Tuesday, July 9, 2024

Marx’s Labour Theory of Value: A Concise Refutation

As an advocate of Post Keynesian economics, I reject Marx’s economic theories in the three volumes of Capital because they are founded on the false Labour Theory of Value (LTV).

Here is a concise case against the LTV, although I limit myself only to some of the most serious criticisms of the theory:

(1) Marx’s Argument for the LTV is Logically Flawed: Marx does not prove it is a real Empirically-Relevant Concept
In chapter 1, volume 1 of Capital, Marx assumes that, when one commodity exchanges for another, this entails an equality:
“Let us take two commodities, e. g., corn and iron. The proportions in which they are exchangeable … can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron: e. g., 1 quarter corn = x cwt. [hundredweight] iron. What does this equation tell us? It tells us that in two different things—in 1 quarter of corn and x cwt. of iron, there exists in equal quantities something common to both. The two things must therefore be equal to a third, which in itself is neither the one nor the other. Each of them, so far as it is exchange value, must therefore be reducible to this third. ….

Along with the useful qualities of the products themselves, we put out of sight both the useful character of the various kinds of labour embodied in them, and the concrete forms of that labour; there is nothing left but what is common to them all; all are reduced to one and the same sort of labour, human labour in the abstract.” (Marx 1906: 44–45).
First, one must immediately ask: what exchange ratios is Marx talking about here?

Is the equation “1 quarter corn = x hundredweight of Iron” completely abstract and not meant to apply to the real-world? If it is utterly abstract, Marx cannot provide any empirical proof that labour value actually exists in the real world.

Or does the equation refer to exchange ratios in real-world 19th century capitalism?

Marx’s argument assumes that in his exchange relation the two commodities are exchanging at their true labour values, but in volume 3 of Capital, Marx abandons the idea that real-world reproducible commodities tend to sell at their labour values.

But, if Marx thinks commodities do not usually sell at their labour values, then the argument in chapter 1 of volume 1 cannot refer to real-world prices!

So Marx’s argument in volume 1 of Capital is completely invalid: there is no empirical proof provided.

Secondly, later in the same Chapter Marx makes this admission:
“Lastly, nothing can have value, without being an object of utility. If the thing is useless, so is the labour contained in it; the labour does not count as labour, and therefore creates no value.” (Marx 1906: 48).
This means that having utility (a use-value) and being demanded by buyers are necessary conditions for any commodity having a labour value. It follows logically that labour-power cannot be the only thing that creates value in commodities, since “being an object of utility” is also a necessary condition.

Thirdly, why should human labour have a special status when animal labour has been – and in some countries still is – a fundamental factor of production?

As Piero Sraffa later noted,
“There appears to be no objective difference between the labour of a wage earner and that of a slave; of a slave and of a horse; of a horse and of a machine, of a machine and of an element of nature (?this does not eat). It is a purely mystical conception that attributes to human labour a special gift of determining value. Does the capitalist entrepreneur, who is the real ‘subject’ of valuation and exchange, make a great difference whether he employs men or animals? Does the slave-owner?” (Sraffa, unpublished note, D3/12/9: 89, quoted in Kurz and Salvadori 2010: 199).
Fourthly, Marx never explains how to formulate a system for homogeneous units of socially-necessary labour time to accurately measure and aggregate different heterogenous forms of human labour.

At one point in volume 1 of Capital, Marx states that the market itself accurately measures the value of skilled labour compared with unskilled labour through actual market prices, but this cannot work because Marx in volume 3 admits most commodities do not exchange at true labour values.

Marx’s concept of a homogenous unit of socially-necessary labour time value is therefore undefined, not meaningful, has never been properly formulated by any Marxist, and remains empirically irrelevant for real-world economics.

Finally, the LTV faces the problem of joint production: if a production process produces more than one commodity, such as two or several goods, then how does one calculate socially-necessary labour time? In particular, Ian Steedman has argued that joint production leaves open the possibility that some labour values of commodities produced in joint production can be undefined, nil, or negative (Steedman 1977: 137–183; Nitzan and Bichler 2009: 101).

