Talk:Transformation problem

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Contents 1 Rework 2 Numeric Example Rework 3 Updated References 4 Previous Talk Header 5 Formatting Math 6 from FifelFoo's talk page 6.1 Let’s start from the beginning. 6.2 Problem number 2. 6.3 Solution for r 7 "Econometric" interpretations of Marx? 8 "Supposedly" ? 9 Which prices ? 10 Reply to Mario 11 kudos 12 Non-Sraffian interpretations of Marx? 13 POV 14 The Current Article Make My Head Spin (Simplified Version of Transformation Problems) 15 Simplified Version 16 Simplified Version of Transformation Problems 17 Marxism label 18 Old elaboration material 18.1 Overview 18.2 British classical labour theory of value 18.2.1 Simplest case: labour costs only 18.2.2 Capital costs 18.3 Marx’s labour theory of value 18.3.1 Labour as the "value-creating substance" 18.3.2 Surplus value and exploitation 18.3.3 Variable and constant capital 18.3.4 Value formulas 18.4 Transformation of values into prices 18.4.1 Marx's reasoning 18.4.2 Marx's "error" and its correction 18.4.3 The non-transformation problem 18.5 Formal conclusions 18.5.1 Samuelson's eraser algorithm 18.5.2 Special cases 18.6 Implications and interpretations 18.6.1 Mathematical vs historical transformation 18.6.2 Other Marxist views 18.6.3 Mainstream views 19 references moved from main article 20 References 21 on the recent revert 22 2 Objections to the methematical rendering 23 Dualistic Monism and Labor Theory of Value 24 One - Positive - Yang 25 Two - Negative - Yin 26 Bias

[edit] Rework

I started the process by composing a header that I think is more accessible, more accurate and more balanced than the previous one. The sentence structure may still be a bit too complicated and could stand some editing to make it clearer and more simply stated. Also the remaining exposition is still sorely in need of rework. I think Sraffa's appearance in the overview is a little premature. I don't want to diminish his contribution to the debate, but it was more of an inspiration to others both pro and con than a definite statement on his own part on the topic. Despite the use of linear algebra in the state of the art on this topic I think a simple thee sector numeric example would be more appropriate and more accessible for an ecnyclopedia article on the topic. Also the artilce as it stands focusses too much on the algebraic renditions that show a failure to transform and barely mentions any of the many more renditions that support the transformation. This is a serious NPOV problem from my POV. Finally, I'll try to update the References to include what i cited. --Cplot 06:05, 3 June 2006 (UTC)

A few more explanation of my edits. I removed the statement about Samuelson being the standard reference on this topic which is just wrong. Samuelson simply dabbled in this topic. He was minor Keynesian economist who read enough of Marx to write up a criticism. He is seldom sited in this literature except for the snideness or recklessness of his work on the topic. Second I removed the paragraph suggesting that there is a definitive modern mathematical proof (some kind of slam dunk) regarding the transformation problem. This is patently false and violates the NPOV guidelines. I don't like to trample other people's work, but please show some deference to the community's guidelines. --Cplot 06:20, 3 June 2006 (UTC)

I removed the Steedman / Böhm-Bawerk paragraph I added to the header. I think it was not NPOV and probably not verifiable. I glanced at the latest Steedman article and it seems his response to the proliferation of work using linear production models to vindiate Marx's method is to look back to a golden age of 1920's britain where none of these supportive renditions had yet occured (in a Journal of Economic History of Thought (2004 v26i1) piece entitled "British Economicsts and Philophers on Marx's Theory, 120-1225"). --Cplot 02:27, 6 June 2006 (UTC)

[edit] Numeric Example Rework

I've now drudged through the symbolic (almost numeric) example which IIRC follows Bortkeiwicz's rendition (that's from my recollection, it's been a while sine I've read Bortkeiwicz on this). As I said earlier the problem with that is that's only one rendition that refute's Marx and Ricardo on this issue. This leaves out the many more renditions that support Marx and Ricardo. Also I think the exposition is very difficult to follow at times. I think as it stands it probably does more damage than good to leave it in there.

Also there are several peculiarities about this rendition that create some of the strange artifacts (I don't remember whether those peculiarities are endemic to Bortkeivicz's presentation or if they are just introduced here). One is that the only industry producing means of production (arrows) produces no surplus value. It also receives no profit. This is a strange ad hoc assumption and no justification is provided for that assumption. Is it because the arrow makers face no risk (as many argue is the reason for profit)? Because they don't have to face the fierce beaver in his natural habitat? Second, the only means of subsistance commodity (beavers) is also the money commodity. Third, why in the example do we restrict the value of beavers and arrows to always less than 1? I'm not sure if this has any perverse effects, but I also can't see the reason for the assumption. Marx made the simplifying assumption of a constant value of money (in this case, a constant value of beavers) but I can't tell what keeping the value below 1 does.

I think these peculiarities together are the only reason why you get the result in the "non-transformation" graph at the end. As the value of arrows decreases so too would the value of the money commodity. The quantity of surplus value realized in both the deer and beaver industries would also increase which would effect r. By arbitrarily fixing these variables that in Marx's exmaple move in concert, the stangre results are produced. I envision producing a numeric example where both pro and con can be presented side-by-side in a way that readers can easily understand the differnt renditions. These various renditions typically dispute the normalization and the conservation principle used (e.g, total value; net value-added; surplus value equal to total profit). --Cplot 18:30, 3 June 2006 (UTC)

I think the major fallacy in these critiques turns on the 'equal profit paradox'. The tendency to equal profit can only exist if there are in practice unequal profits(as investment capital flows between different sectors). I added the quote from Marx about fluctuation to highlight this point. The assumption that there is a fixed amount of profit runs contrary to Marx's whole conception - and to observeable reality - and it is not surprising that mathematical models which assume this absurdity are unworkable.--Jack Upland 07:31, 6 June 2006 (UTC)

[edit] Updated References

I may have gone overboard on adding references, but I want to drive home the point that there is an abundance of work on both sides of this issue. And I would even say that the thrust of the POV in the current discussion represents the minority opinon if there's any way to measure that. It certainly is not the majority opinion in the field and by no stretch of the imagination is it the sole proven position. Most of the work cited (espcecially that of Roberts, Mosely, Foley, Duménil and Lévy work through linear systems of equations, are often inspired by Sraffa's work and prove just as definitively that the trnasformation uphlds the law of value. What's more, I wanted to show how active this work is and not settled by Samuelson. If anything Samuelson restarted the whole debate, which for whatever reason lapsed sometime in the first part otf the 20th century. --Cplot 08:48, 4 June 2006 (UTC)

[edit] Previous Talk Header

This appears to be a pretty cursory treatment of what counts as the single most decisive critique of Marxist value theory. If no-one objects, I'd like to submit a far more detailed treatment, with appropriate summaries. Adhib 09:57, 26 Feb 2004 (UTC)

Please do. mydogategodshat 03:43, 27 Feb 2004 (UTC)

Job done. I have deliberately attempted to preserve the link with Eugene, since this seems to be how US-educated students of the topic are introduced to Ladislaus, though this connection can apparently obscure the discrete arguments offered in their two critiques. Adhib 07:57, 4 May 2004 (UTC)

---

I hope things are clearer now. Thanks to Fifelfoo, anyway. Mario 12:22, 10 July 2005 (UTC)

It seems I'm having chronic problems with formatting maths. Could anyone help? Thanks. Mario 13:49, 10 July 2005 (UTC)

[edit] Formatting Math

Dear Mario, <math> </math> are the basic tags for indicating maths. Within these tags you use a T_E^X like description system. See Help:Formula for the specific details. To format a very common variable setting like Ab / Cd you use this: <math> {A_b \over C_d} </math> which displays like this:

I'll copy our discussion from my talk page to here later on, so we can talk it out. Fifelfoo 23:07, 10 July 2005 (UTC)

I'm intending to go through and bring things up to style anyway. Another style point you should consider. Variables in body text should be in <math> </math>, not in <i> </i>. HTML tags (like <i> </i>) are not wiki style. Use emphasis (''emphasis'') or strong emphasis ('''strong emphasis''') instead. But you're using too much emphasis anyway, terms should probably be put in "quotes" instead of emphasised in standard wiki style. Fifelfoo 00:34, 11 July 2005 (UTC)

[edit] from FifelFoo's talk page

Thanks for your edits, which are mostly useful improvements on my text. There are however a few things which I feel you got wrong. To avoid misunderstandings, I propose now to discuss them with you, one by one, before going on to new edits.

[edit] Let’s start from the beginning.

Soon after the definition (unaltered from my text) you write: “The transformation problem comes into being when Marxist economics are used to predict opportunity costs. Within Capital Volume I states the relations of value between commodities, and the nature of the relations of production in a productive environment. Volume III describes the relationships between distributors of production. A solution to the transformation problem would unite Marx's statements regarding the structure of production with Marx's statements regarding the nature of distribution.”

As it stands, this appears to say that the “transformation” problem was not introduced by Marx himself. But this is just not true. Chapter 9 of Capital Volume III bears the title: “Formation of a General Rate of Profit (Average Rate of Profit) and Transformation of the Values of Commodities into Prices of Production”. Within it, you will find several tables, devoted to numerical examples, similar to my Table 2.

Hence, a more factual way to put things would perhaps be something like: “The transformation problem was formulated by Marx in Chapter 9 of Capital Volume III, where he also tried to solve it.”

If you want to add something specific about the role of this problem within Capital’s wider system, you might perhaps use Marx’ own words, taken from the same Chapter: “In Books I and II we dealt only with the value of commodities. On the one hand, the cost-price has now been singled out as a part of this value, and, on the other, the price of production of commodities has been developed as its converted form.” In fact: “Without such deduction the general rate of profit (and consequently the price of production of commodities) remains a vague and senseless conception.” On the other hand: “The transformation of values into prices of production serves to obscure the basis for determining value itself” since “The actual difference of magnitude between profit and surplus-value — not merely between the rate of profit and the rate of surplus-value — in the various spheres of production now completely conceals the true nature and origin of profit not only from the capitalist, who has a special interest in deceiving himself on this score, but also from the labourer.” In Marx’ view, the solution of the “transformation” problem is then also the way to see through such concealment.

My only objection to this would be the introduction of the Marxian notion of cost-price, which is a really unnecessary complication, as it also requires some proper (and critical) explanation. Mario 8 July 2005 11:15 (UTC)

I agree about the edits. I haven't read Volume III (it having no impact, despite Marx's assertion about the transformation of value into money-price being a moment when I am deceived as to the nature of my exploitation) as like the Autonomists I find my exploitation at the moment of usurption of my work (and the control of that value) :). I think your expressions, as quotes, should go in (I'll do it myself next edit) with a sentance to re-explain the quote (this is good style).Fifelfoo 00:34, 11 July 2005 (UTC)

Thanks. I assume you have read my latest edits to the article and are referring to that. By the way, sorry I didn't wait longer for your reply. As to Volume III, I think you really should read it, before writing on its content. You'll see that the transformation of value Marx talks about there is not into money, but into (relative) prices, i.e., the same exchange ratios between commodities Marx started from in Chapter I of Volume I. It all goes back to that, the very beginning which I have now quoted in the article. As to the way you "feel your exploitation", I think I can see your point, but I do not believe it has any relevance for Marx' treansformation problem, seen from a NPV. For the rest, I'll wait to see your next edit, See you. Mario 01:37, 11 July 2005 (UTC)

[edit] Problem number 2.

