13.07.2023
Lcontent and price
Moshé Machover expands on his arguments in favour of applying statistical reasoning to the problems of analysing capitalism at its most basic level
What is the relationship between the amount of labour embodied in products and the price paid when these products are sold and bought as commodities? In other words, what is the relationship between the life activity of the workers and the alienated form of money? This is among the central topics discussed in a recent book coauthored by Emmanuel Farjoun, David Zachariah and myself.^{1} Its title is a bit of a mouthful, so I will refer to it by its punchier subtitle, A Labor theory of capitalism (briefly, LTC).
In writing our book we had in mind a reader who is a supporter of the interests of the working class, but is not necessarily familiar with Marxian political economy. However, the present article, summarising some ideas presented in LTC, is addressed specifically to Marxists, who presumably have some knowledge of Marx’s economic theory. If you do have such knowledge, this article will seem somewhat familiar, but also somehow offbeat, as our approach is unorthodox and bypasses a major controversial and unresolved issue in the Marxian theory of price.^{2} I will try to make the exposition as simple as possible, and accessible to readers without technical expertise.
Two levels
Under capitalism, economic activity (society’s material metabolism) takes place at two levels: the ground level of production and consumption; and the superimposed level of circulation, the market. At the ground level, goods and services appear as products. A product may end up as a consumption item, or serve as input in the production of some other products. Thus, for example, electricity is a product that may be consumed for domestic lighting, or utilised for powering a machine operated in production.
The passage of most products, from the point of their production to the point of their use (as a consumption item or as input in production), is mediated by the market. Here, at this level of the economy, goods and services appear as commodities, undergoing transactions of saleandpurchase. Thus, electricity must be sold by the producer company and paid for by its user  except where that user happens to be the electricity company itself, consuming it inhouse. The market existed, of course, in older economic systems, but has acquired an overarching role under capitalism.
Each of the two levels of the economy is associated with a measure that attaches a numerical value to goods and services.
First let us consider the market. Here, commodities have an obvious common measure: price. This measure is in most cases immediately observable: a commodity normally comes with a price tag attached to it (figuratively if not physically). But it is also mysterious: the price of a commodity does not belong to it as an inherent attribute, but is assigned to it behind the scenes by a process that needs to be uncovered.
Now consider the ground level of the economic metabolism. Here products have a socially natural common measure: their labour content (briefly, L‑content). This requires some elaboration. Every product has direct inputs of (some or all of) the following three kinds: (a) labour, (b) previously produced products, (c) free gifts of nature (unprocessed natural resources). For example, production of wheat requires direct inputs of (a) farming labour, (b) previously produced inputs, such as seeds, fertilisers, fuel for powering farming machinery, etc, and (c) rain and sunshine. Now, inputs of kind (b) were themselves produced using inputs of the same three kinds, which are indirect inputs of the endproduct (wheat, in our example).
In the following diagram the first line shows schematically the direct inputs of a given product. In the second line the direct inputs of kind b (the previously produced inputs) are in turn resolved in terms of their inputs. Pushing this analysis further and further back, the b section dwindles away, and we end up at the limit with just two kinds of ultimate inputs: labour and gifts of nature.^{3}
The L‑content of a product is the total amount of direct and indirect labour input required (under prevalent social and technical conditions) to produce it, measured in labour time, say workerhours.
This is essentially what Marx  following Adam Smith and David Ricardo  defined as “the magnitude of the value of any article”.^{4} However, in LTC we avoid using the term, ‘value’, for this magnitude and stick to calling it ‘L‑content’  a practice that I shall follow here. Our main reason is that the term, ‘value’, is loaded with multiple connotations that we wish to sidestep. In particular, we would like to avoid confusion with ‘value added’  a quantity of money on which value added tax is levied in many countries.
Our detailed definition of L‑content in LTC differs in some technical details from Marx’s definition of value. These differences, however, do not affect the present discussion. So you may assume that in what follows ‘L‑content’ is just another term for Marx’s ‘measure of value’.