There are, however, some core insights about labour that I assume Marxists agree with, as follows:
(1) human labour is a fundamental factor input in modern capitalism,

(2) the cost of labour is frequently a huge part of cost-based, mark-up prices, and

(3) labour is fundamentally different from other commodities.
But these insights are held as true in Post Keynesian economics. The LTV can be cast aside as unnecessary, unproven, and with no causal power of explanation, just like, say, the Neoclassical concept of the “natural rate of interest.”

(2) Marx’s “Law of Value” in the text of Volume 1 of Capital contradicts Volume 3
In volume 1 of Capital, Marx defended in his text a “law of value” in which homogeneous socially-necessary labour time units were the anchor for the price system in modern capitalism. That is to say, individual commodity prices are supposed to gravitate towards their real labour values. Volume 1 also contained two footnotes hinting at the different theory of “prices of production” in Marx’s draft of volume 3 (which Marx had already written before he published volume 1). But the text left readers with the impression that Marx really did think that the prices of real-world reproducible commodities in 19th-century capitalism tended to equal labour values, because Marx said this again and again in the text. This and Marx’s theory of surplus value that was necessarily different between firms with different compositions of capital led to the famous “Transformation Problem.”

But in volume 3 of Capital, Marx stated that the “exchange of commodities at their values, or approximately at their values, requires, therefore, a much lower stage than their exchange at their prices of production, which requires a relatively high development of capitalist production” (Marx 1909: 208–210). So Marx now thought that exchange of commodities with prices at their true labour values only happened in the pre-modern world of commodity exchange when workers owned their own means of production.

Crucially, Marx in volume 3 now only defended the view that the “law of value” only ultimately and indirectly explains prices, and defended three aggregate equalities:
(1) the sum of surplus value = sum of profits;

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

(3) the value rate of profit = the money rate of profit.
Marx also now accepted that Classical “prices of production” became the anchors for the real-world 19th-century capitalist price system, which contradicted his “law of value” in volume 1.

This contradiction was pointed out by many critics of Marx and even sympathetic Marxists.

Engels was deeply concerned by this contradiction, and in his “Supplement and Addendum to Volume 3 of Capital” of 1895 (Engels 1991 [1895]) Engels claimed that Part one of volume 1 of Capital was actually referring to the pre-modern word of commodity exchange, even though the text frequently refers to 19th-century capitalist commodity prices.

Marxists must explain why Engels tried to explain the contradiction between volume 1 and volume 3 of Capital this way, if Marx only intended his “law of value” in volume 1 – that commodities tend to exchange at true labour values – to be either (1) totally abstract and not meant to apply to the real world, or (2) only ever meant to apply to the pre-modern word of commodity exchange.

(3) Volume 3 of Capital is Theoretically and Empirically Wrong
It is well known that the work of Ladislaus von Bortkiewicz showed that two of the three aggregate equalities defended by Marx in volume 3 of Capital fail, and that the sum of surplus value = sum of profits quality cannot be defended unless under very special assumptions (see Bortkiewicz 1906; 1907a; 1907b; 1907c; English translations in Bortkiewicz 1949 and 1952; see also here).

Moreover, as Ian Steedman has argued, (1) Marx’s Transformation solution is internally inconsistent as the value rate of profit S/(C + V) does not explain money rate of profit when commodity prices do not equal labor value, and (2) Marx failed to transform the prices of non-labour inputs (constant capital) in his transformation tables (though this was a minor problem) (Steedman 1977: 29–31). In short, Marx’s logical inconsistency is that he “assumes that S/(C + V) is the rate of profit but then derives the result that prices diverge from values, which means precisely, in general, that S/(C + V) is not the rate of profit” (Steedman 1977: 31).

But, in addition to this, in volume 3 of Capital, Marx holds that Classical “prices of production,” with an equal rate of profit, are the anchors for the price system. However, Post Keynesian economics shows us that this is empirically false. The real world does not have a strong tendency to equalisation of profit rates, and even Marxists like D. Zachariah have found strong empirical evidence against such a tendency (Zachariah 2006: 18).

