The transformation problem assessed

Desai takes up this century-old controversy in his fourth chapter. It is difficult to see what point he is actually making. First he outlines the problem, as it is perceived. We discuss this next. Then he throws the usual accusations of schoolboy arithmetical errors at Marx. Next he partially forgives Marx his trespasses. “In any case, while he was wrong in the details…his solution has stood the test of time.” (Marx’s Revenge p 64) On the same page he quotes the research of Anwar Shaikh to show that “empirically the theory stands up very well.” What more could anyone ask for? Finally he throws in some quirky comments of his own.

Throughout Volume I of Capital, Marx assumes that commodities are sold at money prices proportional to their values, in terms of the socially necessary labour time required for their production. In Volume III, Marx moves on to analyse ‘the process of capitalist production as a whole’. This involves looking at the interaction of ‘many capitals’. It is at this stage that Marx introduces the notion of prices of production (called cost prices in the Grundrisse and Theories of Surplus Value). Let us simplify the presentation as much as possible by assuming that capitalist production is carried out by only two firms. These firms have different organic compositions of capital. One is more capital intensive than the other.

The value of a commodity can be resolved into three parts:

• Constant capital ‑ This passes its value unchanged to the final product. This comprises all the expenses incurred by the capitalists apart from wages. Thus constant capital can be divided into fixed capital, such as machinery and buildings, which passes its value gradually to the final product in the form of depreciation. Then there is circulating constant capital, such as raw materials, which are entirely consumed in the production process and pass their entire value to the final product.
• Variable capital – so called by Marx because it yields a surplus to its buyer, the capitalist, in the process of production. For the capitalist this is money capital in hand to hire labour power.
• Surplus value – conventionally divided into rent, interest and profit. The whole of the capitalist class lives off the unpaid labour of the working class. At this stage Marx has not introduced merchant capital, interest bearing capital and the costs of circulating commodities, which all absorb a slice of the action.

Likewise the capital mobilised in a firm may be represented by these three parts, labelled C + V + S in Marxist economics. Note that, in the case of the unit of capital, the rate of profit is calculated on the total constant capital outlaid; whereas in the value of a commodity, C represents just the depreciation of constant capital involved in the production of the product.

Our two capitals have the following values:

a)       C500 + V100 + S100

b)       C100 + V100 + S100

The rate of profit is calculated by dividing the profit (S – at this stage we ignore the division of surplus value between different fractions of the capitalist class) by the costs (C + V).

Note that the rate of profit for (a) is S/(C + V), which in this case is 100/600, or about 17%.

The rate of profit for capital (b) on the other hand is 100/200, a healthy 50%.

This result is impossible. It is a basic precept of Marxist economics that there is a tendency for the rate of profit to equalise over the different sectors in production. This tendency exists precisely because individual capitalists continually search out super profits – and in doing so eliminate them through the flow of capital from low profit to high profit sectors.

Values and prices of production

Marx introduces this part by explaining that, “the whole difficulty arises from the fact that commodities are exchanged not just as commodities but as products of capital.” (Capital Vol III p 175) How does the tendency for profit rates to equalise manifest itself?

Within an industry it happens by the setting of a certain level of technology as standard through competition between the capitalists within that sector of production. The standard level of technology will correspond to a given level of productivity that in turn produces a benchmark value, a given quantity of socially necessary labour time to produce the commodity. Laggards can only stay in business by selling their products at a price below their individual value (higher than the average because productivity is lower) and perhaps by paying lower wages. Leading firms that innovate will make a super profit for a time as the individual value of their product is lower than average because of higher than average productivity. This super profit will disappear as their competitors are forced to retool.

