REBLOG: Ian Wright offers his very interesting solution to the transformation problem
I’m happy to say that my article on Marx’s transformation problem has now been published in the Cambridge Journal of Economics. After a little negotiation with Oxford University Press, I am able to link to a free version of the article from my website. Here it is.
Marx’s transformation problem and Pasinetti’s vertically integrated subsystems
This article is quite theoretical, and I’ve mentioned it previously Here, I want to be a little more blunt, in order to simplify the main message.
First, a frequent claim, both on the right and left of the political spectrum, is that the classical labour theory of value, and especially Marx’s version, is provably false, in virtue of a transformation problem. My paper unequivocally demonstrates the opposite: I prove that equilibrium prices, even in a capitalist economy with positive profits, represent the labour time actually supplied by workers. So the central claim and intent…
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The Real Movement 
Hi Jehu,
I’ve been enjoying trawling through your blog as I get to grips with Capital. Your view of the transformation problem seems quite intuitive to me, especially as I’ve pondered the nature of fiat currency from some time before I became interested in Marx.
How far do you agree with Wright’s solution? I only ask because you seem to have been influenced by Postone, while Wright doesn’t think much of him from the comments on his blog.
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I don’t agree with Wright at all. I just thought his article was an interesting example of how mixed up one can get approaching the problem with math rather than thinking the problem through step by step. As Moseley points out in his version of the transformation problem solution, Marx begins with money-prices (exchange values).
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Thanks, that makes things clearer. At the risk of sounding lazy, that’s the appeal of something like your approach… no pages of algebra to wade through!
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Beat me to it.
I am stuck on the claim that “equilibrium prices … represent labor time…”.
One obvious problem is that Marx says nothing about equilibrium and the concept has no use in his theory.
Less obvious is that if prices “represent” something else, namely “labor time”, that suggests that “labor time” exists separately and apart from prices. Yet one need do no more than take a hard look at Chapter 1, Vol. 1 to figure out that socially average labor time and its temporal quantification is imminent in prices — they are two moments of a single (complex) social relation.
Prices *mediate* concrete labor through the logic of a socially average labor time and that logic resides in the fully developed capitalist phenomenon of commodities and exchange prices.
Also, just a note: Marx’s theory is not split into a “micro-” and “macro-” economics. There are no claims in there that make sense only for the total capital in aggregate, etc. That mistake is from Mosley.
Whatever mathematical problem this guy set himself, I don’t think it has much to do with Marx.
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…sigh…
You say “Marx says nothing about equilibrium and the concept has no use in his theory”. Here’s a quote from Capital volume 3, in the context of Marx discussing prices of production:
“The competition between capitalists — which is itself this movement toward equilibrium — consists here of their gradually withdrawing capital from spheres in which profit [is] below average, and gradually investing capital into spheres in which profit is above average.”
And many more examples can be presented. In fact, it makes no sense at all to discuss out-of-equilibrium or disequilibrium processes without reference to equilibrium. Marx was concerned both with the turbulence of capitalism and its ability to stably reproduce itself over time, i.e. *both* equilibrium and disequilibrium. Of course, there’s much more to say here.
And of course prices and labour time are connected by the dynamics of the law of value. But they are not the same thing! This is like confusing the thermometer with the fire, and Marx was no fool. If you’d like to understand their “mediated” relationship a little better take a read of:
https://ianwrightsite.wordpress.com/2017/06/07/karl-marxs-invisible-hand/
Best wishes.
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Thank you Ian.
I think your reply was helpful in that I believe I now see more clearly the essence of our disagreement.
You wrote: “I prove that equilibrium prices, even in a capitalist economy with positive profits, represent the labour time actually supplied by workers.”
A few considerations:
Marx discusses the condition in which prices generally equal values in Chapter X of V3. In such a state: Capital is perfectly mobile as is labor. All labor is simple labor – e.g. all hourly wages are the same. Workers have no preference as to what they do but simply (with no friction) go wherever they are needed and to whichever task — it is all the same. Capital’s dominance is absolute. This dystopian absurdity is to dispose of the equilibrium of prices as having material sensibility as an achievable condition, even “approximately”.
You quoted Marx to show that the concept of equilibrium had a role in this theory. I demur. What you quote: “The competition between capitalists – which is itself this movement toward equilibrium – consists here of their gradually withdrawing capital from spheres in which profit is for an appreciable length of time below average, and gradually investing capital into spheres in which profit is above average”.
In Chapter XXII, Marx is talking about an equilibrium of *rates of profit* for each *capitalist*, which in context has only an extremely indirect and complex relation to market prices of individual commodities. E.g., the role of the credit system in this chapter.
In both instances, Marx is identifying “equilibrium” as essential an element of the conscious rationality that describes self-understanding in a capitalist society (and thus appears in “political economy” literature) — but that is an abstract rationality detached from material reality (via the fetish, no less). He is describing the insanity of the prevailing rationality of self-understanding in a capitalist society.
Against those objectively insane concepts of equilibrium, Marx has explained the nature of Value, which more adequately explains the real movement of capitalist society.
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Marx, in the few lines I quote, is referring to the objective process of the formation of a general profit rate (across all sectors of a capitalist economy). This lawful tendency is discussed throughout volume 3, although see especially chapter 9 on “the formation of a general rate of profit”. Note that this tendency toward the formation of a general profit rate is equivalent to the formation of prices of production, where all capitals earn the same return. Marx’s prices of production are an equilibrium concept. You think you’re disagreeing with me, but you’re disagreeing with Marx (which is fine, of course, but perhaps you should think further why you reject Marx’s concept of prices of production). Of course, Marx is well aware that this process toward the formation of prices of production is only a tendency that is not empirically realised. Nonetheless the reallocation of capital across sectors, and the continual search for higher returns, is a real, objective process that is actually happening all the time. The variance of the distribution of individual profit rates is bounded by this stabilising tendency. Best wishes.