In the real world, there are two factors that prevent any strong tendency to equal rates of profit:
(1) the strong barriers to entry in many capitalist sectors (including aggressive use of capacity utilisation as a barrier to entry, patents and intellectual property law), and

(2) the significant, persistent differences in profit mark-ups in different sectors and industries.
Diffrent capitalist firms have the power to charge divergent mark-ups on their cost-prices, and there is no evidence these mark-ups get competed away.

Once we reject the idea of “prices of production” as empirically relevant and operative in modern capitalism as the anchors for the price system, then Marx’s theory of price determination in volume 3 of Capital is falsified.

Even if, hypothetically, one accepts the concept of labour value as meaningful, there is no logical reason to think Marx’s three aggregate identities – such as “the sum of surplus value equals sum of profits” or the “sum of values equals sum of prices” – would hold true when prices depart so radically from “prices of production.”

Conclusion
Marx’s argument for labour value in volume 1 of Capital is hopelessly flawed. It does not prove labour value exists, and Marx’s concept of a homogenous unit of socially-necessary labour time unit is undefined, not meaningful, has never been properly formulated by any Marxist, and remains empirically irrelevant for real-world economics.

Worse still, Marx’s “law of value” in volume 1 of Capital contradicts volume 3, which means his economic theory is not consistent, but internally inconsistent.

Finally, the “prices of production” are not causal anchors of real-world prices. Marx’s theory of price determination in volume 3 of Capital is false, since real-world prices depart significantly even from “prices of production.”

A final point is to be kept in mind.

We know that Marx’s LTV in the text of volume 1 of Capital (published in 1867) contradicts the LTV in volume 3 (which Marx never published in his own lifetime).

But volume 1 of Capital also contains two absurd footnotes that contradict what is said in the text about the LTV (namely, footnote 24 in Chapter 5, and footnote 9 in Chapter 9) and these footnotes appear to admit that prices of production are the anchors for the price system in 19th century capitalism, and that such prices of production do not correspond to true labour values.

So it seems clear these footnotes hint at the different and contradictory theory Marx had already sketched in the draft of volume 3 of Capital and also in a number of private letters as follows:
(1) a letter to Engels of August 2, 1862 (on this letter see here);
(2) an exchange with Engels between June 26 and June 27, 1867;
(3) a letter to Engels of 8 January, 1868 (on this letter, see here);
(4) an exchange with Engels from April 22 and April 30, 1868, and
(5) in a letter to Ludwig Kugelmann on 11 July 1868.
However, if Marx really held his “prices of production” theory in private from 1862 to 1868, this theory utterly demolished and smashed up the “law of value” that Marx had been defending in the actual text of volume 1 of Capital, and showed that book to be a tendentious work of communist propaganda.

In reality, Marx was perfectly capable of holding contradictory views and especially for polemical or propagandistic purposes.

Why was this the case? We know Marx was perpetually short on money and nearly bankrupt multiple times after he came to London. Marx was almost always financially dependent on Engels after 1849 (apart from brief periods where Marx inherited money that never lasted long). We also know that Engels was pressing Marx for a new economic work that attacked capitalism as early as 1863 (Fabian 2011: 430) but Marx dragged his feet for years on end with feeble excuses and infuriated Engels (Fabian 2011: 438–443). By 1866 Engels severely cut the money stipend he gave to Marx and was effectively condemning Marx to penury and bankruptcy (Fabian 2011: 442), so Marx desperately tried to placate Engels and finish the first volume of Capital.

It is likely that, under pressure from Engels to produce a work in defence of communism, Marx’s ideological commitments skewed volume 1 so that it presented capitalism in the worst light possible and with an extreme and dogmatic defence of the labour theory of value, including the idea that prices tend to equal their labour values, which, in view of his work on the first draft of volume 3 of Capital (which he had already written from 1863–1865), he knew to have severe problems, such as the transformation problem, and contradicted his “prices of production” theory in volume 3.