But this is not how an economy wide rate of profit is established. The technology appropriate to different industries can remain at very different levels of capital intensity for epochs. Agriculture has been regarded as labour intensive compared with most sectors of industry for centuries. So the rate of profit will not equalise between different industries because the organic composition of capital tends to equalise (we assume the rate of exploitation is not an important explanatory difference of different industry-wide profit rates). But since capitalism is a profit-driven system, since capitalists will always put their money where there is the expectation of a higher rate of profit, there must be capital flows between industries causing a tendency for the rate of profit throughout the economy to equalise.

Marx accepts this. He knew it all along, even when he was writing Capital Volume I on the assumption that commodities sold at prices proportional to their individual values. In fact Capital Volume III was mostly drafted before Volume I was written.

In Volume III Marx reveals that commodities are not and cannot be sold at their individual values, if a general rate of profit is to be formed throughout the economy.

A numerical example

If capitals (a) and (b) are to share in an equal rate of profit, then we have to work out the economy wide profit rate first:

Total C is 500 + 100 = 600. Total V is 100 + 100 = 200. Total S is 100 + 100 = 200. The overall rate of profit in the economy is 200/800 (S/(C + V) = 25%.

For the rate of profit to tend to equalise, surplus value ‘awarded’ to each capital is adjusted as we show below:

a)       C500 + V100 + S150

b)       C100 + V100 + S50.

So the commodities produced by capital (a) are sold at a price above their value while commodities produced by capital (b) (which is less capital intensive) are sold at a price below their value. What has happened is a redistribution of values between sectors. What has also happened is the formation of prices of production which differ from individual values. These prices of production are not the same as everyday market prices. They are the axis around which market prices fluctuate. Marx had no problem with this process, which he saw as an essential modification of the presentation in Capital Volume I and the necessary form of appearance of the law of value in capitalist society.

The second change is that capital (a) is awarded more surplus value than was actually generated, while capital (b) has to make do with less. Surplus value has been redistributed between the capitals, but the amount generated by capital in the economy as a whole is unchanged.

The critics

Bohm Bawerk

The publication of Capital Volume III in 1894 was greeted by a storm of criticism. The neoclassical economist Von Bohm Bawerk wrote a paper titled Karl Marx and the Close of his System accusing him of ‘incoherence’. Why did Marx start talking about values and then reveal a couple of thousand pages later that prices of production ruled the economy? Bohm Bawerk responded like this because, like most neoclassical economists, he was a positivist. He had what Engels, quoted at the beginning of this review article, called a metaphysical outlook. He looked at the economy and he didn’t see value. He saw prices. He analysed price movements and was incapable of seeing below the surface of events. An incorrect method leads to incorrect conclusions.

“It seems to be correct to begin with the real and the concrete…The economists of the seventeenth century e.g. always begin with the living whole, with population, nation, state, several states etc.; but they always conclude by discovering through analysis a small number of determinant, abstract, general relations such as division of labour, money, value etc. As soon as these individual moments had been more or less firmly established and abstracted, there began the economic systems, which ascended from the simple relations such as labour, division of labour, need, exchange value to the level of state, exchange between nations and the world market. The latter is obviously the scientifically correct method. The concrete is concrete because it is the concentration of many determinations, hence unity of the diverse.” (Grundrisse p 100-101) That is Marx’s method in Capital.

Von Bortkiewicz

Von Bortkiewicz followed up the debate with a paper in 1907 pinpointing what was seen as a simple logical inconsistency in Marx’s work (Wertrechnung and Presirechnung im Marxschen System). Von Bortkiewicz’s point was that Marx had produced prices of production from values as the ‘output’ of his economic model. But the inputs remained in value terms. Marx was a victim of his own mathematical naivety. Von Bortkiewicz, incidentally, was a friend of Walras. He also supervised Leontief’s thesis in Berlin.