Unlike price  a superficial quantity, which is overtly attached to a commodity  a product’s L‑content inheres in it at birth, as it were, but is by no means easy to quantify exactly. It requires a highly complex calculation. The direct labour input that goes into a given product (using prevalent methods of production) is often fairly easy to quantify; but to this must be added the L‑content it inherits from its previously produced inputs  of which there may be a large number, each with its own previously produced inputs. A precise calculation of a product’s Lcontent is in most cases unfeasible, and an approximate estimate is the best we can expect. (By the way, very similar difficulties arise, for example, in quantifying the carbon footprint of a product.)
Note that products and commodities are not identical categories; they merely overlap. On the one hand, many kinds of product are not commodities. Examples of this are material objects and services provided free as public goods by the state or charities; and those produced privately for the producer’s domestic use or given as gifts. On the other hand, there are many kinds of commodity that are not products: they have no labour input and hence have zero Lcontent. Example of this are virgin land or untapped mineral resources held as property; and a great variety of abstract commodities, such as patents, copyrights and other transferable legal rights. Presentday money is also a commodity  indeed a universal one  that is not a product. Of course, the overlap between the two categories is very large: in a modern capitalist economy a huge number of products are also commodities.
The relationship between the two measures, Lcontent and price, is of prime interest, for two reasons. For the classical economists, there was no doubt the purely scientific drive of trying to explain price in terms of Lcontent: science generally aims to explain surface phenomena by means of deeperlevel ones. But Marx’s main motive for investigating this relationship was promoting the interests of the working class. For workers, individually and collectively, Lcontent arises directly from their activity as direct producers; whereas price is an alienated quantity fixed by alien forces. Marx’s great insight was that in order to analyse and expose the exploitation of labour by capital  the core antagonism between the two main classes of capitalist society  it is necessary to delve into the ground level of the economy and observe the division of the Lcontent created by workers into two parts: the share kept by them (in the surface form of money wages), and the ‘surplus’ share appropriated by capital (in the surface form of profits).
A central idea I pursue in the present article is the following. Since the numerical value of Lcontent of products is not directly observable, it is important to have a ‘bridge’ connecting price and Lcontent, allowing the conversion of monetary units into units of Lcontent: workerhours.
The importance of such a bridge from a working class viewpoint cannot be overstressed. Suppose, for example, that a worker is paid at the rate of €30 per hour. She can relate immediately to this sum of money as a consumer: she knows what mix of consumer goods she can buy for it. But what does this sum of money represent in terms of her lifeactivity as a producer? Now, suppose that scientific investigation reveals that the rate of conversion between the two measures is €60 per workerhour. Then she realises that what she receives for one hour of labour is equivalent to onehalf of what her class contributes to the social product! This knowledge is empowering in the class struggle.
As we show in LTC, there are other useful applications of such a bridge. One such application, which I will discuss later on, is a way of quantifying the rate of increase of the productivity of labour, which is an enduring longterm trend in the capitalist economy.
Simplified model
In volumes 1 and 2 of Capital, as well as in Value, price and profit,^{5} Marx assumes that the price of a commodity is proportional to its Lcontent.^{6} For the sake of precision, he remarks a couple of times that this proportionality applies to what Adam Smith calls a commodity’s “natural price”, around which actual market price fluctuates and to which it gravitates when supply and demand are at equilibrium. But, apart from these remarks, and in all the numerical examples he presents in the first two volumes of Capital, he takes actual prices to be proportional to Lcontent. This means, for example, that if commodity A has three times the Lcontent of commodity B, then the price of A will be three times the price of B. Put another way: if we divide the price of A (as measured, say, in euros) by its Lcontent (as measured in workerhours) and do the same for commodity B, we get the same result in both cases.
I would like to introduce here a bit of terminology. We call the ratio between the price at which a given commodity is soldandbought and its Lcontent the price rate of that commodity.^{7} Thus the assumption that prices are proportional to Lcontent is equivalent to saying that all commodities soldandbought (in a given short period of time) have the same price rate.
There is no evidence or any other good reason to believe that such proportionality between price and Lcontent ever existed in reality, except perhaps in an extremely rough approximate sense.^{8} Marx uses this model as a simplified didactic tool for exposition of his innovative theory of exploitation: capital exploits labour by paying workers for only part of the Lcontent created by them, and appropriates for itself the remaining ‘surplus’. But in volume 3 of Capital, he abandons this simple proportionality fiction and puts forward a much more complex hypothesis regarding the relationship between the two measures.