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Ian, I thank you for your engagement. I’m very serious about that. It is personally helpful to be challenged to scrutinize my own understanding and expression. It’s an honor. I will leave it with this:
You wrote: “Marx, in the few lines I quote, is referring to the objective process of the formation of a general profit rate (across all sectors of a capitalist economy).”
The level at which a general rate of profit emerges in its most objective expression is at the price of loanable capital. The level at which competition gives rise to the general rate of profit is the level of competing capitals – competing owners of loanable capital. With the full development of “financialized” capital, the competition among owners of loanable capital is completely abstracted from the level wherein the cost-prices of individual commodities are settled.
In other words, the general rate of profit ultimately has no fixed relation to the prices of individual commodities other than as an estimated statistical average. In particular, the general rate of profit – and even the imaginary Shangri-La in which competition among capitals ends in a tie – does not equalize profits on individual commodities. As always, the rate of profit on individual commodities is determined solely by the organic composition of their production, and by their market price. The distribution of surplus among competing capitals is a very far off process.
It is absolutely true that many individual actors in a capitalist economy act *as if* there were a tendency towards price equilibrium. That belief has explanatory power even though it is not a true belief except in a wholly circular, tautological sense (the average equals the average). Equilibrium has no role in Marx’s theory. A prevailing belief in equilibrium has an important role in Marx’s theory.
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I think (and I’m relatively new to all this, so bear with me) from another of Wright’s posts that he thinks Marx (and Ricardo) didn’t frame things quite rightly with regards to the transformation. So he distinguishes between ‘technical costs’ of production (labour time, physical capital) and ‘social costs’ (state taxes, money-capital) and claims that classical labour theory only thought of prices in the first sense, whereas they’re actually the sum of both. So he is performing a minor correction of Marx in order to salvage the LTV, at least from his perspective…
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Thomas, you re-state that “Equilibrium has no role in Marx’s theory”. But the opposite is the case. Marx’s theory makes no sense without the concept of equilibrium. Why? Because Marx aims to identify the underlying laws of motion of capitalist society, and laws have equilibrium states (attractors). We need to theorise the relationship between multiple laws, their interaction within a complex system (a totality), and their joint determination of empirical reality.
E.g., the law of the formation of the general rate of profit has an equilibrium (prices of production) that, in empirical reality, is not fully realised; it therefore acts as a tendency, and bounds the variation of profit rates.
E.g., the law of value itself, which in simple commodity production has an equilibrium where prices are proportional to labour-values. But, again, even in simple commodity production, the accidental vagaries of supply and demand, and the continual re-allocation of labour between sectors, ensures this equilibrium is not fully realised, and therefore the law acts as a tendency.
Just because empirical reality does not exhibit equilibrium states in no way implies the absence of laws and their corresponding equilibria. If Marxists thought this way, they would reject the law of value: because when we examine market prices we find no obvious relationship between them and labour time. As Marx says:
“in the midst of all the accidental and ever fluctuating exchange relations between the products, the labour time socially necessary for their production forcibly asserts itself like an over-riding law of Nature. The law of gravity thus asserts itself when a house falls about our ears. The determination of the magnitude of value by labour time is therefore a secret, hidden under the apparent fluctuations in the relative values of commodities.”
The point is this: we cannot understand the out-of-equilibrium dynamics of capitalism without understanding the underlying laws, their equilibria, and how they interact.
I give some more details here: https://ianwrightsite.wordpress.com/2017/06/07/karl-marxs-invisible-hand/
Best wishes, Ian.
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> “Because Marx aims to identify the underlying laws of motion of capitalist society, and laws have equilibrium states (attractors).”
The mathematical concept of an attractor assumes a mathematical function indexed by time — a way of computing, in this case, “the state of capitalism” at a given point of time provided with a precise enough initial condition and some mathematical laws of motion.
There are no such laws in Marx. Even concepts like the tendency of the rate of profit to fall don’t entail such a function. The concept of attractors here is misplaced.
You quote chapter 1 on the fetish, the passage mentioning “a secret, hidden under the apparent fluctuations in the relative values of commodities.”.
The secret is the concrete labor that is being mediated by the exchange of commodities, and the mechanisms of that mediation. In day to day life we see the objects in the market, their prices, and in the most abstract way imaginable the fact that they are all “produced” — we imagine laws of the sort you describe, laws that would explain the motion over time of these objects and quantities. The secret – the real key to understanding the motion of these objects – is different from that surface appearance. The secret is the concrete social meaning of this exchange system as a mediator of labor.
It is absolutely true that Marx’s theory makes time-based predictions (and very good ones, I think). These are not derived with reference to the kind of mathematical function you are imagining.
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Thomas, Marx devoted considerable time and energy to studying the mathematical calculus and differential equations. His copious notes on the topic have been published and are available online. Why did he study them? Because, in a letter to Engels, he hoped they could capture the laws of motion of capitalism. This work does not appear in Capital, which is restricted to natural language, and some simultaneous equations describing the reproduction schemes in vol 2. Best wishes, Ian.
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Well done! Congratulations!
#SelfEducate #AbolishSurplusLabour #SolidarityNotCharity
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