Desai agrees with von Bortkiewicz. “He multiplied outputs by the price/value ratio but forgot that inputs are also goods and should also be similarly ‘transformed’.” (Marx’s Revenge p 64) As we see in the section on reproduction, what is an output for one capitalist (for instance bus-bars) may be an input for another. Von Bortkiewicz could help Marx in his naivety! He was a pioneer of a new approach that treated the economy as a set of simultaneous equations (input-output tables) where inputs and outputs could be solved mathematically. All you needed was an equal number of equations and unknowns. These economists often set up their simultaneous equations simulating the inputs and outputs of the economy in terms of a corn model. Since corn can be consumed or ploughed back into production as seed, it can be used to denote a ‘one commodity’ economy.

The main problem of Von Bortkiewicz’s and all the later mathematical solutions from a Marxist point of view was that they all produced results where either total value was not equal to total price of production or where total surplus value was not equal to total profit. From a materialist view either values or surplus value was being conjured out of the ether or made to disappear by our mathematical magicians. This opened the way to the notion of profit as a mark-up or result of swindling that we reject when we conceive of capitalism as a system based on exploitation of the working class.

Sraffa

Von Bortkiewicz was followed by generations of mathematically sophisticated economists who developed input-output models of the economy. In particular Piero Sraffa produced a slim book in 1960 Production of Commodities by means of Commodities that spawned a whole industry of Marx-refutations. Sraffa had actually edited the collected works of David Ricardo, the illustrious classical economist and predecessor of Marx. The Marxists labelled his school as post-Ricardian.

Steedman

This trend reached its peak in the book Marx after Sraffa by Steedman in 1987. From ‘correcting’ and ‘tidying up’ Marx’s anomalies, Steedman took the next logical step. Why bother starting with the ‘detour’ through value at all, since it was so imperfect? Why not just deal with the relationship between inputs and outputs to work out the surplus generated in the economy? Then slap on class struggle to work out the distribution of the surplus between workers and capitalists. Value was ‘redundant’!

Nobody can object to economists like Steedman following this procedure. What we can object to is his passing this off as a critique of Marxism. It is no more a critique of Marxism than it is a critique of egg mayonnaise or ballroom dancing. It is just nothing to do with egg mayonnaise, ballroom dancing or Marxist economics.

Steedman certainly generated some funny results. On p 264 of Marx’s Revenge, Desai notes, “one could have negative surplus value, yet positive profits.” For anyone trained as a materialist and a Marxist, this is just not possible. Marxists nevertheless may find themselves intimidated by economists like Steedman. He produces a weighty book almost entirely made up of algebra which purports to refute Marxism. Our advice is: if you were drawn into the socialist movement and a study of Marx because you wanted to fight for a better society - don’t give up right away just because you have problems getting your head round Steedman’s algebra!

Ever since 1907 we have been challenged to spot the logical flaw in the procedure of von Bortkiewicz and his successors. Of course, there is no logical flaw – given their initial premise. The whole method and starting point of the critics of Marx are wrong.

The entire approach of input-output analysis is predicated on the economy clicking instantaneously into equilibrium states. We say it doesn’t do that. But note that the maths of von Bortkiewicz and the others is not ‘real maths.’ It does not process real information about a real economy ‘out there’ somewhere. All the algebra does is to follow through the equilibrium and market clearing assumptions of the model and come to the conclusion that the results will differ from those of Marxist analysis. What a surprise!

The Cambridge capital controversy

Conventional neoclassical theory postulates a universal principle of diminishing returns to a factor. If more capital is thrown at production, we expect its marginal productivity and hence the return (the rate of interest) to fall.

But how do you measure the quantity of capital? Capital goods are naturally heterogenous. How can one compare a fork lift truck to a turret lathe or a bank of PCs in an office? The only thing they have in common is they can all be had for money. How much money? How do we value capital? By its return. And how do we calculate its return? We calculate it by the quantity of capital deployed.

It has to be said that Sraffa and his disciples delivered blows against orthodox neoclassical economics, in particular their capital theory. In 1962 Sraffa asked, “What is the good of a quantity of capital…which, since it depends on the rate of interest, cannot be used for its traditional purpose…to determine the rate of interest?”