At the beginning of the third paragraph your edit reads: “It has been demonstrated to the satisfaction of most economists that a general solution to the transformation problem does not exist.”

Now, as it is still stated in the introductory paragraph of the article, the transformation problem is a mathematical one, concerning the existence of a set of functions with certain well-defined properties. So what you have written here amounts to something like: “It has been demonstrated to the satisfaction of most economists that 2 + 2 = 4”. This is slightly ridiculous but of course strictly true, since indeed most economists agree with that. However, it may be actually seriously misleading if it is taken to mean – as it well might – that the conclusion 2 + 2 = 4 is essentially subjective, so that any numerate non-economist (and even some economist) might disagree with it. Maths is not an opinion, as I am sure you agree.

My suggestion here would be just to revert to my original formulation: “It can be shown that, contrary to Marx’ opinion, such a general rule does not exist, so that his transformation problem has actually no solution, outside some very special and unrealistic cases.” This of course has the extra indication that Marx got his maths wrong (“contrary to Marx’ opinion”). Yet this is not only true, but the object of a later sub-section in the article. So why censor it? Mario 8 July 2005 16:29 (UTC)

Mathematical demonstrations depend on the quality of the demonstration. For example

1. ,
2. , therefore
3. i = j!

I have no capacity to follow Sraffa's proof, but until there's two sources attesting to Sraffa's proof which are themselves undisputed (appreciations and analysis of the demonstration, or two textbooks of PE holding Sraffa's demonstration as true) I can't follow the article asserting Sraffa's correctness.

Merely stating 2 + 2 = 4 isn't sufficient, and some mathematicians spend a great deal of time exploring the basic nature of integer operations.

As you noted later in the article there are disputants to Sraffa's demonstration, and I'm aware of Mandelian Marxist-activists who dispute Sraffa on this.

My edit was one of caution where Sraffa's demonstration was only single sourced. Fifelfoo 00:34, 11 July 2005 (UTC)

Oh, dear! As to "Sraffa's proof", I'm sure that if you tried you could really follow Sraffa's reasoning. You see, a truly technically proper proof of Sraffa's proposition involves some linear algebra, and has been given by other authors [see Samuelson (1971) and the references quoted there]. However Sraffa himself was a funny, old-fashioned chap, and believed in not using maths, but just ordinary discoursive logic, when explaining things to others. So his Chapter VI does not even mention eigen values. It's all pure verbal reasoning an intuition, and – with a little effort – you would certainly be able to follow it. But this was in 1960. Since then there have been scores of works with the proper maths in it. Just look at Samuelson (1971) and the bibliography at its end, if you don't trust me. Your Mandelian friends just don't know what they are talking about. As for me, I have never "noted earlier" that the proof is disputed (which, technically, it is not). I have only noticed – thanks to you – that some innocent people simply refuse to accept it, on non-mathematical grounds. Which brings me to my earlier attempt to distinguish between scholars and activists. On reflection, I agree with you that there is no objective way to trace an exact boundary – and so I have dropped the subject. Yet charlatans do exist, and this, I feel, is a macroscopic case in point. You don't write it into Wikipedia, of course. But you keep it in mind. Cheers. Mario 02:22, 11 July 2005 (UTC)

Maybe we can paraphrase or summarise Sraffa's reasoning. I'm reasonably conversant with Volume I, but I'm not going to be able follow a mathematical proof. So if we can use a mathematical demonstration and follow it up with Sraffa's discursive logic that would be great. I expect we can use Samuelson's bibliography (and Samuelson himself) to indicate the firm agreement around the demonstration. Having some more graphs to indicate that the value => price-ratio issue is central would be good. Fifelfoo 02:27, 11 July 2005 (UTC)

As I said in this article, the proof happens within a framework. This framework is an analytical structure called a linear production model. So what you propose is to write an article on linear production models. That is certainly a very good idea, and should be done, but it means writing a big, technically complex and separate article. Given time, I might have a try at it. Then the Transformation article could have a link to it. That would be great, but not for now. As things stand, we already have a special-case proof in the new Non-Transformation sub-section, which does not require Sraffa's result. I designed the "Smith plus arrows" little model precisely because it allows to side-step the "reduction" to dated quantities of labour. I think that for the time being that proof should be enough. We are not really asking our readers to take anything on faith. Yours Mario 03:57, 11 July 2005 (UTC)

[edit] Solution for r

For FifelFoo: it's right as it's standing, as you can see solving from the previous expression. Mario 13:03, 12 July 2005 (UTC)

[edit] "Econometric" interpretations of Marx?

Econometrics is a branch of statistics. It has to do with fitting relationships to observed economic data and the like. It has nothing to do with the subject of this article. --Mario 21:34, 12 July 2005 (UTC)

[edit] "Supposedly" ?

The lead section was: "According to the conventional interpretation, in Karl Marx's Economics the transformation problem is the problem of finding a general rule (or set of functional relationships) to "transform" Marx’s "economic values" defined and used in Capital's Volume I into the "competitive prices" (or " prices of production") of Capital's Volume III. This specific problem is supposedly first mentioned by Marx himself in Chapter 9 of Capital's Volume III (a manuscript which Marx did not publish during his own life), where he also tried to solve it." Yet Capital's Volume III was edited by Engels, and its Chapter 9 bears the title “Formation of a General Rate of Profit (Average Rate of Profit) and Transformation of the Values of Commodities into Prices of Production”. Presuming nobody really wants to accuse Engels of forgery, I have eliminated the bolded bits. --Mario 14:59, 14 July 2005 (UTC)

I guess the point was that Vol III was a draft (as acknowledged by Engels and only lightly edited by him) and it's a bit rich to carry on about Marx's 'mistake' (essentially an oversimplification) without pointing this out.--Jack Upland 22:22, 21 January 2006 (UTC)

[edit] Which prices ?

I have noticed a new paragraph recently added to the article, which begins thus: "Some Marxian authors argue, in the tradition of Oskar Lange, that Marx's critics mistake the significance of his value theory, in good part because they operate with a "deformed" notion of prices, price formation, price aggregation, and the real use of prices." I would just like to point out that the prices relevant to the transfotmation problem, and dealt with in the article, are Marx's own prices of production, as defined and used by him in Capital's Volume III. This being so, the added bit on "deformed" prices in the transformation problem looks to me – with all due respect – as entirely nonsensical. Poor Lange cannot now defend himself, but that seems no excuse to libel him. I'll wait a few days, and if nobody provides some counter-argument I'll then delete the paragraph in question. --Mario 21:15, 23 July 2005 (UTC)

[edit] Reply to Mario

Thank you Mario, for your comment on my insert. I am not intending to libel anybody. To clarify my view in a simple essay if you care to read it, my interpretation of the transformation problem is different from yours. I do not think there is a general rule specifiable in terms of mathematical functions or simultaneous equations by which prices could be derived from values, and in that way prove the existence of values. At best, such modelling might clarify some of the main factors of what is involved. After all, economic "values" themselves can only be quantitatively expressed or stated either in units of labour-time, or in prices. The project is therefore doomed from the start if its purpose is to prove the concept of value, and can only produce poetry e.g. about beavers and deers. If I am e.g. a psychotherapist and I tell my client what his problem is and how he can solve it, I am not going to be successful if the problem is really a different one, framed in a different way. To succeed, I must first find out what the client's problem really is, and how he sees that, so that I can specify terms of a solution usefully. What neoclassical economists like Samuelson typically do is that they tell Marx what his problem is, or impute a problem to him. Maybe it kindles their vanity, but it helps nobody. At best you can say they have earnt money talking nonsense. So what is the real problem here? Marx tried to find a way of modelling the distribution of profit income, under the condition where each enterprise produces different amounts of output value and contributes to the total value produced by all, while the total value product produced by all enterprises together, prior to sale, affects the profit subsequently returned to each, on the assumption of a uniform profit rate established through competition, and that all output is sold. The problem remains essentially the same whether we take one sector or several sectors. His primary aim in so doing is to identify the main parameters of real economic competition, on the assumption that this competition is fundamentally about realising the maximum surplus value as profit income, and to identify the general outcomes towards which competition will tend to move. To do this, he examines simple and "pure" cases to show what is involved. However, this exercise already assumes the existence of output values as distinct from output prices - production prices or otherwise - and does not prove the existence of values at all. The only "proof" we can have here, is that output values have verifiably been produced, while what their sale prices will finally be, is as yet uncertain, prior to sales. Yet, assuming all output is sold, we must theoretically assume at the very least a systemic relationship between total output values prior to sales, and output prices after sales. Their identity in aggregate is at best a methodological assumption; Marx often assumed they would be approximately equal in reality, but acknowledges in chapter 49 of Vol. 3 that under dynamic conditions they will diverge; Engels later argues the same thing in a letter to Conrad Schmidt. There is no logical proof possible which would demonstrate that Marx's concept of value is true, and others false; any such "proof" would be metaphysical, and insofar as you argue this you must be correct. Hence Marx's own irritation about "dumb" critics who accused him of failing to prove his concept of value to be true; his reply was, that these critics failed to see the problem he tried to solve. The attempt to furnish a proof of this type just confuses the theory of value itself, with the object which the theory aims to explain. At best, we can say that Marx's concept of value is either logically coherent or not coherent, and we can logically specify the limits of the application of the concept or investigate that empirically. We could also say his concept is more or less coherent than that of its rivals. But that does not mean that there is no empirical proof possible; of course there is, namely we can devise all sorts of tests of whether or not relative price movements, social processes of exchange and economic behaviour observably really do occur in the way Marx claims or predicts they will do (as Shaikh, Ochoa and Cockshott among many others have tried to do). And we can compare our results with alternative explanations of the same phenomena, to check which is most credible. These tests could be based on e.g. statistical or historiographical evidence or on direct observation. Ultimately, the choice to accept or reject the theory however depends on its explanatory and predictive power. It is very obvious though that if imperfect competition exists (e.g. oligopolies and monopolies) or if output fails to sell, then Marx's simple models are simply not sufficient anymore. In that sense you must be correct, if you argue Marx examines only "pure" or "special" cases, and does not offer a comprehensive theory of prices, only an abstract summary of overall outcomes under idealised conditions. Obviously the very notion of economic competition itself implies the attempt to block competitors, but the aim of Marx's exercise is to assess the overall results to which the process will tend. Marx is not trying to state an equilibrium condition either; after all, he generally already assumes abstractly all output is sold or distributed in his examples. In fact, Marx has no "equilibrium theory" in the neoclassical sense, only a theory of economic reproduction which dynamically states the conditions of capital accumulation on an increasing scale. A capitalist economy is, according to Marx, in "equilibrium" if it can successfully reproduce its social relations of production, but this process is compatible with all sorts of market fluctuations (disparities between supply and demand). It is only when great disparities develop between supply and demand in critical or strategic areas, that the reproduction of the relations of production itself is threatened, and only in that case a real "disequilibrium" of the capitalist economy occurs. What people such as Lange and Kalecki among others tried to do, is to develop a more realistic theory of prices consistent with this notion. This does not mean that all neoclassical theory is nonsense; its weakness is only that it typically assumes prices and exchange happen without inquiring further into their nature, as if exchange was a natural process and not a social one, and as if all prices are ontologically in the same class; that it assumes that markets will naturally tend towards equilibrium; and that it lacks a coherent, unified portrayal of capitalist social relations. The result of that is a pragmatic, ad hoc eclecticism which may offer perfectly valid explanations of particular cases, but not a profound explanation of the system as a whole. That is why Oscar Lange tried to integrate the insights of classical political economy with neoclassical economics.

