William Baumol and the transformation problem

William J. Baumol, who died last week at the age of 95, was one of the pre-eminent mainstream economists of his generation.  He taught for more than 40 years at Princeton University and at New York University, where he retired in 2014. His work touched on monetary policy, corporate finance, welfare economics, resource allocation and entrepreneurship, but he was best known for the principle that came to bear his name: Baumol’s ‘cost disease’.

Baumol’s cost disease is the idea that personally delivered services — musical performances, medical care, education and garbage collection, for example — naturally and inevitably increase in price year after year. Improved technology may allow bagels and cars to be produced more efficiently and therefore more cost effectively, but, as Baumol famously observed, a Mozart string quartet requires today the services of four musicians, the same manpower it took in the 18th century.

This idea had immediate relevance in public policy, particularly in the areas of health care and education, because it showed why important public services could not be measured for cost-effectiveness in the same way as manufacturing in the capitalist sector.  They provided services for need, not profit.

“The critical point here is that because politicians do not understand the mechanism and nature of the cost disease, and because they face political pressures from a similarly uninformed electorate, they do not realize that we can indeed afford these services without forcing society to undergo unnecessary cuts, restrictions and other forms of deprivation,” he wrote in his 2012 book The Cost Disease.  It is a matter of public choice not ‘efficiency’.

Baumol was prolific in his economic research, particularly in looking at the role of ‘entrepreneur’ as innovator rather than as capitalist.  He also produced one of the main mathematical economics textbooks of the 1960 and 1970s – it was pretty dry, as I remember.

Baumol was a liberal.  He advised Hillary Clinton and various Democrat leaders and was strong advocate of public healthcare and education.  And he was a trustee for Economists for Peace and Security, a liberal UN body of economists opposed to nuclear weapons, along with Kenneth Arrow (who has also recently died) and JK Galbraith.

But what is less known is that in the early 1970s Baumol engaged in a mainstream debate with leading Keynesian Paul Samuelson on the validity and purpose of Marx’s value theory.  Samuelson had launched an attack on Marx’s theory as it began to gain some traction among student activists in those revolutionary days ((Paul A. Samuelson’s “Understanding the Marxian Notion of Exploitation: A Summary of the So-called Transformation Problem between Marxian Values and Competitive Prices, “J. Econ. Lit., June 1971, 9 (2), pp. 399-431).

Like Eugene Bohm-Bawerk tried to do in the late 1890s, and like Keynes in the 1930s, Samuelson wanted to expose the fallacies of Marx’s theory in case economics students became infected with Marxism.  Keynes called Marx’s value theory “scientifically erroneous and without application to the modern world’ (Keynes, Laissez-Faire and Communism, quoted in Hunt 1979: 377).  Samuelson’s approach was to argue, not that Marx’s value theory was illogical because values when measured in labour time could not equal prices measured in markets (as Bohm-Bawerk claimed), but that his theory of value was irrelevant to an explanation of the movement of market prices and therefore to any understanding of modern economies.

Samuelson argued that Marx’s ‘transformation’ of labour values into prices of production was unnecessary.  Market prices are explained by the movement of supply and demand, so what need of a value theory?  Indeed, it could be erased.  “The truth has now been laid bare.  Stripped of logical complication and confusion, anybody’s method of solving the famous transformation problem is seen to involve returning from an unnecessary detour… such a transformation is precisely like that which an eraser is used to rub out an earlier entry (i.e. value – MR) after which we make a new start to end up with a properly calculated entry (i.e. price – MR)”.

Well, Baumol carefully took Samuelson to task in his essay, The transformation of values: what Marx really meant. In so doing, he made an important contribution in explaining and validating Marx’s theory of value. Baumol points out that Samuelson, along with post-Keynesian Marxists like Joan Robinson, misunderstood Marx’s purpose in the so-called transformation of values into prices.  Marx did not want to show that market prices were related directly to values measured in labour time. “Marx did not intend his transformation analysis to show how prices can be deduced from values”.  The aim was to show that capitalism was a mode of production for profit and profits came from the exploitation of labour; but this fact was obscured by the market where things seemed to be exchanged on the basis of an equality of supply and demand.  Profit first comes from the exploitation of labour and then is redistributed (transformed) among the branches of capital through competition and the market into prices of production.

For Marx, that only labour creates value is self-evident. “Every child knows that any nation that stopped working, not for a year, but let us say, just for a few weeks, would perish…. This constitutes the economic laws of all societies, including capitalism. And every child knows, too, that the amounts of products corresponding to the differing amounts of needs, demand differing and quantitatively determined amounts of society’s aggregate labour”, Letter from Marx to Kugelmann, 11 July 1868, MECW, vol.43, pp.68-69.