So basically neoclassical economics derives the price of capital from the rate of profit (or the rate of interest as they usually call it) and the rate of profit from the price of capital. This procedure, as the left Keynesian economist Joan Robinson observed, was ‘perfectly circular.’ This is the absurd theory that Sraffa is ridiculing. Neoclassical economics cannot give us a theory of distribution, which is what all this apologetic stuff about ‘rewards’ to factors of production is supposed to do. J. B. Clark spells it out, “What a social class gets is, under natural law, what it contributes to the general output of industry.” (Distribution of Wealth, 1899)

In the post-Ricardian view the return on capital depends in part on the class struggle, which determines the distribution of income between wages and profits. The distribution of income, in turn, determines the return on capital. We do not have space to deal fully with the Cambridge capital controversy, as it does not directly impinge on the assault on Marxism. Suffice it to say that Samuelson, a defender of the prevailing orthodoxy, was forced into unconditional surrender (A summing up). Of course this does not prevent colleges and universities all over the world from dinning this discredited theory into the heads of unfortunate economics students. Joan Robinson was also anxious to turn the debate into a wholesale assault on the notion of equilibrium (see the section on Equilibrium). She understood that methodological issues were at the heart of the differences and characterised the debate as ‘history versus equilibrium.’

Where we stand

What is the Marxist position on the evaluation of capital goods? We believe that capital goods have a value proportionate to the labour time congealed within them just like consumer goods. We agree that individual capitalists have no interest in or understanding of the labour theory of value. They ‘value’ or rather price capital goods according to the return on them. This ‘illusion of competition’ produces prices that are totally at odds with their values in Marxist terms. This is still more the case when, in the overwhelming majority of cases, ownership of the means of production exists through share ownership. The ‘value’ of a company in terms of total share price bears no relationship to the physical assets the company owns. This gives rise to the phenomenon of fictitious capital, valueless pieces of paper that nevertheless entitle their owner to a share in surplus value.

The expression ‘rewards to factors of production’ is, of course, a loaded one. George Bernard Shaw wrote a letter to The Times criticising the bourgeois economist Mallock in these terms. “Interest is paid mostly to people who could not invent a wheelbarrow, much less a locomotive.” No more than rustic ignorance is “the notion that the people who are now spending, in weekend hotels, on motor cars or in Switzerland, the Riviera and Algeria the remarkable increase in unearned incomes recently noted, have ever invented anything, ever directed anything, ever even selected their own investments without the aid of a stockbroker or a solicitor, or even as much as seen the industries from which their incomes derive.” (Quoted in Dobb – Arguments on socialism p 7)

Even if we accept there should be a ‘reward’ to capital as a factor of production (and there is not a single reason why we should accept that) why should the reward accrue to its owner? Marx realised the whole notion of factors of production was devised to invent a justification for the reward to capital. Land, labour and capital “have about the same relation to each other as lawyers’ fees, red beet and music.” (Capital Vol III p 814)

[Note: Most of the quotes on the capital controversy used here and in other parts of the review article are taken from a survey in the Journal of Economic Perspectives Vol 17, no 1, 2003, pp199-214 by Cohen, A. and Harcourt, G. called Whatever happened to the Cambridge capital theory controversies? Geoffrey Harcourt was the original chronicler of the debate in Some Cambridge Controversies in the Theory of Capital, 1972]

The transformation problem: the solution

How can Marx be defended from his schoolboy mistakes in not transforming inputs? He doesn’t have to be. Marx was not a prophet. He was first of all a revolutionary.  All revolutionaries make mistakes. If Marx was mistaken, we should admit it now. But, in any case, if we admit his procedure was wrong, what conclusions should we draw?