When Marx refers to the transformation of commodity output values into prices of production for output, he uses the term "transformation" in a dialectical sense of a metamorphosis of categories which reflect a real process of reciprocal interaction between different factors involved, in particular, the interaction between what individual actors or enterprises do, and the aggregate outcome of what they do, as a process of continual mutual adjustment. The real process is that you buy inputs for a given price, withdraw them from the market, and produce outputs with them which have a value; but what the actual market prices of those new outputs will be, is uncertain until sales, and only after sales can costs be deducted to obtain gross profit. The theoretical problem then is that the magnitude of that profit will be co-determined by the activity of all enterprises in the sector; in the same way, we can divide a whole economy into sectors and examine their interaction. Assuming competitive conditions and supply-demand balance, what will in that case regulate (set the limits, level or range) of market prices of output in the longer term? Presumably the average or ruling costs and the average profitability. But that is fairly trivial; the question now is how enterprises will respond to this reality, and that is where value theory really enters the picture. Enterprises will not simply aim to realise the average rate of profit, they aim to realise above average profits. The production prices that are the norm, independently of what any particular enterprise does, mainly act as a competitive constraint or limitation. What enterprises then do is to try and cut costs and get as much work out of the workers as they can, and they will try to do this regardless of whatever prices are in the market, about which they have no perfect foreknowledge anyway. This process cannot be grasped simply in terms of a rational response to price fluctuations, it must be grasped in terms of value relations, and in fact we cannot even do our accounts or aggregate prices without assuming some value-theoretic principle. Hence business people will freely refer to "real values" as distinct from market prices, something which Ricardo already noticed. But for Marx, as he explicitly says, values are not average prices, values deviate from production prices, and the concept of value is necessary not to explain statics, but to explain dynamics, the continual adjustment to market forces escaping from the control of economic actors.

In summary, Marx's critics argue he keeps assuming what he needs to explain, because rather than really "transforming values into prices" by some quantitative procedure, such that prices truly are inferred from labour-values, he either (1) equates values and prices, or else (2) he combines both values and prices in one equation. Thus for example either Marx infers a rate of profit from a given capital composition and a given quantity of surplus-value, or else he assumes a rate of profit in order to find the amount of surplus-value applying to a given quantity of capital invested. But this maneouvre cannnot contain logical proof of any necessary relationship between values and prices, nor proof that capitals of the same size but different compositions (and consequently different expenditures of labour-time) can obtain the same rate of profit. Marx explicitly argues both that prices deviate from values, and that the sum of prices is equal to the sum of values in a purified capitalism, but, critics claim, he fails to show quantitatively how a distribution process could then occur such that price magnitudes correspond to value magnitudes, and such that a uniform profit rate returns equal profits to capitals of equal sizes. In that case, there is again no proof of any necessary relationship between values and prices, and Marx's entire presentation seems an endless, unwarranted theoretical detour. So formulated, I think the controversy about the transformation problem can be said to involve both a real problem and a pseudo-problem. The real problem is (1) to understand how and why exactly values and prices must differ but are necessarily related, (2) how exactly the process of the equalisation of the rate of profit occurs, if the law of value really exists, and (3) what proof exists that the law of value really influences relative movements of actual prices. The pseudo-problem is the attempt to do this with the aid of a model containing simultaneous equations which assumes both that (1) the sum of prices equals the sum of values, and (2) that a uniform rate of profit applies to the returns on all capitals invested, despite varying capital compositions. Because such a model, which implicitly aims to state an equilibrium condition in abstraction from the temporal dissynchrony between the valorisation and realisation of capital under competitive conditions, can only reveal simple logical paradoxes of the type that (1) it is impossible to uphold the postulate of a uniform rate of profit and the postulate of total values=total prices at the same time, that (2) to find production-prices, a uniform rate of profit must be assumed, while at the same time to find a uniform rate of profit, production-prices must already be assumed, or that (3) a price level must be assumed, rather than be deduced from labour-values. Such a model I think poses a pseudo-problem, because it (1) misunderstands Marx's theory of the nature of capitalist markets, and the real dynamics of business operations under competitive conditions, and (2) it misunderstands the reason and significance of why prices must deviate from values according to Marx's theory. To illustrate the absurdities which are mooted, Ian Steedman once complained that Marx acted as though the same good has different prices depending on whether it is purchased or sold. That criticism would be valid if production did not exist. But since production does exist, inputs are bought at one set of prices and new, different outputs are sold at other prices... and between those transactions, a value-forming process occurs. User:Jurriaan

I must apologize with everybody for being the (involuntary) cause of this avalanche of prose by our new friend Jurriaan. To atone for my sins, I have carefully waded through all the 2,171 words of it. My conclusion is that – whatever else one might think of Jurriaan's well-meaning effort – it does not address my original complaint about his edit on supposedly "distorted" prices. His contention that " What neoclassical economists like Samuelson typically do is that they tell Marx what his problem is, or impute a problem to him" is just factually mistaken. The problem was very clearly formulated by Marx himself in Chapter 9 of Capital's Volume III, which bears the title “Formation of a General Rate of Profit (Average Rate of Profit) and Transformation of the Values of Commodities into Prices of Production”.

Rebus sic stantibus, I will now delete the incriminated paragraph. --Mario 10:19, 29 July 2005 (UTC)

Well, you haven't responded at all to what I said, nor does your presentation do justice to Marx's chapter 9 of Vol. 3. But I don't mind if you take the paragraph out. Moreover, I think your presentation contains some straightforwardly false interpretations of Marx's concepts. Obviously you can start talking about beavers & deers and suchlike when the problems get difficult. This might solve an immediate problem of frustration with the problem, but it does not solve the problem itself. I will try in future to write up an alternative presentation of the so-called transformation problem, then people can compare both presentations (I lack time for this at present, too many other jobs). BTW I said that economic "values" themselves can only be quantitatively expressed or stated either in units of labour-time, or in prices. This is not strictly true, since as I mentioned elsewhere, they can also be stated as trading ratios between different commodities. User:Jurriaan

I think that Mario's response is snide and unsatisfactory. You cannot incessantly demand that people explain themselves and complain when they do. No logical analysis of capitalism is possible without simplistic assumptions. (Mainstream economists, for example, are happy to make the absurd assumption that normal profit is zero.) To point out that Marx's mathematical models become more and more intractable as more 'real world assumptions' are made is true (and accepted by Marx). But as a mathematician would say, this refutation is trivial.--Jack Upland 22:40, 21 January 2006 (UTC)

[edit] kudos

an excellent article...I read this about a week ago and it still is very much stuck in my mind. thoughtful. i realize it needs some specialized background knowledge, but it seems as simple as it could possibly be. for someone who is pretty conversant with capital, vol. 1 this comes as an interesting revelation (and gives real impetus to finally reading the other books).

[edit] Non-Sraffian interpretations of Marx?

I happened to come across this paper by Fred Moseley (who's referenced in the article in what seems to be another argumentative context entirely, unless I'm quite confused), which describes and references at least two other ways of formalizing Marx's assertions about value that would have significant differences for the transformation problem. While I'm no economist, and am not qualified to rewrite the article, it'd be nice if someone who's better prepared to deal with the terminology could check this out. If I understand correctly, results would be different without the assumptions that "(1) the fundamental givens in Marx’s theory are assumed to be the physical quantities of the technical coefficients of production and the real wage and (2) the rate of profit is determined simultaneously with prices of production and both are derived from the above physical quantities." (from the linked paper) I can't find, in the existing Wikipedia article, a specification of at what time each value is determined, or follow the argument well enough to deduce this, and so confirm that it indeed makes these assumptions.

Why does this matter? Well, Moseley argues that Marx doesn't make a logical error at all. Even the existence of alternative interpretations makes the article's claim that "the modern mathematical proof that Marx's transformation problem has no general solution has never been formally questioned" misleading, at least. And I do know that some modern Marxists deny, for example, that the rate of profit ought to be determined simultaneously with prices of production (Chris Harman, a British Trotskyist, in Explaining the Crisis, 1984, for one).

All I'm going to do is try to find a place to add a qualifying sentence, but a more thorough examination and possibly rewrite by someone with some formal economics education would be good.

DKalkin, 12/7/05

Dear DKalkin, I'am sorry I only saw your enquiry just now and so did not reply earlier. It seems to me that your statement of Sraffa's "assumptions" reveals a rather basic misunderstanding. As far as I know, it is a generally accepted fact among economists that Sraffa's work, being static, has formally nothing to do with the determination of prices in the historical or causal sense. It is just a set of (timeless) conditions that prices must satisfy at any given point of time to be the "natural" prices Smith and Ricardo were talking about. Looked at this way, there is clearly no question of either "fundamental givens" or "simultaneity" of things. Nevertheless, it may well be that some non-expert author has "interpreted" (or reinvented) Sraffa in the dynamic way you say, and/or maintained that Marx's production prices are not basically the same things as Ricardo's natural prices, or whatever. These would be classic "tiny minority" points of view, rather like flat-earth theories, Although the official Wiki policy on NPOV intimates that all such theories should be ignored, I would of course have no objection to their proper mention within the article. However, I just happen to have no personal knowledge of such extreme oddities, nor much interest in them, and so I'm clearly not the right person to do it. Yours Mario 15:08, 14 January 2006 (UTC)

[edit] POV

While this is a well-written article, it does not conform to NPOV requirements. I have done some editing to partly rectify this. Controversially perhaps, I have toned down what I see as an attempt to rescue classical heroes like Adam Smith from being condemned along with Marx because their views were 'different'. If this is to be presented, it should occur on the LTV page, not here, and should be evidenced, not asserted. I have included some links to Marx's works, so anyone can read the original. The article asserted its tables were 'closely' 'similar' to Marx's work, but this is patently false and his algebra is nowhere near as complex as that!