I shall discuss this hypothesis in the next section. But right now I propose to suspend disbelief in the proportionality assumption and work out a simple instructive exercise that will come in handy later on. So bear with me and let us assume that price is strictly proportional to Lcontent. Using this assumption, we obtain a simple way of converting monetary units  say euros  into units of L‑content: workerhours. I illustrate this with the following example.
Consider a firm whose workers produce widgets, which the capitalist owners of the firm sell on the market as a commodity. Suppose the firm’s workers perform a total of 4,000 workerhours of labour during a given week. These 4,000 workerhours are added to the L‑content of the nonlabour inputs used up during the week. Thus the L‑content of the widgets produced in the given week is the sum of the L‑content of those inputs plus the new 4,000 workerhours directly added by the firm’s workers.
Now suppose the value added of the firm in the given week  which the firm must report to the tax authorities  is €240,000. Please note that here the term, ‘value’, is used not in Marx’s sense, but in the common official and everyday sense. By definition, ‘value added’ is the difference between the sale price of the output and the cost price of its nonlabour inputs (so these costs exclude wages!). In our present example, the firm sold widgets for a total of €240,000 over and above what it paid for the nonlabour inputs used up in their production. What does this new €240,000 pay for? Clearly, it is the price of the new L‑content of 4,000 workerhours created by the workers! Dividing the former quantity by the latter, we get €60 per workerhour. This is the price rate of what the workers added to the nonlabour inputs in the given week. Each workerhour of labour performed during production of the widgets is worth €60 to the firm.^{9} For the record, here is the general formula we have used to arrive at the price rate:
Note that so far we have not made use of the proportionality assumption. What this assumption implies is that we should get the same bottom line, the same price rate, irrespective of which firm or which product we consider. The rate whereby units of money are converted to workerhours according to our general formula should be the same, whether we consider widgets or any other product sold as a commodity; this ratio would apply uniformly to the entire economy.
I pointed out in the beginning that the L‑content of a product is a hidden quantity, not amenable to precise calculation. But in this simplified model we would be able to calculate indirectly the L‑content of any product sold as a commodity in the given week. In our example we found that the price rate was €60 per workerhour. If this holds uniformly across the economy, it follows that in the given week each euro in the price of such a commodity represents one workerminute of L‑content.
For the formula we have just used for the price rate, we needed the following data: the value added and the total number of workerhours employed by the given firm. There is an alternative formula for calculating the price rate, which uses instead of the latter data (total number of workerhours), two other data: the wage share, defined as the share of the value added, which the firm pays as wages; and the average wage rate (ie, average pay for one hour of labour). This formula can be derived from the previous one by a simple algebraic manipulation:
For example, suppose that the widget firm pays onehalf of its €240,000 value added as wages (the other half is retained by the firm as profit). This means that the wage share is half, or 0.5. Thus €120,000 is paid out in wages for 4,000 workerhours. It follows that the average wage rate is €30 per workerhour. Using our new formula, we obtain:
 which is the same result we got before.
Let me point out the great importance of the wage share as a parameter in the present simplified model. The proportionality assumption implies that the wage share in money terms is equal to the share of the wages in terms of L‑content. Thus, in our illustrative example, since the wage share is half of the value added, which is quantified in money terms, it follows that what the workers receive is also equal to half of the L‑content they contribute to the product.^{10}
Transformation
In volume 3 of Capital, Marx abandons the simplified model and replaces it by a much more complex one.^{11} His reason for discarding the simplified model was a good one. As a simple deduction shows, the proportionality assumption implies that a firm’s rate of profit would depend inversely on the ratio between its fixed capital used in production and the amount of labour performed in production.^{12} The higher this ratio, the lower the rate of profit. In other words, firms in which the amount of fixed capital per unit of labour is high would derive a lower rate of profit than firms which have a smaller amount of fixed capital invested per unit of labour. This is not quite the case in reality; so the simplified model appears to be refuted by empirical evidence.^{13}