It is worth repeating the words of the young Marxist Hilferding in his reply to Bohm Bawerk. “Is it really true, however, that in default of a knowledge of the ratio” (between values and prices of production) “the law of value becomes unworkable? In striking contrast with Bohm-Bawerk, Marx looks upon the law of value not as the means for ascertaining prices, but as the means for discovering the laws of motion of capitalist society. Experience teaches us that the absolute height of prices is the starting point of this movement, but for the rest the absolute height of prices remains a matter of secondary importance, and we are concerned merely with studying the law of their variation.” (Hilferding’s article Bohm Bawerk’s Criticism of Marx is hard to find in text. Both it and Bohm Bawerk’s Karl Marx and the Close of his System are available on the www.marxists.org website)

Desai seems to suggest that if Marx was mathematically naïve enough not to understand the inconsistencies his attempt to solve the transformation of values into prices of production led to, then as a consequence we should all give up trying to change society for the better. As if young people who were drawn into socialist politics because capitalism produces mass unemployment, poverty and war should accept the system because Marx made a mistake in some manuscripts he wrote over a hundred years ago! This is not only ridiculous in itself, it shows a basic lack of understanding as to what Marx was about.

Profits and innovation

Desai remarks, “I can accept that prices are proportional to values but still refuse to say that all profits come from the exploitation of labour.” Desai shows a fundamental incomprehension of Marxist economics when he goes on, “Logically there are formidable problems in showing that profits come from surplus value alone…for one thing the Marx calculus neglects the importance of innovations which raise productivity dramatically across many industries.” (Marx’s Revenge pp 64-65)

As we demonstrate below, a doubling of productivity means a worker is capable of producing twice as many use values as before. But the worker adds the same value, worked up into twice as many commodities. The value and hence the price of the commodities will fall. In An introduction to Marx’s theory of value (on this website) we gave the example of what happened to ballpoint pens after the Second World War in the section on Marxist economics. This is what is happening now to computer memory. This is what happened a hundred years ago when Henry Ford and other pioneers turned car manufacture from a handicraft process for luxury goods to mass production for a mass market and reduced the value and price of an auto accordingly. This is how capitalism constantly revolutionises the production process.

But what is Desai trying to prove about innovations? Marx does not ignore this - he is the economist above all others who emphasises this as the life process of capitalism. How do we reward ‘innovation’ – an abstract noun? If Desai means we should reward the innovator, then how? Under capitalism intellectual property is one of the most important property rights going. Contrary to legend, Bill Gates did not invent most of the innovations associated with Microsoft. He bought them. Should he be rewarded for being richer than the inventors? That seems perverse. Maybe he was just craftier than the people he negotiated with? That still doesn’t seem a very good reason for him to be the richest person in the world.

Meghnad should give up trying to assess the distribution of income under capitalism from some notion of fairness. He has enough of a background in left wing economics to know that when the bourgeois economists go on about ‘rewards’ for factors of production, that is just apologetics for capitalism. There is no fairness under capitalism. When Marx used the labour theory of value, he did so because it explained capitalist development, not because it should “allow labour to possess and enjoy the whole of its produce”. These are the final words of Thomas Hodsgkin’s 1824 pamphlet Labour defended against the claims of capital. Hodgskin was a diamond geezer and that was a fine slogan in its time (he was probably a syndicalist rather than a socialist) but his ideas are no longer an influence on those striving to change society.

Marx and equilibrium

Part of the misunderstanding of Marx’s approach lies in the infatuation with equilibrium, which is hard-wired into bourgeois economists’ brains. We dealt earlier with general equilibrium theory, and the occult optimising significance of equilibrium. Marx, on the other hand, regarded equilibrium at most as a moment of becoming as an inherently dynamic system lurched from one non-equilibrium position to another.

Meghnad seems to be unaware that a substantial group of Marxist economists working in academia have taken a stand against the tendency to assimilate Marx into orthodox economics. Marx and Non-equilibrium Economics, edited by Freeman and Carchedi, takes up the academic onslaught on Marx’s method. They make the point strongly that Marx’s work is regarded as ‘sequential and non-dualistic’. What does this mean?