Total surplus value is produced from exploitation of work forces employed by various capitalists – the difference in value measured in labour time between that time needed for the wages of the labour force and the price of the commodity or service produced realised in the market place for the capitalist.  But not the surplus value or profit achieved by each capitalist’s workforce does not go directly to the individual capitalist.  Each capitalist competes in the market to sell its commodities.  And that competition leads to profits being redistributed because profits tend to an average rate per unit of capital invested.

The transformation of values created by labour into prices in the market means that individual prices will differ from individual values.  As Baumol says, Marx knew that individual prices of production differed from individual values; unlike Ricardo who could not solve this transformation.

So total surplus value is converted (transformed) into total profit, interest and rent, with the market deciding how much for each capitalist.  Yes, ‘supply and demand’ decides profit or loss for an individual capitalist.  But that is just the appearance or result of the distribution of profit through market competition but created by the overall exploitation of labour in the production process.

Baumol’s explanation was a starting point for a more comprehensive answer and defence of Marx’s value theory developed by Marxist scholars like Carchedi, Yaffe, Kliman, Freeman, Moseley and others over the last 40 years since Samuelson’s attack.

Baumol’s interpretation of Marx’s theory provides a powerful answer not only to Samuelson but also to the ‘standard interpretation’ of the transformation problem, as Fred Moseley has named it in his book, Money and Totality (a book that explains in detail all the theoretical issues raised by mainstream and other heterodox economists and answers them).

Values in a commodity do not have to be ‘transformed’ into prices, as Robinson and Samuelson interpret Marx’s theory.  Prices are the appearance in the market of the exploitation of labour in production process.  As Fred Moseley says, if you accept Samuelson’s interpretation of Marx’s transformation of values into prices then “values do in fact cancel out and play no role in the determination of prices” (p229). However, this is not Marx’s theory.  Individual values are not converted into individual prices of production: “individual values play no role in Marx’s theory of prices.  What happens is that “total new value produced by current labour … is determined (in part) by the total surplus value produced, which in turn (in part) determines the general rate of profit and ultimately, prices of production… prices of production are not determined by multiplying transformation coefficients for each commodity by the individual values, but by adding the average profit to given money costs”.

There is no need to transform the values of constant capital (machinery etc) and variable capital (labour power/workforce) into prices.  They are already given as prices from the market in the previous process of production.  The only transformation that takes place is the transformation of the total new value from the production process in a re-distribution through market competition, with profits going to the various capitalists depending on the size of capital each advanced at the start of production.

As Baumol says, the distribution of surplus value from society’s central storehouse now takes place via the competitive process which assigns to each capital profits (or interest or rent) an amount strictly proportional to its capital investment.  “This is the heart of the transformation process – the conversion of surplus value into profit, interest and rent.  It takes from each according to its workforce and returns to each according to its total investment” p53

Marx’s transformation is temporal: you start (t1) with given money capital to invest in plant, machinery and labour and you get new value created by the exertion and exploitation of labour (t2).  The surplus value comes from after covering the cost of capital (constant and variable).  This is then redistributed through competition in the market, which drives all towards an average rate of profit.  Thus total value (dead labour and living labour plus surplus value) still equals total prices (based on the given cost of invested capital plus an average rate of profit), but total surplus value is transformed into profits, interest and rent and distributed according to the size of the capital invested.

Here is Marx’s actual schema for this transformation.

You can see that total values (TV) equal total prices (TP), but individual capitals have commodities with different values (V) to prices (P) because of the redistribution of surplus value (s) into profits (p) by the market.  There is no transformation of constant (c) and variable (v) capitals because they are already transformed (into money prices) in a previous production period.

Indeed, Baumol’s (and Marx’s) transformation has since been supported empirically.  Carchedi has shown that the money price average rate of profit is close to the value average rate of profit (i.e. across a whole economy). Other scholars have shown that when an individual sector’s production is measured in value terms (i.e. in labour time) and then aggregated, the total value is pretty close to total prices measured in money terms.  Thus Marx’s transformation of value into prices is not irrelevant even to relative price determination.

But, as Baumol said, it was not Marx’s purpose to show that.  He wanted to show that it is the exploitation of labour that creates value (through the private appropriation of the product of labour power) and that lies behind profit, interest and rent.

Profit is not the reward for ‘risking capital’ (money for equipment etc); or rent from ‘providing’ land; or interest for ‘lending’ money; thus rewards to various factors of production.  Baumol comments: “Such nonsense is precisely what Marx’ analysis anticipates and what it is intended to expose. Again, let Marx speak for himself. “In Capital-Profit, or better Capital-Interest, Land-Rent, Labor-Wages of Labor, in this economic trinity expressing professedly the connection of value and of wealth in general with their sources, we have the complete mystification of the capitalist mode of production.  …This formula corresponds at the same time to the interests of the ruling classes, by proclaiming the natural necessity and eternal justification of their sources of revenue and raising them to the position of a dogma.” (Volume III, Chapter 48, pp. 966-67).