The transformation hypothesis (briefly, TH) is presented in part 3 of volume 3 of Capital, especially in chapter 10. I call it a ‘hypothesis’ because, in my opinion, this is what it is: I know of no evidence for its validity; its plausibility is a matter of judgment.
The basic conceptual assumption underlying the TH is that at equilibrium the unit prices of all types of commodities produced by the economy have determinate numerical values, which Marx calls prices of production; and the rates of profit accrued by capitals in all production firms are equal.
Of course, everyone knows that if you shop around you will find that the same type of commodity is sold at the same time by different sellers at a variety of unit prices; and rates of profit vary greatly both within industries and between them. So the equilibrium that the inputoutput model describes is an ideal one.
However, it is implied that the real economy is driven by market forces  the forces of competition  towards an ideal equilibrium of this sort, and is only prevented from actually reaching it by various disequilibrating forces, that act as ‘noise’.
A crucial further assumption of the TH is that the uniform rate of profit at equilibrium is equal to the average rate of profit that would obtain if all commodities were sold at prices proportional to their L‑content. This assumption connects the model posited by the TH with the simplified model of volume 1, and therefore justifies regarding the TH as a modification  albeit a farreaching one  of the old model.
The TH has been challenged on at least two grounds, is widely regarded as problematic, and has given rise to a prolific controversy. I will outline this controversy very briefly, because the highly technical issues raised by it have nothing to do with my arguments for disregarding and bypassing the TH.
The first and oldest argument against the TH is that, when it is cast in rigorous mathematical form, it leads to a system of equations that is more than likely to be inconsistent, hence unsolvable.^{14} Some orthodox Marxist economists have argued for a different mathematical representation of the TH, which results in a consistent system of equations. Of course, consistency is only a necessary condition for the validity of the TH, but not a sufficient one. For that, some positive evidence would be required.
The second argument against the TH was mounted in 1983 by Emmanuel Farjoun and me in our book Laws of chaos^{15} (briefly, LOC), which is a prequel to LTC. We argue that the uniformity assumption  namely the assumption that a competitive economy tends to a state of equilibrium at which rates of profit are equal across the economy  is fallacious. By the way, Marx inherited this assumption from David Ricardo, and in LOC we show that it has also been shared by several modern nonMarxist mathematical economists.
However, let me put these controversies aside, as my reason for avoiding the TH is that it is barren: it has no useful or even testable consequences. At best, it is an attempt to provide a highly theoretical explanation of how the equilibrium price of any given product is determined by L‑content  not just its own L‑content, but that of virtually all products in the economy. (This is because of the way the numerical value of the assumed uniform rate of profit is defined.) I do not believe that such a deterministic explanation is possible. But, even if it were, the TH does not provide us with a way of calculating the price of production of any product, so that it might be tested against real empirical data.
Worse still: the TH does not deliver a means of converting prices back into units of L‑content. It breaks the bridge between the two measures, which was suggested by the simplified model, but does not construct an alternative route. This is a very serious problem, because Marx’s own theory of exploitation, which is of great importance to the working class, and which we would like to uphold in essence, depends on reasoning in terms of L‑content, not of prices.
We are faced with a dilemma: the bridge between the two measures supported by the simplified model is faulty, as it rests on the fallacious proportionality assumption. The TH does not provide us with any viable bridge at all. In fact, it leads nowhere.
I will now proceed to show how the faulty bridge can be repaired. Bypassing the TH, we shall take another route.
Methodology
In LOC Farjoun and I proposed a methodology for dealing with macroeconomic problems inspired by statistical mechanics, a branch of physics. Instead of seeking laws governing the behaviour of single objects  the price of a particular commodity, the rate of profit of an individual firm  we look for laws governing mass collections, ensembles, populations.
In this article, addressed to nonspecialists, I will not provide formal definitions of technical terms, such as ‘population’, ‘statistical variable’ and ‘distribution’. Instead, I will start with a simple illustration that is probably familiar to most readers: a population pyramid. Look, for example, at the population pyramid of the United Kingdom shown in the Wikipedia article, ‘Demography of the United Kingdom’.^{16} What this pyramid shows is the distribution of a statistical variable across a population. The ‘population’ in this particular instance is literally a human population  that of the UK in a recent year. The ‘statistical variable’ here is age (measured in years). And the pyramid itself depicts the ‘distribution’ of this variable across the population: it shows the part of the population in each age range.
