here, too, there is no ‘right’ or ‘wrong’. With LIFO (meaning ‘Last In, First Out’), Dell would calculate its costs currently, based on the price of its most recently purchased inputs. With FIFO (or First In, First Out), it would compute the cost historically, based on the price of the most dated inputs in its inventory. The two methods can have dramatically different financial consequences — depending on the rate of inflation, tax laws, transfer pricing, currency movements and other assorted considerations, including the duration of the production run and the path of technical change. But, then, there is no objective yardstick — that is, other than the laws, habits and customs of bourgeois society — to tell us which method to use. Now, unlike the accountants, who deal with observable prices, Marxists do not even know what abstract labour looks like. So it seems that their quest for the Holy Grail here is a bit presumptuous.

Theoretically, however, historical valuation is far more ‘flexible’ than a current one. Current valuation as used by the conventional approach requires all instances of a given commodity to have one and only one value, so that a barrel of oil has the same value whether it appears as an input or an output. By contrast, historical valuation as used by the TSSI allows each barrel of oil to have its own value — depending on its particular temporal position in the production process. This difference allows the TSSI to appear more theoretically ‘robust’ than its conventional alternative — but that appearance is misleading. Obviously, if the same commodity can have multiple values, the likelihood of the valuation system as a whole being logically inconsistent is much reduced.

Prices as values

Labelling these considerations ‘theoretical’, though, is somewhat misleading — for the simple reason that TSSI really is more of an accounting device than a scientific proposition. The definitional nature of the TSSI is evident from its second assumption. According to this assumption, Marx had in mind not two systems, but one. Recall that, in the standard dual-system view as formalized by Bortkiewicz, labour values and prices of production are determined separately, each in their own distinct system, and that the question is whether or not the former can be mathematically ‘transformed’ into the latter. This question does not even arise in the TSSI. Here, there is only one system for both prices and values and therefore nothing to transform in the first place.

The language of the last sentence is a bit deceptive. In fact, the single system articulated by the TSSI does not have prices and values. It has prices as values. The distinction is crucial. The conventional Marxist approach argues that labour values are the cause of prices. This causal link is meaningful because the definitions of the two magnitudes are different. Prices are counted in money, whereas values are counted in labour time. The two magnitudes could be used interchangeably — but only if the theory is correct.

The setup of the TSSI is completely different. Here, there is no point in asking whether or not prices are equal to values, simply because values are defined by market prices. What the empirical studies do out of necessity and with much unease, the TSSI marshals with fanfare and as a vindication of Marx. The value of constant capital used by Dell is defined here as the market price the company paid for its (depreciated) capital, raw materials and semifinished goods. Similarly, the value of the labour power it employs is defined as the money wages paid to its workers. Finally the company’s surplus value is defined by subtracting from its current dollar revenues the constant and variable capital, as well as an unknown discrepancy that may arise from unequal exchange.83 Labour is still held responsible, by definition, for the creation of all value in the aggregate. But it is no longer necessary for any of the underlying computations. Individual values are defined as the sum of market prices, with the result that the single-system equations no longer contain embedded labour coefficients.

New interpretationists do not see a problem with this circularity. Duncan Foley, for instance, argues that when Marxists define values by prices they do nothing different than Newton, who defined force by mass and acceleration (F = m × a). In each instance the definition serves a purpose insofar as it ‘decisively disciplines and directs scientific investigation in conceptual and fruitful ways’ (2000: 28). And, of course, there is nothing wrong with definitions per se.

But there is an important difference between the two cases: whereas Newton offers one definition for force, the new interpretationists have two for value: one based on price, the other on labour time. And since value is made proportionate to both price and labour time, it follows that prices are proportionate to labour time and that the labour theory of value is true before we even begin. Kliman and McGlone (1999: 44) claim that this is a ‘circular, Hegelian type’ of explanation, although it isn’t clear how this supposedly dialectical technique differs from the positive neoclassical habit of defining the quantity of capital by its price or the marginal product of labour by the wage rate. Given these considerations, it is perhaps little wonder that, while the definition of force enabled Newton to accurately describe, explain and predict the movement of actual bodies, the concepts of utils and labour values enable their theorists to say pretty much nothing about the actual movement of prices.

Proponents of the TSSI argue that this is what Marx had in mind. And maybe they are right. But if that was Marx’s intention, it seems unclear why he would bother to call the result a theory of value, let alone a labour theory of value. The TSSI says nothing about labour, save for asserting that labour creates all values. And it is not a scientific theory in the sense of cause X (value) explaining consequence Y (price). It merely states the truism that current money prices are the sum of past money prices, plus a deviation.

Writers who advocate this approach emphasize that they do not claim Marx’s value theory to be empirically valid. Their only purpose is to show that his framework is logically consistent and fully in agreement with his analytical claims. But in the process of achieving this purpose, they seem to have shifted into reverse. Whereas Marx’s labour theory of value claims to reason phenomena according to their ‘essence’, the TSSI advocates move in the very opposite direction. Not only have they turned his theory into an irrefutable tautology, but by defining labour values in price terms, they have made it practically impossible to transcend the very appearance they wish to explain. They have ended up with a dogma.

  1. Some, like Karl Polanyi (1944: Ch. 6), argue that labour (or labour power from a Marxist perspective) is really a fictitious commodity, since, unlike true commodities, human beings generally are not produced for the purpose of sale on the market. This reasoning is vulnerable on three counts, all related to the notion of ‘purpose’. First, it is not at all clear that labour power isn’t produced for the market (aren’t capitalist institutions geared very specifically for the production and reproduction of human workers, and isn’t it true that most people in capitalist societies indeed raise their children with an eye to their future saleability?). Second, it isn’t clear whose purpose counts here: the purpose of the worker’s parents? Of the worker herself? Of her employer? Of the capitalist class more broadly? Finally, why is the original purpose of conceiving a child of any significance — given that most people end up selling their labour power regardless of anybody’s intentions?