But none of this mattered to Marx, who was a lazy, diseased, perpetually broke drug addict (likely addicted to opium: Fabian 2011: 28, 30, 113, 272), who was happy to be a parasite on Engels by currying favour with the latter through the severely flawed but anti-capitalist first volume of Capital. We know Engels paid off Marx’s debts after volume 1 of Capital was published and promised him financial security through gifts of money (Fabian 2011: 443).

And this, in my view, is why Marx’s economic theories are such an incoherent, contradictory mess: the Communist hack Karl Marx just didn’t care, and deliberately stopped any attempt to publish volume 3 of Capital, which would have quickly exposed his fraud in volume 1.

Years later when Marx was dead and Engels published volume 3 in 1894, the inevitable happened: hostile critics of Marxism and even some sympathetic supporters of Marx pointed to the devastating contradiction between the LTV in volumes 1 and 3. Marx’s intellectual fraud and charlatanry were exposed to the world.

Of course, Marx was long dead and had laughed all the way to the bank by continuing his life of bourgeois parasitism, having extracted the surplus value from the hard-working proletarian workers in Engels’ cotton factory.

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

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

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

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

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

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

Engels, F. 1991 [1895]. “Supplement and Addendum to Volume 3 of Capital,” in Karl Marx, Capital. A Critique of Political Economy. Volume Three (trans. David Fernbach). Penguin Books, London. 1027–1047.

Fabian, George. 2011. Karl Marx: Prince of Darkness. Xlibris Corporation, US.

Kurz, Heinz D. and Neri Salvadori. 2010. “Sraffa and the Labour Theory of Value: A Few Observations,” in John Vint et al. (eds.), Economic Theory and Economic Thought: Essays in Honour of Ian Steedman. Routledge, London and New York. 189–215.

Lee, Frederic S. 1998. Post Keynesian Price Theory. Cambridge University Press, Cambridge and New York.

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

Marx, Karl. 1909. Capital. A Critique of Political Economy (vol. 3; trans. Ernst Untermann from 1st German edn.). Charles H. Kerr & Co., Chicago.

Nitzan, Jonathan and Shimshon Bichler. 2009. Capital as Power: A Study or Order and Creorder. Routledge, Abingdon, UK and New York.

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

Zachariah, Dave. 2006. “Labour Value and Equalisation of Profit Rates: A Multi-Country Study,” Indian Development Review 4: 1–20.

Further Reading
“Marx’s ‘Law of Value’ in Volume 1 of Capital,” February 4, 2016.

“Why Marx’s Labour Theory of Value is Wrong in a Nutshell,” June 28, 2015.

“Engels’ View of the Theory of Value in Volume 1 of Capital in the 1890s,” August 12, 2015.

“Prolegomena to the Study of Marx’s Capital (Updated),” June 2, 2015.

“Dühring’s Review of Capital and Marx’s Letter to Engels of 8 January, 1868 on the Labour Theory of Value,” May 12, 2015.

“Marx’s Letter to Engels of 2 August, 1862 on Prices of Production,” January 19, 2016.

Paul Cockshott’s “Why Labour Theory of Value is Right”: A Refutation

The Marxist Paul Cockshott presents his defence of the Labour Theory of Value in this video:



It appears that Paul Cockshott defends the Labour Theory of Value (LTV) found in volume 1 of Capital, albeit in a grossly simplified way.

He defines the LTV in three senses, as follows:
(1) The average price of a good will be proportional to the average amount of labour used to make it;

(2) The value added in an industry will thus be roughly proportional to the labour it uses.

(3) Price quantities are thus the indirect representation of underlying quantities of human time.
Unfortunately, this is not an accurate representation of Marx’s actual “law of value” in volume 1 of Capital, where Marx defended in his text a “law of value” in which homogeneous, socially-necessary labour time units were the anchor for the price system in modern capitalism. That is to say, individual commodity prices are supposed to gravitate towards their labour values (even though volume 1 contained two footnotes hinting at the different theory of price determination in Marx’s draft of volume 3, so that volume 1 was not even internally consistent).