Continuing POV problems include:

• The 'erasor algorithm', which is merely snide jibe.
• The straw-man imputation to Marx of the belief in a mathematical rigidity to the capitalist system - I've added some quotes to clear this up.
• The discussion of the historical relevance of LTV in which a sentence of Engels is attacked by a dozen footnotes. While it might be expressed in a neutral tone, the presentation goes against basic fairness. Prices in non-market economies is a complex and I believe much misunderstood topic anyway. Engels is merely giving historical grounding to Smith's deer and beaver fable, which the article endorses. This is of course different to merchant prices which are monopolistic in these societies.--Jack Upland 03:10, 23 January 2006 (UTC)

I am not a political economist. I TeXified most of the algebra so that it displays nicely on screen. I know Marx wasn't heavy on the old algebra, but when face with screens full of ascii formulae, I just needed to beautify it. If its relevent or not isn't my domain. Fifelfoo 03:15, 23 January 2006 (UTC)

I wasn't criticising the appearance of the algebra which is indeed beautiful. I was just justifying my removal of the phrases suggesting that the tables closely resembled Marx's text - and now any reader can check for themselves. In fact, the more I dig into this article the more it is revealed as an exercise in straw-man pedantry--Jack Upland 19:48, 23 January 2006 (UTC)

[edit] The Current Article Make My Head Spin (Simplified Version of Transformation Problems)

I took a master course in classical economics (taught by a guy called Terry Peach, a known pisser on Srafian interpretation of Ricardo) loooong time ago and we briefly covered the transformation problem. I was immensely impressed by the insight. I came to this page because I wanted to remember what that insight was. I'm greatly disappointed to find out that I can't understand anything on this page. I agree with the objection rased in featured article nomiation. "The prose is too dense and academic for the general lay person to understand". I hold degree in economis. If I can't understand it, how would you expect anyone to understand this. Just looking at sigma sign make my head spin. People who can read/understand this are people who specialise in this topic, who don't need to come here. When we done the transformation problem in my old class, the math was ridiculously simple. There were three industies. The capital industry which produce capital goods,, The wage good industry which produce wage goods consumed by lavourers and the laxury good industry which produce goods which is consumed by people who doesn't work. The distniction presupose class defined society. Each industry's surplus value and rate of profit was culculated according to the organic rate of capital (i.e. capital/labour ration) Then rate of profit for each industry was assumed to gravitate toward the equality under classical assumption, which adjust the organic rate of capital (ratio of capital to labour). What I vaguely remember was that Marx didn't solve the math, but instead, presuposed the solution, which produce a hypothetical mathematical conclusion that profit will decrease as capital accumulate. In our class, we actually solved the math, by setting the rate of transformation arbitarry to 1. It was revealed that there was no law of diminishing rate of profit unless you presupose the system for that effect. Writing this help me to remember 90% of what I was told. Can anyone here reformulate the problem under the description I gave above? Please.. Plus, I believe this is the only way to get the featured article status. This insight deserved to be publicised in the front page. This article doesn't have to be Palgrave Dictionary of Economics. Yes there is a place for detailed exposition but I suggest that this is done by linking section by sister wiki pages. FWBOarticle

I can't believe I can remember so much about a lecture which was 5 years ago. Can anyone fill ..... part as well as correcting all the mistake I have made as well as doing math for me. This is based on print out given by my lecturer which (I think) was based on a book he wrote or writing. Does this violate his copyright. Or the formulation is general enough that it is copyright free?

Marx sets out the problem succinctly in Vol 3, Ch 9 (link given on page). There is no 'maths solution' because it isn't inherently a maths problem. The issue is: can Marx explain a tendency to equal profit given his theory? Answer: yes, via redistribution of surplus value through price movements. (By the way, we know that industries don't have equal rates of profit e.g. the low-profit 'capital intensive' IT industry.) The issue about the declining rate of profit is different. This is not about different sectors but the economy as a whole. As the proportion of direct labour input ('living labour') declines overall, so does the overall surplus value and capitalists must squeeze the workers more. That's the theory. As far as I can see apart from the exploitation thesis, the only presumption is that industry will become more mechanised etc (hardly controversial).--Jack Upland 09:19, 30 January 2006 (UTC)

I think the classical assumption, which Marx, Adam Smith, Ricard and all other adheres to assume that capital will migrate twoard more profitable industry, giving somewhat evenly distributed rate of profit across the economy. Plus, as I stated, the one covered in our class merely set the rate of transformation to 1 so my wording may have been incorrect. FWBOarticle

A tendency is not the same as a mathematical rule. See quote from Marx at end of section on 'Marx's error' in article.--Jack Upland 07:36, 2 February 2006 (UTC)

[edit] Simplified Version

I have cut this out of the article because it is full of spelling mistakes and is incomplete. If anyone wants to fix it up here, fine, but we shouldn't have "works in progress" in the article. It also repeats the confusion (which I pointed out above) between the "declining rate of profit" and the "transformation problem". And it lengthens an already overlong article...--Jack Upland 07:31, 2 February 2006 (UTC)

"Overlong article" which no body read or understand.(^_^) Really, "Simplest case: labour costs only" is misleading. It is the simplest in the sence that less variable is involved. The complexity of math and reasoning remains the same, somewhat making the section redundant. Often someone who really understand the topic do not have to resort to overlong or complex explanation. Some topic can be reduced to high school math level. The detailed, more complex explanation can be done in other wiki linked page. FWBOarticle

I agree the article is already overlong and unreadable. The same area is covered on the Labor Theory of Value page in a much shorter time. But this is no reason to add to the existing article a roughly drafted section.--Jack Upland 09:20, 3 February 2006 (UTC)

PLEASE DON'T REVERT THIS UNTIL SOMEONE'S COMPLETED THE ARTICLE!!!!!!!!!!

[edit] Simplified Version of Transformation Problems

Though the comprehensive explantion of the transformation is complex, its core insight can be explained in suprisingly simple manner. Imagine a class society comprising labourer, capitalist and leisure class, whose industries are defined by such class distinction. Because this is a capitalist economy, production is done by combined input of workers and capital (tool and machinery). The profit of capitalist is determined by...... Industry 1 produce wage goods (food, cloths, housing and so on) which are consumed by workers. Industry 2 produce capital goods (machinery, fuel, tools and so on) which are utlised by industry. Industry 3 produce luxury goods which are consumed by leisure class who does not work.

In the initial state, the ratio of capital to labour (called organic ratio of capital) are different among these industries and in this ecample, arbitraly set at 20%, 30%, 40% respectively. In this system, surplus value is determined by...... Consequently, the rate of profit is determined by ........

Industry\Rate	Organic Ratio of Capital	Surplus Value	Rate of Profit

Wage Goods Industry

Capital Goods Industry

Leizure Goods Industry

(I need help here)

The main feature of this economy is that output of wage and capital goods industries are iput of all three industries while the output of Leizure Goods Industry is not used as input in other industries. Marx, like other classical economists assumed that higher rate of profit attract capitalist to shift his investment toward such industry which result in eventual equalisation of rate of the profit of all industries and change in the organic ratio of capital of each industry.

Marx's fundamental question was the relationship between the rate of profit and the capital (or organic rate of capital? me don't know.). To do this, the "exchange value" among each industries's inputs and outputs have to be transformed (or synchronised) into prices to obtain mathematical solution of the rate of profit in relationship to the capital.

Marx did not solve this "transformation problem". Instead, in Das Capital, he presupposed the mathematical solution, which led to the (hypothesised) conclusion that there is a inverse relationship between the rate of capital accumulation and the rate of profit. This is the fundamental basis of Marxian proposition. Each capitalist must increase capital to increase his profit. However, in totality, such progresive capital accumulation within the capitalist system lead to diminishing retun of profit, which, in turn, force capitalists to progressively exploit and degrade workers which in the end lead to a revoultion and the collapse of the capitalist system.

The actual solution of the equation of the above model can be achived by setting the ratio of transformation to artibary number of 1. The solution actually revealed that there is no fixed relationship between the organic rate of capital and the rate of profit unless such (inverse) relation is presuposed in outset. This imply that Marxian argument over capital accumulation, labour exploitation and the fate of capitalism is incorrect. Another (Slafian) insight is that the capital does not determine the rate of profit which also refute one of the core assumption of neo classical economics. Thefore, the solution to transformation problem is considered as the fundamental refutation of marxian economics and neo classical economics.

[edit] Marxism label

I think there's a problem when this article is labelled as part of a Marxism series when it is actually a critique of Marxism and one which bears little relation to what Marx actually said. Moreover, it elicits the response that Marxism is complicated and incrutable, which is unfair given the fact that it is really the criticism that merits this description.--Jack Upland 05:58, 6 May 2006 (UTC)

What amazes me about the article and the discussion here is that those who leaped to compose this artilce admit at one point or another to 1) not reading Capital volume 3, 2) suggesting Sraffa (who inspired muchh of the current research in this area pro and con) is a single source and later attributing Sraffa's work to "Siafa" whoever that is. This artilce should be cut back to a stub until someone has time to write something useful.--208.54.95.129 20:51, 2 June 2006 (UTC)

On second glance the arcticle reads like it's from a time capsule. Most of the path breaking work, pro and con, has occured in the last thirty years but the artcile basically ends with cursory work from over thirty-five years ago. When it does mention work since then (e.g., Foley, Moseley) it completely mischaracterizes those positions. --208.54.95.129 01:14, 3 June 2006 (UTC)

Firstly, transformation problem is definitely marxisian if not marxist. Ricardo and Marx clearly consider the problem to be fundamental. Main fault of the previous version is Srafian POV soapboxing. For example, why has "Labour theory of value" (exchange value) not explained in the first palce. Why did we not explanin how Marx (or Ricardo) dealt or define the problem jumping into Sraffian solution. Moreover, Ladislaus Bortkiewicz's "alleged" solution should come first before anything and he was definitely not a Sraffian. btw, I'm FWBOarticle. Vapour

Just to clarify much of the discussion above refers to the old version which I pasted below. The new version is written from primarily a Marxist point of view (that's my background). It could use more information about Ricardo and Smith and subsequent theorists like Bortkiewicz (as you mention). Above i suggested redoing the numerical example from a unified approach. This way we could develop something like a 3 commodity system and discuss how the varioius approaches understand the numeric example. As it stood before the numeric example was very biased only towards Bortkiewicz's work and failed to consider the bulk of the mathematical work that has occured since 1970: much of which supports Marx's conclusions.

So if someone with some algebreic inclinations wants to put together such a linear production model to get the process started, others could then join in and add in the other points of view. This way we could demonstrate with a simple numeric example the different approaches to equality conditions: e.g., sum of values equals sum of prices; sum of profits equals sum of surplus value and the net product in values equals the net product in prices. --Cplot 01:26, 23 June 2006 (UTC)

[edit] Old elaboration material

I've removed this from the main page to here since it may have pieces that could be rescued as part of a correct NPOV elaboration of what I wrote for the header. I know much time must have gone into this, but it just is so out of date and so misstated it just had to go.--Cplot 06:59, 11 June 2006 (UTC)

[edit] Overview

The production of any commodity generally requires both labour and some produced means of production (or capital goods), like tools and materials. The amount of labour so required is called the direct labour input into the commodity. But also the required capital goods have in their turn been produced (in the past) by labour and other capital goods; and so on for these other capital goods, and so on. The sum of all the amounts of labour, that were direct inputs into this backwards-stretching series of capital goods produced in the past, is called the indirect labour input into the commodity. Putting together the direct and indirect labour inputs, one finally gets the total labour input into the commodity, which may also be called the total amount of labour "embodied" in it, or its direct and indirect labour contents.

Now, according to Chapter I of Capital's Volume I, the Marxian "value" of a commodity is defined as its total amount of embodied labour. On the other hand, the (relative) "competitive price" of the same commodity is the ratio at which it is exchanged with other commodities in a competitive market system, and this ratio tends to be given by its relative cost of production. The transformation problem, studied by Marx in Chapter 9 of Capital's Volume III through a set of numerical examples, is hence the problem of finding a set of functions that transform the ratios between amounts of embodied labour into such relative prices.

In a critique of Marx's work, Bortkiewicz (1906). argued that Marx's presentation was flawed. Bortkeivwicz used a system of linear equations to render a variation of Marx's example. With the second half of the twentieth century Leontief’s and Sraffa’s work on linear production models provided a general framework within which the rekindled debate has centered.

Although he never actually mentioned the transformation problem, Sraffa's work was largely intneded to rescue much of Ricardo's insights that had been disparaged by neo-clasical economists such as Marshall and to show that Ricardo's work presented an important crtique of Marshal's concept of capital: what became known as the capital controversy. Sraffa’s (1960) Chapter VI on the "reduction" of prices to "dated" amounts of current and past embodied labour gave implicitly the first general proof, showing that the competitive price P_i of the i ^{− th} produced good can be expressed as

,

where n is the time lag, l_in is the lagged-labour input coefficient, w is the wage and r is the "profit" (or net return) rate. Since total embodied labour is defined as

,

it follows from Sraffa’s result that there is generally no function from E_i to P_i, as was made explicit and elaborated upon by later writers. However, Sraffa there may have provided a particular interpretation that maintained Ricardo's understanding of what it meant for a price to express the value of a commodity.