  2. Marx commonly refers to ‘socially necessary labour’ as shorthand for ‘socially necessary abstract labour’. Although Marx himself didn’t, we use the latter expression since, as we shall see, only abstract labour can be added up.

  3. ‘Value, therefore, does not stalk about with a label describing what it is. It is value, rather, that converts every product into a social hieroglyphic. Later on, we try to decipher the hieroglyphic, to get behind the secret of our own social products; for to stamp an object of utility as a value, is just as much a social product as language. The recent scientific discovery, that the products of labour, so far as they are values, are but material expressions of the human labour spent in their production, marks, indeed, an epoch in the history of the development of the human race, but, by no means, dissipates the mist through which the social character of labour appears to us to be an objective character of the products themselves’ (Marx 1909, Vol. 1: 83).

  4. Knowledge of prices enables computation of the various stock and flow ratios of the price system, such as the money rates of profit and exploitation, money income shares, the money rate of accumulation, etc. Hence, for the sake of brevity, whenever we refer to prices we also refer to the ratios that can be derived from them.

  5. On the intertwined evolution of probability and statistics, scientific measurements and liberal political economy, see Hacking (1975; 1990), Porter (1995), Alder (1995; 2002) and the collection of Klein and Morgan (2001).

  6. Denote, for the i-th sector, unit market price by mpi, unit labour value by lvi and the level of output by qi. The correlation across sectors between unit price and unit value associates mpilvi, whereas the correlation across sectors between the total price of the output and the total value of the output associates qi × mpiqi × lvi. Note that in the latter correlation qi is common to both magnitudes.

  7. On the issue of spurious correlation, see Freeman (1998) and the debate between Kliman (2002; 2005; 2007: Ch. 11) and Cockshott and Cottrell (2005). The latter writers argue that, since commodities have no universal quantities (a box of breakfast cereal cannot be directly compared to a passenger aircraft), the correlation between their unit price and unit value is meaningless. This problem of incomparable units could easily be bypassed by correlating relative prices with relative values. In our example here, we would correlate the ratio between the price of cereals and the price of aircraft on the one hand with the ratio between the value of cereal and the value of aircraft on the other.

  8. To avoid undue attention, these assumptions are often tucked in endnotes and technical appendices. Commonly, the researcher will state them cryptically, with minimal discussion and seldom with an apology. See, for example, Wolff (1975: 936), Ochoa (1989: 427–29), Shaikh and Tonak (1994: 80–81), Alemi and Foley (1997: 2) and Cockshott and Cottrell (2005: 312).

  9. Some Marxists have questioned the wisdom of empirically testing the labour theory of value, lest the results prove inconclusive: ‘Suppose, for example, that the correlations between embodied labor coefficients and market prices had turned out to be much lower, or to fall over time, or to be low in certain capitalist economies. Are we to conclude that the labor theory of value does not hold, or is weakening over time, or holds only in some capitalist economies?’ (Foley 2000: 20). The writer leaves these questions unanswered.

  10. In fact, it is not entirely clear why labour mobility should equalize the rate of exploitation rather than the wage rate only, although for some reason this question has attracted relatively little attention.

  11. Bortkiewicz’s arguments were summarized in Paul Sweezy’s Theory of Capitalist Development (1942) and later included in his translated collection, Karl Marx and the Close of his System (1949).

  12. Save for special assumptions, this inequality means that in simple reproduction the overall price of the wage goods produced by the system differs from the total value of wages (so workers consume less or more than capitalism makes available to them); that the overall price of investment goods differs from the total value of the used up constant capital (so there is net investment or divestment); and that the overall price of luxuries is different from the total profits of capitalists (so they must save or dissave).

  13. Prices of production, writes Marx, ‘are conditioned on the existence of an average rate of profit’ which itself ‘must be deduced out of the values of commodities. . . . Without such a deduction, an average rate of profit (and consequently a price of production of commodities), remains a vague and senseless conception’ (1909, Vol. 3: 185–86, emphasis added).

  14. For reiterations of this view, see also Mattick (1972), Baumol (1974), Fine and Harris (1979: Ch. 2) and Harvey (1982: 35–38).

  15. The question of whether or not commodities are ‘purposely’ produced for the market and the relevance of such purposiveness for political economy are discussed in footnote 1 above.

  16. As we shall see later in the book, according to Veblen the issue is not automation but the hologramic nature of production. The fact that production is social means that we cannot impute output to ‘its’ producer even in the simplest of social settings.

  17. We much prefer Marcuse’s translation to the official one given in Marx (1857: 704–5).

  18. Key collections and reviews of this literature include Freeman and Carchedi (1996), Foley (2000), Freeman, Kliman and Wells (2000) and Kliman (2007).

  19. Andrew Kliman (2004: 23, Table 2.1) compares the different interpretations on how well they replicate Marx’s theoretical claims.

  20. For a concise exposition of the TSSI, see Kliman and McGlone (1999). Other versions include the particular ‘New Interpretation’ attributed to Foley (1982) and Duménil (1983) and the ‘Simultaneous Single System Interpretation’ associated with Wolff, Roberts and Callari (1982) and Moseley (1993), among others.

  21. This discrepancy, although unknowable for individual commodities, disappears in the aggregate since, by assumption, unequal exchange cannot create value, only redistribute it.