Sequential

The introduction to the book first takes up the meaning of ‘sequential’. “The work of Carchedi, Freeman (et al)…demonstrates that this universally-accepted procedure…incorporates the assumption of equilibrium and market-clearing and has to be abandoned. This is the first conclusion that can be drawn from this book.” (p xi)

‘Sequential’ means Marx does not see the economy as a set of simultaneous equations to be solved. He saw economic processes taking place in real time. In particular he knew that rising productivity in producing outputs would have an effect on the price of inputs. But he did not see this process as a ‘uniform and instantaneous devalorisation.’

The same is true of the formation and reformation of prices of production. The formation of prices of production is caused by capital flowing in search of a higher profit. The aggregate result is a tendency for the rate of profit to equalise. Since these changes are the consequence of decisions by fallible human beings, it is obvious that they are a process and not an instantaneous outcome. Marx is clear. “The comparison of value in one period with the value of commodities in later periods…is no scholastic illusion…but rather forms the fundamental principle of the circulation process of capital.” (Theories of Surplus Value Vol II p 495)

Non-dualistic

What about ‘non-dualistic’? “The second conclusion, however, is just as vital. All interpretations of Marx agree that both the value and the price of any commodity are made up of two components: the value of constant capital and the value-product, or the value added by living labour. But virtually all modern presentations further propose that the value transferred by constant capital is equal to the value of the elements which make it up, that is, the value of the consumed means of production and raw materials.

“This view was not Marx’s…In fact the value transferred by constant capital is measured by the value as measured by the money advanced to purchase the elements of this capital.  Likewise the value of variable capital is measured by the money advanced to pay the labourer, not the value of the products he or she consumes.” (ibid p xi)

Isn’t this obvious? For the buyer, prices are data measured in money. When a capitalist buys labour power and means of production, he is not interested in whether their money prices represent values or prices of production. He is interested in how much hard cash he has to lay on the table. The terminology of Marxist economics is foreign to him. What interests him in his acquisitions is their use in the production process, and how much that use value is going to cost in money. The transformation question, in the form it was posed by Von Bortkiewicz and his successors, does not exist for him.

The case of labour power

The third point made in passing in the last paragraph may need underlining. The capitalist lays out constant capital and variable capital in money form. Constant capital passes its value unchanged to the final product. Variable capital is so called because it is that part of the capitalist’s outlay that can yield a surplus. It is his expenditure on wages, on the purchase of labour power. Variable capital is not actually variable when it exists in the form of a fixed pot of money. It becomes variable capital when it is laid out as wages and spent by the workers to perpetuate their labour power.

The workers take this money and buy and consume various commodities to keep themselves and their families alive. Why should they care whether these commodities are sold at their prices of production or their values? They consume them. By the time they get back to the workplace they have in many cases disappeared. They cannot, in other words, be regarded as inputs even in the same sense as the chocolate sprayed over a Mars bar is an input (circulating constant capital).

So what happens? The commodities are consumed by the workers to help reproduce a new generation of wage workers. But labour power is not produced capitalistically, but through a network of social relations such as the family.

To take a concrete example, the worker is paid his or her wages. He or she spends part of this on a curry on Friday night. The curry is an output for someone out there in the economy. Fortified by this and other nourishment ingested over the course of the weekend the worker succeeds in turning up to work on Monday morning. His or her labour is now an input into the economy (his labour, not the worker himself). We would regard this labour input as a later round of production and reproduction in real time, not a solution of simultaneous equations. Can any post-Ricardian out there explain why it is important to ‘transform’ the curry (which has already been transformed in another way by passing through the worker’s digestive system) from values to prices of production?

The criticism of Marx’s approach essentially boils down to the complaint that he is not an equilibrium economist. Equilibrium has no place in his analysis. This criticism is quite correct. Marx has a fundamentally different method from neoclassical or post-Ricardian economists – dialectical economics.

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