This article uses a very simplified linear production model to survey Marx's labour theory of value, starting from its precursors in British classical economics. It then illustrates one of the simple proofs of the lack of solution for the transformation problem, highlighting Marx's formal error in his attempt to find one. Finally, it summarizes some possible implications of this result, as Marxists and non-Marxists see them.

[edit] British classical labour theory of value

Marx's value theory was developed from the labour theory of value discussed by Adam Smith and used by many British classical economists. It became central to his economics.

[edit] Simplest case: labour costs only

Consider the very simple example used by Adam Smith to introduce the subject. Assume a hunters’ economy with free land, no slavery and no significant current production of tools, where beavers (B) and deer (D) are hunted. In the language of modern linear production models, call the unit labour-input requirement for the production of each good l_i, where i may be B or D (i.e., l_i is the number of hours of uniform labour normally required to catch either a beaver or a deer; notice that we need to assume labour as uniform in order to be able, later on, to use a uniform wage rate).

Then—Smith noticed—each hunter will be willing to exchange one deer (which costs him l_Dhours) for beavers. The ratio —i.e. the relative amount of labour embodied in (unit) deer production with respect to beaver—gives thus the exchange ratio between deer and beavers, the "relative price" of deer in units of beavers. Moreover, since the only costs are here labour costs, that ratio is also the "relative unit cost" of deer for any given competitive uniform wage rate w. Hence the relative amount of labour embodied in deer production coincides with the competitive relative price of deer in units of beavers, which can be written as (where the P stands for absolute competitive prices in some arbitrary unit of account, and are defined as P_i = wl_i).

[edit] Capital costs

Things get less simple if production uses some scarce capital good as well. Suppose that hunting requires also some arrows (A), with input coefficients equal to a_i, meaning that to catch for instance one beaver you need to use a_B arrows, besides l_B hours of labour. Now the unit total cost (or absolute competitive price) of beavers and deer becomes:

P_i = wl_i + k_Aa_i,(i = B,D)

where k_A stands for the capital cost incurred in using each arrow.

Now, this capital cost is made up of two parts. First, there is the replacement cost of substituting the arrow when it is lost in production. This is P_A, or the competitive price of the arrows, times the proportion of arrows lost after each shot. Second, there is the net rental or return required by the arrows' owner (who might or might not be the same person as the hunter using it). This can be expressed as the product rP_A, where r is the (uniform) net rate of return of the system.

Summing up, and assuming a uniform replacement rate h, the absolute competitive prices of beavers and deer may be written as:

P_i = wl_i + (h + r)P_Aa_i

Yet, we still have to determine the arrows' competitive price P_A. Assuming arrows are produced by labour only, with l_A man-hours per arrow, we have:

P_A = wl_A

Assuming further for simplicity h = 1 (all arrows are lost after just one shot, so that they are circulating capital), the absolute competitive prices of beavers and deer become:

P_i = wl_i + (1 + r)wl_Aa_i

Here l_i is the amount of labour directly embodied in beaver and deer unit production, while l_Aa_i is the labour indirectly thus embodied, through previous arrow production. The sum of the two,

E_i = l_i + l_Aa_i

gives the total amount of labour embodied.

It is now obvious that the relative competitive price of deer can no longer be generally expressed as the ratio between total amounts of labour embodied. With a_i > 0 the ratio will correspond to only in two very special cases: if either r = 0; or, if . In general the two ratios will not only differ: may change for any given , if the net rate of return or the wages vary.

As it will now be seen, this general lack of any functional relationship from to —of which Ricardo had been particularly well aware—is at the heart of Marx's transformation problem.

[edit] Marx’s labour theory of value

[edit] Labour as the "value-creating substance"

Marx defined the "value" of commodities as the total amount of socially necessary labour embodied in their production. He developed this special brand of the labour theory of value in the first Chapter of Capital's Volume I. Due to the influence of Marx's particular definition of value on the transformation problem, he is quoted at length where he argues as follows:

"Let us take two commodities, e.g., corn and iron. The proportions in which they are exchangeable, whatever those proportions may be, 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. 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." […]

"This common 'something' cannot be either a geometrical, a chemical, or any other natural property of commodities. Such properties claim our attention only in so far as they affect the utility of those commodities, make them use values. But the exchange of commodities is evidently an act characterised by a total abstraction from use value." […]

"If then we leave out of consideration the use value of commodities, they have only one common property left, that of being products of labour. […] 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." […]

"A use value, or useful article, therefore, has value only because human labour in the abstract has been embodied or materialised in it. How, then, is the magnitude of this value to be measured? Plainly, by the quantity of the value-creating substance, the labour, contained in the article."

Karl Marx, Capital Volume I, Chapter 1

However, contrary to popular belief, Marx did not deny the role of supply and demand influencing price:

It suffices to say that if supply and demand equilibrate each other, the market prices of commodities will correspond with their natural prices, that is to say, with their values as determined by the respective quantities of labor required for their production.

Value, Price and Profit Chapter 2

It may be incidentally noticed that the uniform-labour assumption of modern linear production models makes their labour inputs quantitatively equivalent to amounts of Marx's "human labour in the abstract". The quantitative aspects of Marx's value and price theories—which include the transformation problem—can thus be expressed in the mathematical language of such models: see Samuelson (1971).

[edit] Surplus value and exploitation

Within the quantitative relationships relevant to the transformation problem, labour plays a twofold role according to Marx. First, labour is itself a commodity which is produced, exchanged and used as a means of production—labour is thus a kind of capital. The "labour value" of each unit of labour is the amount of labour embodied in the goods that make up the real subsistence wages rate. This amount of labour will be denoted here as l_W (with 0 < l_W < 1 in any viable system). In our previous example, the Marxian value of the direct-labour input required by unit beaver and deer production is thus l_Wl_i. Like that of any other means of production (or capital), this value is entirely transmitted to the product.

However, this is not all. Being the "substance" of value, direct (or "living") current labour has for Marx the further property of creating and transmitting to the product a further amount of value, over and above its own. Formally, this property derives from the definition of value and the above assumption that 0 < l_W < 1: less than one unit of labour is embodied in the wage goods that pay for (or "produce", so to speak) one unit of labour. This extra value is called surplus value and denoted by s. The amount of surplus value created in unit beaver and deer production will be denoted here as s_i.

If the actual real wage is the subsistence wage used to calculate l_W, all this surplus value created by labour will be received by the owners of the capital goods, called "capitalists". This is what Marx denoted as exploitation of labour.

[edit] Variable and constant capital

As labour produces in this sense more than its own value, the direct-labour input is called variable capital and denoted as v. The amount of value which labour transmits to the deer in our previous example, varies according to the intensity of the exploitation. In our previous example one has v_i = l_Wl_i.

By contrast, the value of other inputs—in our example the indirect (or “dead”) past labour embodied in used up arrows—is transmitted to the product as it stands, without additions. It is hence called constant capital and denoted as c. The value transmitted by the arrow to the deer can never be greater than the value of the arrow itself. In our previous example one has c_i = l_Aa_i.

[edit] Value formulas

The total value of each produced good is obtained as the sum of the above three elements: constant capital plus variable capital plus surplus value. In our previous example:

p_i = c_i + v_i + s_i = l_Aa_i + l_Wl_i + s_i

Where p_i stands for the (unit) Marxian value of beavers and deer.

However, from the definition of Marxian value as total labour embodied it must also be true that:

p_i = l_Aa_i + l_i = E_i

Solving for s_i the above two relationships one has:

This necessarily uniform ratio is called by Marx the rate of surplus value, and it allows to re-write Marx's value equations as:

p_i = c_i + v_i(1 + σ) = l_Aa_i + l_Wl_i(1 + σ)

[edit] Transformation of values into prices

Like Ricardo, Marx knew that relative labour values— in the above example—do not generally tally with relative competitive prices— in the same example. However, in the third volume of Capital he argued that competitive prices were obtained from his values through a transformation process, whereby capitalists redistributed among themselves the given aggregate surplus value of the system, in such a way as to bring about a uniform rate of return r on the capital goods they owned in all production lines. This happened because of the capitalists' tendency to shift their capital towards the sectors where it earned higher returns. Marx's attempt to give a detailed account of this process is found in chapter 9 of Volume III.

[edit] Marx's reasoning

The two following tables adapt the deer-beaver-arrow example already seen above (which, of course, is not found in Marx, and is only a useful simplification), to illustrate Marx's approach. In both cases it is assumed that the total quantities of beavers and deer captured are Q_B and Q_D respectively. It is also supposed that the subsistence real wage is one beaver per unit of labour, so that the amount of labour embodied in it is l_W = E_B = l_Aa_B + l_B < 1.

Table 1—Composition of Marxian values in the deer-beaver-arrow production model

Sector	Total Constant Capital Qici	Total Variable Capital Qivi	Total Surplus Value σQivi	Unit Value ci + (1 + σ)vi
Beavers	QBlAaB	QB(lAaB + lB)lB	σQB(lAaB + lB)lB	lAaB + (1 + σ)(lAaB + lB)lB
Deer	QDlAaD	QD(lAaB + lB)lD	σQD(lAaB + lB)lD	lAaD + (1 + σ)(lAaB + lB)lD
Total			σ(lAaB + lB)(QBlB + QDlD)

Table 1 shows how the total amount of surplus value of the system—in the last row—is determined.

Table 2—Marx's transformation formulas in the deer-beaver-arrow production model

Sector	Total Constant Capital Qici	Total Variable Capital Qivi	Redistributed Total Surplus Value rQici	Resulting Competitive Price vi + (1 + r)ci
Beavers	QBlAaB	QB(lAaB + lB)lB	rQBlAaB	(lAaB + lB)lB + (1 + r)lAaB
Deer	QDlAaD	QD(lAaB + lB)lD	rQDlAaD	(lAaB + lB)lD + (1 + r)lAaD
Total			rlA(QBAB + QDaD) = σ(lAaB + lB)(QBlB + QDlD)

Table 2 then illustrates how Marx thought that this total would be redistributed between the two industries, as “profit” at a uniform return rate r over constant capital. First, the condition that total “profit” must equal total surplus value – in the last row of table 2 – is used to determine r. The result is then multiplied by the value of the constant capital of each industry, to get its “profit”. Finally, each (absolute) competitive price in labour units is obtained, as the sum of constant capital, variable capital and “profit” per unit of output, in the last column of Table 2.

Tables 1 and 2 parallel the tables in which Marx elaborated his numerical example in Chapter 9 of Capital's Volume III.

[edit] Marx's "error" and its correction

It was however soon pointed out that Marx's formulas for competitive prices were mistaken.

First, competitive equilibrium requires a uniform rate of return over constant capital valued at its price, not its Marxian value, contrary to what is done in Table 2 above. Secondly, competitive prices result from the sum of costs valued at the prices of things, not as amounts of embodied labour. Thus, both Marx's calculation of r and the sums of his price formulas do not add up in all the normal cases, where—as in the above example—relative competitive prices differ from relative Marxian values.

Indeed, the formally correct way to compute competitive (relative) prices is today very well known. In the greatly simplified model of Tables 1 and 2, where by assumption the wages rate is given and equal to the price of beavers, the most convenient way is to express such prices in units of beavers, which means normalising w = P_B = 1. This immediately yields the (relative) price of arrows as

P_A = l_A beavers.