The data for such a distribution pyramid may be derived directly from a population census; but the laws of statistics (based on the mathematical theory of probability) provide a cheaper way of obtaining a very good approximation. If we take a large, random sample of the population, the shape of the pyramid of age distribution in the sample will be, with very high probability, very close to the pyramid of the population at large. (The larger the sample, the higher the probability and the closer the approximation.) In particular, important characteristic values of the atlarge distribution will be closely approximated in the sample. For example, the average age of the sample will be very close to that of the entire population. And the same applies to the ratio of males to females.
This statistical law is used by compilers of price indexes. The index serves to estimate the rate of price inflation from month to month, but it would not be feasible to look at the price of each commodity (or each consumer commodity, in the case of the consumer price index) on the national market. So the compilers of the index look at a sample  a sufficiently large and diverse, representative ‘basket’ of commodities  and by comparing its change of total price from one month to the next, they calculate a very good approximation to the real value of the rate of inflation.
Now let us turn to the economy of a large capitalist domain, such as the US, the European Union or China (or the entire global capitalist economy). Let us look at the relationship between the two measures  price and L‑content. While the assumption of strict proportionality between them is untenable, there is quite suggestive evidence for positive correlation. This evidence is necessarily imprecise, episodic and impressionistic, because the L‑content of a product can normally only be estimated as a rough approximation. But it has nevertheless led many scholars, long before Adam Smith, to put forward versions of the thesis of proportionality.^{17} Rejecting this assumption, what we advocate is addressing the relationship using the tools of statistics.
So, consider a ‘population’ comprising all the transactions of commodity saleandpurchase in the economy during a given period  say one particular week. In this population, consider the price rate of the commodity soldandbought in a given transaction. Recall that this is equal to its price divided by its L‑content. In the imaginary simplified model, price rate was a constant  the same for all transactions in the given week. But here, in the more realistic picture of the economy, price rate is a statistical variable  taking possibly different values for different transactions in the population.
The average value of price rate of our entire population will be of interest: it is, of course, equal to the total price of all commodities in the population divided by their total L‑content. The same applies to each selected group, each ‘basket’ of the commodities in the population; it has its price rate, equal to its total price divided by its total L‑content.
Now comes a crucial point: according to the laws of statistics, the price rate of any large and diverse ‘basket’, or sample, of the population is with high probability very close to the price rate of the entire population. It follows that the price rates of any two such baskets are, with very high probability, approximately equal, to a high degree of approximation.
Thus the proportionality of price to L‑content is retrieved as a correct law: not for individual products sold as commodities, but for representative baskets. Admittedly, this law is not deterministic, but probabilistic; not precise, but a good approximation. But such are lots of scientific laws governing the real world.
This law of proportionality allows us to reconstruct the bridge: to calculate the rate of conversion from monetary units to workerhours  the overall price rate for the entire economy. To do this, we must consider not an arbitrarily chosen single firm, but a large representative sample of firms or, indeed, all firms engaged in production in the given economy. We use the same formulas as in the first part of this article. The rate is given by the ratio,
or, equivalently, by the ratio,
Of course, here the quantities in these formulas  value added, etc  are not those for a single firm, but for the entire ensemble of firms.
Note that the resulting rate is an average for the entire economy. So, for example, if the rate is €60 per workerhour, it does not mean that every product sold for €60  or indeed any particular product sold for this price  embodies one workerhour of L‑content. What it means is that €60 will buy a representative basket, a mix of commodities that embodies one workerhour (to a high degree of approximation). Also, if a worker is paid at the rate of €30 per hour, it means that with this sum of €30 she can buy a representative mix of commodities that embodies 30 minutes of labour performed by the workforce of the given economy.
In LTC we use statistical reasoning to analyse several other aspects of the capitalist economy. I will end this article with a brief discussion of one of these.
Labour productivity