It is no accident that it is the Keynesians and post-Keynesians like Joan Robinson that were (and are) the most vehement against Marxist economic theory – because Marxism is the main opponent of Keynesian influence in the labour movement.

William Baumol may have been as mainstream an economist that you could find – an exponent of the neoclassical equilibrium and marginalism.  But he was also a surprisingly acute observer of Marx’s exploitation theory of capitalism.  As a result, he could show the Keynesian (and neo-Ricardian) claim that Marx’s value theory was an ‘irrelevant and unnecessary detour’ was wrong.  For that, we can thank him.


21 Responses to “William Baumol and the transformation problem”

  1. Rgl Says:

    If I remember, Keynes did not try to refute Marx’s Labour theory of value directly, but instead tried to undermine Ricardo’s own theory believing, wrongly, that marx and Ricardo were joined at the hip.

  2. Anton Says:

    Hello, Michael.
    Off-topic: do you happen to know where the famous Okishio’s article “Technical Change and the Rate of Profit” can be found in digital form? It was first published on Kobe University Economic Review, issue 7, but I have trouble finding it on the Web – only newer issues are available.

  3. Magpie Says:

    Michael Roberts,

    You might enjoy reading

    Baumol, W. J.. (1983). Marx and the Iron Law of Wages. The American Economic Review, 73(2), 303–308.

    In that article Baumol debunks one of the myths anti-Marx scribblers love.

    One question: I haven’t read Moseley’s book yet, although I’m planning to read it. To what extent, do you believe, is Moseley indebted to Baumol’s reply to Samuelson?

    • michael roberts Says:

      Thanks – I have not read this piece by Baumol Will do. I think Moseley goes further than Baumol in dealing with all the interpretations of Marx’s transformation that accept the view of Von Bortkowiecz and the neo-Ricardians that Marx needed to be ‘corrected’ because he had not ‘transformed’ all the value in a commodity into prices. But Moseley is is of course sitting on the shoulders of other scholars that I mentioned in my post who came after Baumol.

  4. Dr Brian Philip Parkin Says:

    As ever, an interesting and thought-provoking piece. However, a minor corrective; Marx did not state that only labour power creates value. Although labour power is the necessary active agent in the production of value, in his Critique of the Gotha Programme, he stresses that labour power and nature in combination are the source of value.

    • michael roberts Says:

      Agreed – but as he says you need labour power to mould nature.

    • Carlos Says:

      Labor is not the only source of wealth (use values) to be more precise. Nature contributes as well (that is the whole ecological critique). However, he does not specifically attribute that role to nature as it regards the creation of value. Only living labor creates value. And I believe Moseley spends a good deal of effort on this point.

      • Carlos Says:

        Wealth is also created in non capitalist societies, labor in general is also part of nature (think of the example, of “savages” killing other animals to eat them. They are engaged in useful labor.) Humans are also part of nature. However, the creation of value is a specific feature of capitalist production. Unused labor power does not create value, only living labor engaged in the production of value (and surplus value).

  5. Wal Buchenberg Says:

    Thanks for the nice text.
    Republished (partly) in Karl-Marx-Forum:



  6. billjefferies Says:

    Samuelson observed that if you assume that inputs are identical with outputs then there is no need for the labour theory of value. He was right, there is no doubt about that. The purpose of the labour theory of value is to provide a standard of value against which the value of physical output can be measured, so if the physical “value” or price of output can be measured directly, by a straight physical comparison, why bother with a separate standard?

    Problematically, all of the Marxians and Marxists, including Fred and Andrew, who have attempted to defend Marx’s value theory, assume just this, that outputs are identical with inputs. This is particularly the case with Andrew who emphasises the point in numerous examples, but if they assume, that prices can be determined physically, then what is there to solve (or defend)? Nothing. As the raison d’etre of value theory has been rendered superfluous in advance.

    I have shown in two papers published in Critical Sociology Piero Sraffa and the Production of Commodities by Means of Magic (and a reply to leading Sraffian Gary Mongiovi that are available on my page on Researchgate) that the assumption of identical inputs and outputs means that production is impossible, and surplus is a production of nothing or “magic” as I put it. The Sraffians (and Marxians) assume that inputs are “unchanged” during production, when the purpose of production is to change inputs into physically different outputs. Once this assumption is abandoned then the validity of value theory is reasserted.