Substituting this into the relative-price condition for beavers

1 = l_B + (1 + r)l_Aa_B

gives the solution for the rate of return as

Finally, the price condition for deer can hence be written as

As the reader can check, this latter result, which gives the correct competitive price of deer in units of beavers for the overly simplified model used here, is generally inconsistent with Marx's price formulas of Table 2.

This discrepancy has, however, been alternatively explained as due to the time frame of production rather than a logical error, i.e. in this simplified model, capital goods are purchased at a labour value price but final products are sold under prices which reflect redistributed surplus value. On this view, price levels are set by a dynamic equilibrium which cannot be captured by a static mathematical formula.[1]

After all, Marx added the following proviso:

In spite of the great changes occurring continually, as we shall see, in the actual rates of profit within the individual spheres of production, any real change in the general rate of profit, unless brought about by way of an exception by extraordinary economic events, is the belated effect of a series of fluctuations extending over very long periods, fluctuations which require much time before consolidating and equalising one another to bring about a change in the general rate of profit. In all shorter periods (quite aside from fluctuations of market-prices), a change in the prices of production is, therefore, always traceable prima facie to actual changes in the value of commodities, i.e., to changes in the total amount of labour-time required for their production.

Capital Volume 3, Chapter 9

[edit] The non-transformation problem

Moreover, it is now easy to show that deer's relative embodied labour defined as can vary, while at the same time the correctly defined relative price P_D remains constant. This follows from the fact that in our simple model e_D varies with l_A while—as long as the real wage is given—P_D does not. Thus any change in the labour input required by arrow production will affect the Marxian value of deer relative to beavers, but will leave the economic value of deer (i.e., its exchange rate with beavers) totally unaffected.

The diagram on the right shows this through a numerical example. All the input coefficients, bar l_A, have been given arbitrary numerical values. The two curves show the numerical corresponding values of P_D and e_D (on the vertical axis), calculated as l_A varies along the horizontal axis. As one can see, P_D is a horizontal line, showing constancy, while e_D is a falling curve.

This appears to prove that the competitive exchange ratio between deer and beavers has actually nothing to do with relative total embodied labour, contrary to the above-quoted claim by Marx in Capital's Volume I.

[edit] Formal conclusions

[edit] Samuelson's eraser algorithm

As it has been shown in the literature, the above result holds true in general, including the more complicated models that Marx actually used. In Samuelson’s (1971) words, this means that the "transformation" of Marxian values into competitive prices must generally take the form of an eraser algorithm, described as follows:

"Contemplate the two mutually-exclusive alternatives of 'values' and 'prices'. Write down one. Now transform by taking an eraser and rubbing it out. Then fill in the other one. Voila! You have completed your transformation algorithm."

[edit] Special cases

The are just two very special cases where this is not true. The first and best known one is when no "transformation" is actually needed, because competitive prices and Marxian values happen to coincide to begin with. As already noticed, that is the case with either r = 0 or (in the previous example) . In Marxian parlance, the latter condition is described as a uniform organic composition of capital in all production lines.

But there is also a second and less trivial case, unnoticed until relatively recent times. This is a development of Sraffa’s (1960) notion of "standard commodity", and has been called by Samuelson (1971) the case of "equal internal composition of (constant) capitals". It takes place when every production line happens to use all the various produced means of production (including the goods entering the real wage) in the same proportions among themselves. When this is so, the same proportions apply to both value and cost calculations. Marx's transformation procedure—based on value proportions—can then be rescued, as it produces the correct relative costs and competitive prices.

Yet, even when such very special conditions are met, prices can still be computed in the generally correct way, just based on information about input coefficients, with no need for any detour through Marxian values. Moreover, once prices have been thus directly determined, one can formally set up an inverse transformation process, whereby Marxian values are obtained from prices, rather than the other way round.

[edit] Implications and interpretations

The literature summarised above relates to the logical (mathematical) aspects of the transformation problem, as discussed by the numerical examples of Chapter 9 of Capital's Volume III. All the above formal conclusions have ceased to be controversial since more than a generation ago. To many, their upshot appears to be that – since under competitive capitalism prices are generally unrelated to the direct and indirect labour contents of individual commodities – Marx's "value" of Capital's Volume I, and its attendant notions of surplus value, surplus labour and exploitation, are a purely fictional construct, of no theoretical or practical usefulness.

Yet, some controversy still remains, as some Marxist theorists have tried in various ways to rescue Marx's system, or at least some parts of it, from this apparent logical failure.

[edit] Mathematical vs historical transformation

Frederick Engels – the editor of Capital's Volume III – hinted since 1894 at a possibly alternative way to look at the whole matter. His view was that the pure Marxian "law of value" of Volume I and the "transformed" prices of Volume III applied to different periods of economic history. In particular, the "law of value" would have prevailed in the pre-capitalist exchange economies – from Babylon to the fifteenth century of the common era – while the "transformed" prices would have materialized under capitalism: see Engels' quotation by Morishima and Catephores (1975) p. 310.

Although Engels was reasoning on the mistaken presumption that Marx's transformation was formally correct, his basic idea does not depend on this, and was later taken up by Meek (1956) and Nell (1973). These authors argued that – whatever one must say of his interpretation of capitalism – Marx's "value" theory keeps its usefulness as a tool to interpret pre-capitalist societies, because – they maintained – in pre-capitalist exchange economies there were no "prices of production" with a uniform rate of return (or "profit") on capital. It hence follows that Marx's transformation must have had a historical dimension, given by the actual transition to capitalist production (an no more Marxian "values") at the beginning of the modern era. Then this true "historical transformation" could and should take the place of the failed mathematical transformation attempted by Marx in Chapter 9 of Volume III.

As Althusser and Balibar (1970) and others have pointed out, this proposal runs counter Marx's own ideas, as expressed in Marx (1859), where one reads:

"The point at issue is not the role that various economic relations have played in the succession of various social formations appearing in the course of history […], but their position within modern society." (En. trans. p.210, italics in the original.)

Moreover, the available quantitative research by economic historians has not generally endorsed Engels' view of antiquity and the Middle Ages as a "value epoch" in the Marxian sense: see for instance Hicks (1969) and Godelier (1973).

However, be that as it may, the proposed "historical" dimension of the transformation problem does not seem to affect in any way the (non-) applicability of Marx's notion of exploitation to contemporary capitalist societies.

[edit] Other Marxist views

Most interpretations of Marx's value theory consider it as an attempt to explain capitalist distribution as the result of labour exploitation, defined through the notion of surplus value. Yet, particularly if the wage is given, distribution is in itself determined by prices. Thus the transformation problem is central to the usefulness of Marx's economics in explaining exploitation, via a linkage from values (and hence surplus value) to prices. Indeed, no positive Marxian theory of labour exploitation through distribution could ever be built without some at least implicit reference to such linkage. Marx's reference was very explicit, and this is precisely why the transformation problem worried him so much.

However, there are also political-economic readings of Capital, such as Harry Cleaver's Reading Capital Politically, that re-define exploitation as a direct control of worked time, unrelated as such to distribution. These readings are usually associated with the autonomist strand of Marxism, which focuses on production as the key economic site within society. These readings of Capital are typically hostile to economics as such, and seek to side-step issues like the transformation problem by claiming that all social arrangements in capitalism (in particular, profit and distribution) are politically determined as contests between classes.

Notice should also be taken of the probabilistic interpretation of Marx advanced by Emmanuel Farjoun and Moshe Machover in Laws of Chaos (see references). They "dissolve" the transformation problem by reconceptualising the relevant quantities as random variables. In particular, they drop the assumption of strict equalisation of profit rates and instead consider an equilibrium distribution of firm profit rates. A heuristic analogy with the statistical mechanics of an ideal gas leads them to the hypothesis that this equilibrium distribution should be a gamma distribution.

Finally, there are Marxist scholars (e.g. Anwar Shaikh, Makoto Itoh, Gerard Dumenil & Dominique Levy, Duncan Foley) who accept that there exists no incontestable logical procedure by which to derive price magnitudes from value magnitudes, but still think that it has no lethal consequences on his system as a whole, for the following reasons.

As it has just been seen, in a few very special cases, Marx's idea of labour as the "substance" of (exchangeable) value would not be openly at odds with the facts of market competitive equilibrium. These authors have argued that such cases—though admittedly not generally observed—throw light on the "hidden" or "pure" nature of capitalist society. Thus Marx's related notions of surplus value and unpaid labour can still be treated as basically true, although the practical details of their workings are admittedly much more complicated than Marx thought.

In particular, some (e.g. Anwar Shaikh) have suggested, following the explicit remarks by Marx and Engels, that—since aggregate surplus value will generally differ from aggregate "profit"—the former should be in fact treated as a mere pre-condition for the latter, rather than a full explanation of it. Using input-output data and empirical proxies for labour-values, Shaikh & Ochoa have provided some statistical evidence to show that, although there may be no incontestable logical deduction possible of specific price magnitudes from specific value magnitudes even within a complex model (in contrast to a probabilistic prediction), even a "93% Ricardian theory" of labour-value appears to be a better empirical predictor of price than its rivals. Real capitalism just seems to function much more like ordinary people, businessmen and accountants understand it, and much less like neo-classical economists insist on portraying it, whatever the beavers and deer happen to be doing. That is probably one reason why, rightly or wrongly, Marx's theory retains its plausibility for many people.

[edit] Mainstream views

Mainstream scholars question the assumption that the basic nature of capitalist production and distribution can be gleaned from unrealistic special cases. Moreover, from the fact that in all such special cases Marx's reasoning can be easily turned upside down, through an inverse transformation process, they argue that Marx's inference:

"Profit is therefore the [bourgeois] disguise of surplus value which must be removed before the real nature of surplus value can be discovered." (Capital Volume III, Chapter 2)

could with equal cogency be “transformed” into:

"Surplus value is therefore the [Marxist] disguise of profit which must be removed before the real nature of profit can be discovered." [Samuelson (1971) p.417]

To further clarify this point, it may be noticed that the special cases in question are also precisely those where J.B. Clark’s old model of aggregate marginal productivity holds strictly true, leading to equality between the equilibrium levels of the real wage rate and labour's aggregate marginal product: see the neo-Ricardian disputes of the Sixties and Seventies. One would thus have a "pure" state of capitalist society where Marx's exploitation theory and its main supposed confutation were somehow both true.

This remarkable result, it is maintained, leads straight to the heart of the matter. Like Clark’s contention about the "fairness" of marginal-productivity wages, so Marx's basic argument—from the "substance" of value to the concept of exploitation—is a set of non-analytical and non-empirical propositions. That is why, being non-falsifiable, both theories may be found to apply to the same formal and/or empirical object, though they are supposed to negate each other, as Karl Popper and many others had argued.

[edit] references moved from main article

[edit] References

These references are certainly relevvant, but it's probably excessiv to include them all on the main page. I mostly placed them there to show how the previous version of the article was pretty much nonsenssical — claiming for example, that nothing had been done on this topic since 1971. The article certainly reflected a position from prior to 1971, but not the current thinkingon the issue (hence thee list of references).