Productivity of labour is of obvious interest to the working class. From the workers’ viewpoint, the natural way to measure it is in terms of L‑content, using what in LTC we call the material measure of labour productivity. First, let us consider an individual type of product  say widgets. The productivity of widgetproducing labour is the arithmetical inverse (reciprocal) of the L‑content of one unit of this type of product: a single widget. Thus, if the L‑content of a single widget is 30 workerminutes, the material productivity of widgetproducing labour is 1/30 widgets per workerminute, or two widgets per workerhour.
Of particular interest is the rate at which productivity increases from one year to the next. In our example, if in the following year, due to increasing productivity, the L‑content of one widget falls to 29.25 workerminutes, this means that the productivity of widgetproducing labour has increased to 1/29.25 widgets per workerminute, which works out at approximately 2.05 widgets per workerhour. This represents an annual increase of 2.5% in the productivity of widgetproducing labour.
What about measuring the aggregate material productivity of labour for an entire economy? This can be defined as follows: take a large representative basket of products produced in a given year; then the value of the measure is the arithmetical inverse of the basket’s L‑content. Of course, this numerical value depends on the size of the basket: a bigger basket will result in a smaller numerical value for material labour productivity. However, here I wish to focus not on the value of the measure as such, but on its rate of change from one year to the next. This rate is the same (to a very good approximation), irrespective of the choice of representative basket, provided we use the same standard basket from one year to the next.
This numerical quantity  the rate of change of the aggregate material productivity of labour  is obviously of very great interest to the working class. It relates directly to their creation of increasing wealth  wealth in real material terms rather than monetary terms. In particular, for wages to keep pace with the creation of this real wealth, they must keep pace not only with inflation, but on top of this also with the rate of increase of real labour productivity. Otherwise, the share of the workers in the new wealth they create will decline.
But there is a problem: direct data on material labour productivity are not available, nor can they be calculated directly, because they involve numerical values of L‑content for an entire standard basket, which, as I pointed out at the start, can only be estimated roughly, but not calculated precisely, even for a single type of product.
However, in LTC we show that the rate of change of material productivity can be derived indirectly from widely available data. Let me outline how we do it.^{18}
I will denote by ‘P’ one of the ratios we used to determine the rate of conversion between price and L‑content:
Here this quantity refers not to a single firm over one week, but to an entire economy over a given year. I would like to look at the change of P over time, from one year to the next. In order to make a meaningful comparison between values of P at different times, we must neutralise the effect of inflation on the numerator  value added  which is measured in price terms. The way to do it is to use inflationadjusted prices (also known as real or constant prices). These are prices that are tweaked, so as to keep constant the total price of the basket of commodities that statisticians use for calculating the price index. In what follows I shall assume that the formula for P uses prices adjusted in this way, so we can ignore price inflation.
Over time, the numerical value of P tends to increase, due to increased productivity of labour  a very powerful longterm tendency in capitalist economies. Indeed, P is used by mainstream (bourgeois) economists to measure the aggregate productivity of labour in the entire economy. We call this the monetary measure of labour productivity in the given economy. The data of this measure for many countries are published and are freely available. In fact, the numerator in this formula  the value added in the economy over the given year  is used as one of the standard ways for quantifying the gross domestic product of the economy in the given year. Hence P is in fact the GDP per workerhour.
The most interesting thing about P is its rate of change from one year to the next. The data for the rate are also published and are freely available. We can exploit this for our purpose: using statistical reasoning, we show that the rates of change of the two measures of labour productivity  the material measure and the monetary measure P  are very nearly equal, to a high level of approximation.
This nearequality between the rate of growth of GDP per workerhour and that of aggregate material productivity of labour can also be used for a deduction in the reverse direction: from L‑content to prices. It implies that this aggregate rate together with the growth of the workforce constrain the GDP growth of a capitalist economy as well as the average rate of profit. It is one of the ways in which labour powers the global economy.
This has massive implications for the future of capitalist expansion.
This article is an edited and expanded version of my talk at the Online Communist Forum on September 4 2022.^{19} I am deeply indebted to Emmanuel Farjoun and David Zachariah for extremely helpful comments