    • Eleutério F S Prado Says:

      The theory of labor value appears in classical political economy to explain equilibrium, that is, natural prices (which, incidentally, can be empirically inferred from the observation of market price series). This theory assumes that market prices are anarchic, and are constantly fluctuating. Its assumption is the turbulent dynamics of prices. Neoclassical theory and, thus, neoricardianism, reverse this logic. They start from equilibrium in order to explain the prices. For them, it is the equilibrium that explains the equilibrium prices. Therefore, the theory of labor value is not necessary. However, neoclassical theory is a mere tautology. More than that, it is a fantasy created in order to impose harmony where there exist disharmony.

    • sartesian Says:

      ^^proof that political economy is, in the last analysis, sophistry

  7. Publicstat (@Publicstat) Says:

    Even if Baumol is right repeating that for KM “Every child knows…”, it is a question of coherence to have a (non tautological) way to go from labour values to production prices. This is why it is so much debated. For me real problem is in passing from individual industry rates of profit to a common rate. That would be the reason of disparities.Only that in “Chapter 9. Formation of a General Rate of Profit,…” Vol III, KM took the decision to eliminate the profits in the input side to simplify (according to Baumol again)

  8. Don Sutherland Says:

    I thought you might be interested in this brief comment of mine on the “analysis” of the the Australian government’s very weird wages assumptions in its latest neoliberal budget: https://www.facebook.com/DonSutherland2017/posts/10154684353761448 Anything you might have the opportunity to add would be appreciated.

  9. Fred Moseley Says:


    I think you are being way too complimentary of Baumol. I agree that he was sympathetic to Marx and Marx’s theory of exploitation, which makes him unique among top mainstream economists, and I appreciate that, but he badly misunderstands Marx’s theory, as they all do.

    Baumol argues that Marx’s labor theory of value (LTV) is in fact not a theory of prices. He does not understand that Marx’s LTV is primarily a macro theory of aggregate prices and more precisely mainly about the total ΔM in the economy as a whole. That is, Marx’s LTV is primarily a macro-monetary theory.

    Baumol also thinks that Marx’s LTV does not provide a theory of micro prices. He agrees completely with Samuelson that the correct micro theory of individual prices is Sraffa’s theory, which has nothing to do with the LTV. He interprets Marx’s LTV as a kind of qualitative, sociological (moral?) theory (“workers are exploited in production” , “labor is the only relevant source of output”) that does not provide any quantitative theory at all – neither a macro theory of aggregate prices (total ΔM) nor a micro theory of individual prices of production. And since Sraffa’s theory of prices also determines the rate of profit, there is no connection between Marx’s qualitative theory of surplus-value and a quantitative theory of the rate of profit. What good is a theory of surplus-value if it cannot explain the rate of profit – and thus has nothing to say about the important question of the effect of technological change on the rate of profit? Tellingly, there is no equation in Baumol’s paper and no verbal expression of a quantitative determination of any variable.

    Unfortunately, as I demonstrate in Part II of my book, most Marxists today (Shaikh, Foley- Dumenil-Mohun, Wolff-Roberts-Calleri, Fine and Saad-Filho) are similar to Baumol in the sense that they have also accepted Sraffa’s theory of prices and the rate of profit while claiming to maintain Marx’s theory of surplus-value in some way. But that is not possible. Sraffa’s theory of the rate of profit does not depend on the labor theory of value in any way. They can’t be combined. They are like oil and water.

    Magpie asked to what extend am I indebted to Baumol. I remember thinking at the time that it is good thing that Baumol emphasized Marx’s point that all the different forms of capitalist incomes (profit, interest, rent) come from surplus labor. But he interprets that as a qualitative theory and accepts Sraffa’s theory of prices and the rate of profit.

    Bill J: I don’t think that inputs and outputs are the same, and I don’t know where you got that idea.

    • michael roberts Says:

      Fred, you are right that Baumol’s insight was limited to a defence of Marx’s theory of the exploitation of labour as the basis of value (profit). But as you say, this is inadequate. In fact,your book provides a clear path to show that Marx had a macro-monetary theory of prices that connects value to prices of production and so is not irrelevant as Samuelson argued and Sraffa proposed.

    • GrahamB Says:

      I think there is a problem the moment physical quantities (or unit prices) are part of the model, even if it includes labour / wages. The incommensurability of commodities based on anything apart from SNLT isn’t just about exchange value, it also applies to production that must transform the physical inputs into something else. This incommensurability is then overcome by having the same physical ‘things’ as both inputs and outputs – from a single commodity corn model to an input-output matrix. Also, they are so abstract given the proportion of end user consumption in the economy, non-equilibrium reproduction, etc.

  10. Ga Says:

    Hello Michael from Manizales (Colombia). I follow with much interest his blog. I wanted to point out something that you do not mention and it is that Keynes was clearly in favor of the theory of labor value but not of his Marxist presentation. See his General Theory cap. 16, pp 213-214.

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