• Marx, K. (1859) Zur Kritik der politischen Oeconomie, Berlin (trans. A Contribution to the Critique of Political Economy London 1971).
• Marx, K. (1867) Das Kapital Volume I.
• Marx, K. (1894) Das Kapital Volume III (ed. by F. Engels).
• Böhm-Bawerk, E., von (1896) "Zum Abschluss des Marxschen Systems" Festgabe für Karl Knies Berlin [trans. P. Sweezy ed. (1949) Karl Marx and the close of his system by Eugen Böhm-Bawerk and Böhm-Bawerk’s criticism of Marx by Rudolf Hilferding with an appendix by L. von Bortkiewicz].
• Bortkiewicz, L. von (1906) "Wertrechnung und Preisrechnung im Marxschen System" Archiv für Sozialwissenschaft und Sozialpolitik 3, XXIII and XXV [trans. "Value and Price in the Marxian System" International Economic Papers 1952 2 5–60].
• Alan Freeman: Price, value and profit - a continuous, general treatment. In: Alan Freeman, Guglielmo Carchedi (editors): Marx and non-equilibrium economics. Edward Elgar. Cheltenham, UK, Brookfield, US 1996.
• Meek, R. (1956) 'Some Notes on the Transformation Problem' Economic Journal 66 (March) 94-107.
• Sraffa, P. (1960) Production of commodities by means of commodities.
• Hicks, J. (1969) A Theory of Economic History Oxford.
• Althusser, L. and E. Balibar (1970) Reading 'Capital' London.
• Samuelson, P.A. (1971) "Understanding the Marxian Notion of Exploitation: A Summary of the So-Called Transformation Problem Between Marxian Values and Competitive Prices" Journal of Economic Literature 9 2 399–431.
• Godelier, M. (1973) Horizon, trajets marxistes en anthropologie Paris.
• Nell, E.J. (1973) 'Marx's Economics. A Dual Theory of Value and Growth: by Micho Morishima' (book review) Journal of Economic Literature XI 1369-71.
• Morishima, M. and G. Catephores (1975) 'Is there an "historical transformation problem"?' Economic Journal 85 (June) 309-28.
• Anwar Shaikh papers: http://homepage.newschool.edu/~AShaikh/
• Alan Freeman papers: http://www.iwgvt.org/index.php
• Fred Moseley papers: http://home.mtholyoke.edu/~fmoseley/
• Fred Moesley 'The New Solution to the Transformation Problem: A Sympathetic Crtique
• Emmanuel Farjoun and Moshe Machover, Laws of Chaos; A Probabilistic Approach to Political Economy, London: Verso, 1983. [2]

• Makoto Itoh, The Basic Theory of Capitalism.
• Gerard Dumenil & Dominique Levy papers http://www.jourdan.ens.fr/~levy/
• Duncan Foley papers http://cepa.newschool.edu/~foleyd/
• Althusser, Louis and Etienne Balibar (1979). Reading "Capital". London and New York, Verso.
• Baeza, Alejandro Valle (1994). "Correspondence between Labor Values and Prices: A New Approach." Review of Radical Political Economics 26(2): 57-66.
• Baumol, William J. (1974). "The Transformation of Values: What Marx Really Meant: Reply." Journal of Economic Literature 12(1): 74-75.
• Baumol, William J. (1986). On Marx, the Transformation Problem and Opacity. Microtheory: Applications and origins. W. J. Baumol. Cambridge, Mass and London, MIT Press: 247.58.
• Bellofiore, Riccardo (1989). "A Monetary Labor Theory of Value." Review of Radical Political Economics 21(1-2): 1-25.
• Böhm-Bawerk's, Eugen von (1949). Karl Marx and the close of his system. Karl Marx and the close of his system & Böhm-Bawerk's criticism of Marx. P. M. Sweezy. New York, Augustus M. Kelley: 9-118.
• Desai, Meghnad (1991). The Transformation Problem. Marx and modern economic analysis. G. A. Caravale. 1 ( Values, prices and exploitation): 3-44.
• Devine, James N. (1990). The Utility of Value: The New Solution, Unequal Exchange, and Crisis. Research in political economy. P. Zarembka. Greenwich, Conn. and London, JAI Press. Volume 12: 21-39.
• Duménil, Gérard and Dominique Lévy (1987). "The Dynamics of Competition: A Restoration of the Classical Analysis." Cambridge Journal of Economics 11(2): 133-64.
• Duménil, Gérard and Dominique Lévy. (1987). "Value and Natural Prices Trapped in Joint Production Pitfalls." Journal of Economics (Zeitschrift fur Nationalokonomie) 47(1): 15-46.
• Duménil, Gérard and Dominique Lévy. (1989). "The Competitive Process in a Fixed Capital Environment: A Classical View." Manchester School of Economics and Social Studies 57(1): 34-57.
• Duménil, Gérard and Dominique Lévy. (1991). "Micro Adjustment toward Long-term Equilibrium." Journal of Economic Theory 53(2): 369-95.
• Fine, Ben (1986). The Value Dimension: Marx versus Ricardo and Sraffa: Introduction. The value dimension: Marx versus Ricardo and Sraffa. B. Fine. London and New York, Routledge and Kegan Paul: 1-17.
• Foley, Duncan (1982). "The Value of Money, the Value of Labor Power and the Marxian Transformation Problem." Review of Radical Political Economics 14(2): 37-47.
• Freeman, Alan (1984). The Logic of the Transformation Problem. Ricardo, Marx, Sraffa: The Langston Memorial Volume. Introduction by, Ernest Mandel. A. Freeman and E. Mandel. London, Verso; distributed in the U.S. and Canada by Schocken Books, New York: 221-64.
• Freeman, Alan and Guglielmo Carchedi (1996). Marx and non-equilibrium economics. Cheltenhaum, UK ; Brookfield, US, Edward Elgar.
• Gleicher, David (1989). "Labor Specialization and the Transformation Problem." Review of Radical Political Economics 21(1-2): 75-95.
• Glick, Mark. (1991). The Classicals and Neoclassicals in Applied Economics: Studies of Competition and Monopoly. Explorations in political economy: Essays in criticisms. R. K. Kanth and E. K. Hunt: 105-22.
• Glick, Mark and D. A. Campbell (1995). "Classical Competition and the Compatibility of Market Power and Uniform Rates of Profit: Comment." Review of Radical Political Economics 27(2): 124-35.
• Glick, Mark and Hans G. Ehrbar (1987). "The Transformation Problem: An Obituary." Australian Economic Papers 26(49): 294-317.
• Hilferding, Rudolf (1949). Böhm-Bawerk's Criticism of Marx. Karl Marx and the close of his system & Böhm-Bawerk's criticism of Marx. P. M. Sweezy. New York, Augustus M. Kelley: 121-83.
• Kliman, Andrew J.. (1998). Value, Exchange Value and the Internal Consistency of Volume III of Capital: A Refutation of Refutations. Marxian economics: A reappraisal: Essays on Volume III of Capital. Volume 2. Profits, prices and dynamics. R. Bellofiore. New York, St. Martin's Press; London: Macmillan Press: 29-42.
• Kliman, Andrew J. and Ted McGlone (1999). "A Temporal Single-System Interpretation of Marx's Value Theory." Review of Political Economy 11(1): 33-59.
• Laibman, David (1973). "Values and Prices of Production: The Political Economy of the Transformation Problem." Science and Society 37(4): 404-36.
• Langston, Robert, Ernest Mandel and Alan Freeman, Eds. (1984). Ricardo, Marx, Sraffa : the Langston memorial volume. London, Verso.
• Mandel, Ernest (1984). Gold, Money and the Transformation Problem. Ricardo, Marx, Sraffa: The Langston Memorial Volume. Introduction by, Ernest Mandel. A. Freeman and E. Mandel. London, Verso; distributed in the U.S. and Canada by Schocken Books, New York: 221-64.
• Marx, Karl. (1971 [1861-63]). Theories of Surplus-Value. Moscow, Progress Publishers.
• Marx, Karl. (1976 [1867]). Capital : a critique of political economy. Vol. 1. London ; New York, N.Y., Penguin Books in association with New Left Review.
• Marx, Karl. (1978 [1885[). Capital : a critique of political economy. Vol. 2. London ; New York, N.Y., Penguin Books in association with New Left Review.
• Marx, Karl. (1981 [1894]). Capital : a critique of political economy. Vol. 3. London ; New York, N.Y., Penguin Books in association with New Left Review.
• Marx, Karl and Friedrich Engels (1936). Karl Marx and Friedrich Engels: correspondence, 1846-1895. New York,, International Publishers.
• McGlone, Ted and Andrew J. Kliman (1996). One System or Two? The Transformation of Values into Prices of Production versus the Transformation Problem. Marx and non equilibrium economics. A. Freeman and G. Carchedi. Cheltenham, U.K., Elgar; distributed by Ashgate: 1996, pages 29-48.
• Mohun, Simon (1994). "A Re(in)statement of the Labour Theory of Value." Cambridge Journal of Economics 18(4): 391-412.
• Mohun, Simon. (1994). Value, Value-Form and Money. Debates in Value Theory. S. Mohun, Macmillan.
• Mosley, Fred (1993). Marx's method in Capital : a reexamination. Atlantic Highlands, N.J., Humanities Press.
• Murray, P. (1993). The Necessity of Money: How Hegel Helped Marx Surpass Ricardo's Theory of Value. Marx's Method in Capital: A Re-examination. F. Mosley. Atlantic Higlands, NJ, Huanities: 37-62.
• Reati, Angelo (1989). "A Note on the Alleged Redundancy of Labor Value." Review of Radical Political Economics 21(1-2): 169-74.
• Roberts, Bruce B. (1981). Value categories and Marxian method: a different view of value-price transformation: viii, 264 l.
• Samuelson, Paul A. (1974). "The Transformation of Values: What Marx Really Meant: Rejoinder: Merlin Unclothed, A Final Word." Journal of Economic Literature 12(1): 75-77.
• Shaikh, Anwar M. (1984). The Transformation from Marx to Sraffa. Ricardo, Marx, Sraffa: The Langston Memorial Volume. Introduction by, Ernest Mandel. A. Freeman and E. Mandel. London, Verso; distributed in the U.S. and Canada by Schocken Books, New York: 221-64.
• Shaikh, Anwar M. (1992). Values and Value Transfers: A Comment. Radical economics. B. B. Roberts and S. Feiner. Norwell, Mass and Dordrecht, Kluwer Academic: 76-90.
• Steedman, Ian (1990). Positive Profits with Negative Surplus Value: A Reply to Wolfstetter. Joint production of commodities. N. Salvadori and I. Steedman. Aldershot, U.K. and Brookfield, VT, Elgar: 122-25.
• Szumski, Jerzy S. (1989). "The Transformation Problem Solved?" 13(3): 431-52.
• Szumski, Jerzy S.. (1991). "On Duménil and Lévy's Denial of the Existence of the So-Called Transformation Problem: A Reply." Cambridge Journal of Economics 15(3): 365-71.
• Wolff, Richard D., Antonino Callari and Bruce B. Roberts (1984). "A Marxian Alternative to the Traditional "Transformation Problem."" Review of Radical Political Economics 16(2&3): 115-35.
• Wolff, Richard D., Bruce B. Roberts and Antonino Callari (1984). "Unsnarling the Tangle: A Rejoinder [Marx's (Not Ricardo's) "Transformation Problem": A Radical Reconceptualization]." History of Political Economy 16(3): 431-36.
• Wolff, Richard D., Bruce B. Roberts and Antonio Callari (1982). "Marx's (not Ricardo's) 'Transformation Problem': A Radical Reconceptualization." History of Political Economy 14(4): 564-82.