By volume 3 of Capital, Marx thought this only happened in the pre-modern world of commodity exchange, but he describes the process as follows:
“The assumption that the commodities of the various spheres of production are sold at their value implies, of course, only that their value is the center of gravity around which prices fluctuate, and around which their rise and fall tends to an equilibrium.” (Marx 1909: 208–210).
We must remember that Marx had no single, consistent Labour Theory of Value. The “law of value” (a phrase which Marx used to refer to the LTV) in volume 1 of Capital contradicts the “law of value” in volume 3. For Marx’s LTV in volume 1 of Capital to work and be empirically proved, all human labour of different kinds must be measurable in a homogenous unit of basic socially-necessary labour time and then compared, and actual real-world prices must tend to move towards their true labour values.

But Paul Cockshott is apparently not even concerned to defend this authentic version of the LTV in volume 1 of Capital. Instead, in a sleight of hand, he has substituted a much weaker version of the LTV whose main definition is that the “average price of a good will be proportional to the average amount of labour used to make it.”

I will discuss this video in the two sections below.

(1). Neoclassical Price Theory
When Cockshott responds to critiques of the Labour Theory of Value (LTV), he begins with the Neoclassical/Austrian theory of flexible prices determined by dynamics of supply and demand. Bizarrely, Cockshott dismisses this by arguing that it is “unfalsifiable,” but this is manifestly not true.

The fundamental prediction of Neoclassical/Austrian price theory is that prices are flexible and will be highly responsive to changes in supply and demand. We can test this empirically. We can easily look at empirical studies of real-world price determination as I have done here and here and see that the vast majority of prices are not highly flexible and determined by dynamics of supply and demand, as in Neoclassical theory.

Instead, most prices are cost-based mark-up prices, which are set on average unit costs plus a profit markup. This theory, however, is inconsistent with Marx’s “prices of production” because there is no real-world tendency towards a uniform, average rate of profit.

So, first of all, Cockshott fails to engage with the Post Keynesian theory of cost-based mark-up prices, which actually is the empirically correct explanation of most prices in modern capitalism. Under the Post Keynesian theory of cost-based mark-up prices, it is entirely normal to find that labour costs are a substantial component of prices, and where labour costs in a particular industry are high, there will be a strong correlation of labour costs with prices. But none of this proves Marx’s Labour Theory of Value.

(2). Correlation of Labour Costs with Money Prices
Next, Paul Cockshott cites this article to prove his definition of the LTV:
Zachariah, Dave. 2006. “Labour Value and Equalisation of Profit Rates: A Multi-Country Study,” Indian Development Review 4: 1–20.
I have already refuted this article here.

Cockshott seems blissfully unaware that the empirical finding that monetary labour costs are strongly correlated with money prices of output commodities is, as we have already seen above, actually one of many strong proofs of the Post Keynesian cost-based mark-up theory of pricing, and indeed of any non-Marxist cost-based mark-up theory of price determination, which have no need for a Labour Theory of Value at all.

So, once again, Cockshott has not proved the LTV, and apparently does even understand that his “proof” is, at the very least, perfectly compatible with the Post Keynesian cost-based mark-up theory of prices.

And Marxists like Cockshott are essentially incapable of defending the actual, authentic definitions of the LTV that Karl Marx used in volume 1 of Capital, and reduce it to a weak claim that does not vindicate Marx or his LTV.

A final point is that Cockshott relies on the data of Zachariah (2006), which admits that the empirical data do not support an equalisation of profit rates, but that is a necessary condition for the existence Marx’s prices of production as used in volume 3 of Capital! It follows logically that, if the existence of prices of production as long-run centres of gravity for real-world prices are refuted by the empirical evidence, then Marx’s economic theory in volume 3 of Capital – which relies on prices of production – is also refuted.

BIBLIOGRAPHY
Marx, Karl. 1909. Capital. A Critique of Political Economy (vol. 3; trans. Ernst Untermann from 1st German edn.). Charles H. Kerr & Co., Chicago.

Zachariah, Dave. 2006. “Labour Value and Equalisation of Profit Rates: A Multi-Country Study,” Indian Development Review 4: 1–20.