E Farjoun, M Machover and D Zachariah How labor powers the global economy: a labor theory of capitalism Berlin 2022. The pdf version is freely downloadable at libgen.is/book/index.php?md5= 72B31D10079180F07FCF7541E2AC326F.↩︎

A useful brief discussion is in Ian Wright’s review of LTC: ‘Understanding capitalist dynamics’ Weekly Worker May 12 2022: weeklyworker.co.uk/worker/1395/understandingcapitalistdynamics.↩︎

An observation to this effect is made by Marx in his Critique of the Gotha programme.↩︎

K Marx Capital vol 1, chapter 1. See also Marx’s Value, price and profit (1865), chapter 6.↩︎

Op cit.↩︎

To be quite precise, this makes sense only for commodityproducts. A commodity that is not a product has a positive price, but zero Lcontent. I shall avoid the cumbersome term, ‘commodityproduct’, and rely on the context to make it clear where the present qualification is meant.↩︎

Another term for this ratio is specific price.↩︎

This is not to deny that there is a positive statistical correlation between the two measures! I shall return to this point below.↩︎

Another way of putting it is that every €1,000 contributed by the workers to the value added of the firm took 1000/60 ≈ 16.7 workerhours to create.↩︎

In Marx’s terminology: the rate of surplus value is 1, or 100%.↩︎

Volumes 2 and 3 of Capital were heavily edited by Engels, from notes left by Marx. In what follows I will not try to disentangle Engels’ editorial contribution to the published text.↩︎

This ratio is essentially what Marx calls “organic composition” of the firm’s capital. Note that the fixed capital of the firm is used, but not necessarily used up, in the course of production. The part that is used up is what Marx calls constant capital.↩︎

Ironically, this seemingly perverse consequence of the proportionality assumption is not as far from reality as all that. There is some evidence that this inverse relationship does indeed hold  not for individual firms, but statistically across firms aggregated into sectors. We discuss this in chapter 3 of LTC.↩︎

The earliest charge of inconsistency is from Ladislaus von Bortkeiwicz in Wertrechnung und Preisrechnung im Marxschen System: eine ‘Ubersicht’ uber die MarxKritik (Archiv für Sozialwissenschaft, 1906). The English translation is entitled Value and price in the Marxian system (1952  downloadable from jphdupre.chezalice.fr/livre/pdf/bortkiewicz.pdf. See also I Steedman Marx after Sraffa London 1977. For a modern mathematical presentation of the consistency problem, see M Machover, ‘The stochastic concept of economic equilibrium: a radical alternative’ (2011), which is downloadable from eprints.lse.ac.uk/36428.↩︎

E Farjoun and M Machover Laws of chaos  a probabilistic approach to political economy London 1983 (second edition 2020).↩︎

Wikipedia lists the following thinkers as having advocated, or having been understood as advocating, this thesis: Aristotle, Thomas Aquinas, Ibn Khaldun, William Petty, John Locke, Benjamin Franklin, Adam Smith, David Ricardo and, of course, Karl Marx. See en.wikipedia.org/wiki/Labor_theory_of_value#Origins.↩︎

For details see LTC section 5.4.↩︎

video: www.youtube.com/watch?v=ix1K HLTzSOY&list=PLQ b1NcwJsXdJF775X4 vgDO0OtMu11SrU&index=12&t=61s.↩︎