[edit] on the recent revert

It is very poor etiquette to transform an entire article without first discussing it on the article's discussion page — not even a little note here. I do think the topic needs much better treatement and I had invited those who prepared the previous versions to work togeteher with me to present the material that didn't violate wikipedia's NPOV pollicy. I think some of the main material in older versions could be rescued, but only after properly reflecting the current state of the art on this topic. --Cplot 19:29, 27 July 2006 (UTC)

Frankly I think the original article could have been kept since, though it was objectionable in parts, it had a tendency to disappear up the black hole of its own pomposity.--Jack Upland 10:27, 28 July 2006 (UTC)

[edit] 2 Objections to the methematical rendering

1) The use of Sraffian's notation seems a bit rich to me. The beavers and dear algebra that follows expresses the same thing in a less bewilidering way, so why throw people off with the high-falootin' sigma symbol? It's like calling the Rate of Profit the "first derivative of the profit magnitude"--just not necessary to confuse lay readers in this way.

2) Each of the input variables in the equation P_i = wl_i + (h + r)P_Aa_i can be reduced to labor, which would make it possible to solve for P_i in terms of E_i. Of course you can argue that these variables are not reducible to labor, but then you are moving off of Marx's turf and moving the goal posts somewhat, setting up a straw man, and so on.

PS- Let's try to avoid crude remarks.

--Rainercale 03:42, 5 May 2007 (UTC)

What some see as crude, I see as truthful.--Jack Upland 10:24, 2 November 2007 (UTC)

[edit] Dualistic Monism and Labor Theory of Value

Dualistic Monism and Labor Theory of Value

The essay is in two parts:

The first part is the "positive" definition of economic value, that is, the explanation of the relations between the 6 couples of polar attributes of economics by means of the general meaning of "identity-duality relationship" as engine of changes. This shows that in every considered period of time the price of the gross product is the representation of the totality time of labor of the system, independently from the function of commodities -i.e. the distinction between means of production and consumer goods- and independently from how they are distributed - i.e. how prices can vary accordingly-.

The second shows how the idea of value as incorporated labor and that of the transfer of the value of the means of production into the produced commodity, which imply that the value of the net product (instead of that of the gross product) coincides or is equal to the totality of labor of the system, violate the meaning of identity duality of all the polar attributes of economics, so that the relationship between prices and quantities of labor is lost, and the real value of the various currencies in terms of quantities of quantified human existence remains unknown.

[edit] One - Positive - Yang

According to the I Ching, which philosophy is also known as Dualistic, or Dialectical Monism, every change has a Sense that is generated, can be understood and represented by means of couples of opposite and identical, different but complementary polar attributes. This simple consideration is perfectly fit for the definition of the nature of economic value, where we have to deal with the following 6 relations, all intertwined, of identity and duality: - Unity of the economic system and multiplicity of the firms that make it up. - Physical transformation and social trasformation, also called production and distribution. - Labor and commodity, or creative value and material value and - Production and consumption in the physical tranformation, and - Commodity and price, or material value and exchange value and - Buying and selling in the social transformation.

An economic system is a unit composed by a multiplicity of firms that produce and exchange commodities, therefore there are two kinds of change: physical transformation, or production, concerning the relationship between humans and physical world, and social transformation, regarding the distribution of the result of those physical transformations between the firms that produce them. This makes of the economic system an organic unit. Since the two kind of transformation are different, their characteristics are independent and can and must be considered separately, but since one of them cannot exist without the other, they must also be considered in their oneness.

Every physical transformation is just but one event, and in this event there are two elements, or values: labor and commodity, which are different and identical. Labor decides the Sense of the transformation according to a plan, a project, and is the essential, or creative value of the event, while the corresponding commodity, for its physical characteristics, is the material value, or use value of that transformation. The gross product can be considered as a single commodity which use value is the quantified material life of the whole system, and its creative value the totality of labor. The use value of a commodity cannot be expressed as a mathematical fraction of the gross product’s use value, but its creative value is a fraction of the whole system’s quantity of time of labor. Physical transformation occurs as a process that is in the same time consumption and production, which, once again, are opposite and identical. The identity-duality relation of consumption-production is generated by the relation labor-commodity, and the identity relationship between labor and product is as well a relationship of identity between labor and consumption. Regarding physical transformation, these considerations don’t depend on distribution and are valid no matter what the commodities’ economic value will be.

Every firm yields the produced commodities to any other firm of the system in exchange for a quantity of commodities produced by them. Commodities are exchanged because they have different use values that satisfy different common needs, and a relation between different use values, as just said, cannot be expressed in quantitative mathematical terms. Indeed, a commodity is such not for its use value, but because it has a price, an economic value, which expresses the quantitative exchange relationship of every commodity with all the other commodities. The relationship of identity between material value and economic value goes together with the relation of identity and duality of buying and selling, opposite and identical. The price for which every single commodity is sold is also the price for which it is bought, and this is also true for the gross product. But while every commodity is exchanged with different commodities and their price change with distribution, the gross product is exchanged with itself, so that its price is constant and is the mathematical one, 1, the unity of the system, to which all prices refer as a fraction of. Price expresses the quantitative relationship between unity and multiplicity, between every commodity and the gross product - or every firm and the whole system - and, consequently, between every single commodity. These considerations about distribution are made without any reference to production, and regard the relative aspect of the economic value.

As creative value and exchange value refer to different changes, there is no reason for them to coincide, that is, the relation between quantity of labor of a firm and quantity of labor of the system, which is constant, normally is not equal to the fraction of the gross product that its price represents, which is variable. In the negotiated exchange, a commodity is bought for its material value, while the quantity of labor spent to produce it is invisible and is only one of the many causes for the magnitude of price, which eventually is the real economic value. But the commodity, or material value, belongs perfectly to both physical and social transformation, which imply each other through the whole system, where the creative value of the gross product is the totality of time of labor, which is constant for every possible distribution as well as its material and economic value are. If the economic value is expressed in monetary terms, the whole price, Dt, of the commodities exchanged in a given period of time, or Gross Product, GP, is the representation of the totality of time of labor, Lt, that produces them:

D_t ≡ GP ≡ L_t

and the mathematical relation:

D_t = L_t

determines the absolute value of the currencies in terms of quantities of social labor.

Prices always represent precise quantities of time of quantified human existence, a fraction of the time of labor of the economic system, of the labor of each for the others, independently from the commodities’ material value and the way they are distributed, that is, whatever they are used as means of production or consumer goods, and however the magnitude of prices can vary in order to ensure the condition of balance (buying-selling identity) for different possible distributions.

For a complete formalization see: Absolute Prices

[edit] Two - Negative - Yin

According to Marx the objective value, or simply value, of a commodity is the quantity of labor spent to produce it. If a commodity is produced by using freely available natural elements, its value is just the quantity of time of live labor. If, instead, it is made by using other commodities, or means of production, its value is calculated as the sum of the quantity of live, or new labor, directly employed to produce that commodity, plus the quantity of labor previously spent to produce the used means of production, which value is considered as indirect, or dead, or crystallized, or embodied labor that transfers into the produced commodities. In other words, the value of a commodity is calculated as a sum of live labor plus the supposed creative value -embodied labor- of commodities considered for their use value -means of production- but expressed by their economic value -in order to allow the variation of prices. But a sum between time of labor and any of those three terms doesn't have mathematical sense and implies a series of problems and contradictions.

Following this conception of value, the representation of the economic activities of the considered period comprehends commodities that are different because produced in different periods of time, that is, the consumed means of production, produced in the previous period, and the commodities produced during the present period. For this reason, in order to maintain the distinction between the two of them one must suppose that production takes place all along the considered period, and distribution, instead, in an instant only at the end of that period and before the beginning of the next one. But since commodities are of different periods, they remain diverse, and even if they had the same use value there is no reason to believe that the quantities of labor embodied and price of the consumed means of production are equal to those of the produced ones. For this reason, when determining the embodied quantities of labor the problem is that while the quantity of live labor of the studied period is known, the quantity of labor embodied in the used means of production must be searched in the characteristics of the previous period, which is not represented. In the determination of prices, the incongruence is that the distribution represented is not that of the produced commodities, which prices are under investigation, but that of the consumed means of production, produced and sold in the previous period, which values and prices therefore should be known, not unknown. In order to study the variation of the characteristics of the system for a variation of distribution, therefore, it is also necessary to suppose that the economic system is static, that is, that in every period commodities are produced and exchanged in the same way, so that, as well as their material value, the price of the consumed commodities can be equal to the price of the produced ones.

In reality the economic activities are a constant flow where the two transformations take place contemporaneously; the commodities represented are only and all those produced and exchanged in the considered period of time, so that the price for which they are sold is necessarily the same for which they are bought and there is no need to consider the system as "static". The sign of equality is not between consumed commodities and produced commodities, but between buying and selling of the same commodities. The static-ness hypothesis forces upon the wrong framework the condition that is always true for the correct one.

In that conception the same representation is used to calculate both embodied labor and prices, overlapping and confusing physical transformation and social transformation. Indeed, the quantity of labor embodied into the commodities cannot be "calculated" by means of considerations regarding only production because it depends on how the means of production are distributed, so that in reality it is distribution that is considered and represented. In this situation, the classical theory of value establishes that the quantity of labor incorporated into the commodities coincides, or is precisely indicated, by the prices calculated in the representation of the socialistic distribution, not deformed by the existence of profit, that is, with the distribution where the net product - for the static-ness hypothesis composed only of final consumer goods - is distributed only as wage proportional to the quantities of labor. In this case, since the quantity of labor embodied in the means of production produced is equal to the quantity of labor embodied into the means of production consumed, the value of the net product coincides with the totality of live labor, so that, as in a system where means of production don't exist, everyone receives from society a quantity of commodities that embody a quantity of social labor equal to the quantity of labor given to society by producing only one kind of commodity. The identity between totality of live labor and net product value is justified by considering the consumer goods as the real (qualitative) end of the whole economic activity, and therefore, directly or indirectly, of the whole labor. But if this were true, since in every period all the commodities, consumer goods and means of production, are consumed and reproduced, the quantity of labor embodied in the consumed commodities would be constantly superior than the quantity of labor that produces them all. Though this absurdity is not recognized as such, other contradictions pop up when considering a variation of distribution. A variation of distribution implies a variation of prices, which is explained as the effect of a redistribution of the value embodied into the commodities, but without changing the quantity of labor objectively embodied. But if the price of the net product is constant and coincides with the totality of live labor, a variation of all prices implies a variation of the gross product's price, which becomes bigger or smaller than the price calculated without profit, that is, than the quantity of labor objectively embodied. This is recognized even by the classical economists as an unacceptable contradiction, known as the problem of transformation, which conceals the currencies' absolute value.

In reality, in the physical transformation the relation of identity between labor and commodity, or creative value (which is not embodied labor) and use value, is simple and direct, and comprehends both labor-production and labor-consumption identities, and doesn't depend on distribution. And in the representation of distribution the sum is between the price of the final consumer goods and price of the means of production, or income and capital, where the income is proportional to the quantity of labor, but it is social labor, not that labor. In every period of time, in order to exist, labor must use, even if in different ways, means of production and consumer goods, and it is employed in the same time in part for the production of means of production and in part for the production of consumer goods, therefore, even in a socialistic distribution, the quantity of social labor indicated by the price of the consumer goods received as salary is inferior than the quantity of labor given to the system. Both value and price of the gross product are constant, while for the net product creative value is constant and the economic value is variable.

Shoujen 06:20, 16 September 2007 (UTC)

What is this? Maoism transmuted to Taoism???--Jack Upland 10:26, 2 November 2007 (UTC)

[edit] Bias

This article shows very little sign of a response to any criticism of it.--Jack Upland (talk) 09:11, 29 December 2007 (UTC)