Talk:Transformation problem

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I do not understand the problem[edit]

In the first chapter of The Capital, Book I, Marx wrote:

"The total labor force of society, [...] is embodied in the sum total of the values of all commodities produced by that society"

Total labor force of society (Labor force, total): 3,288,561,934 workers in 2012 (source: World Bank)

Sum total of the values of all commodities produced by that society (GDP (PPP)): 99,396,280,511,216 International Dollars in 2012 (source: World Bank)

So:

> 3,3G workers working for one year = 99000G PPP$ (in 2012)

> 1 average worker working for one year = 30000 PPP$ (in 2012)

You can calculate the value of a commodity in quantity of work if you can calculate its price in purchasing power parity.

The better is the calculation of purchasing power parity, the better is the professional demographics assessment, the more accurate is the calculation of the amount of work in goods.

--Ascax (talk) 19:35, 15 December 2016 (UTC)

The problem is about individual prices. As I note in the section immediately below, it is meaningless to say that total labour is equal to total prices.--Jack Upland (talk) 21:00, 15 December 2016 (UTC)

I may have misrepresented myself : GDP is not total prices.

GDP is amount of product, not amount of prices.

But, incidentally, the products have a price, so we can establish an equivalence between quantity of work and price.

GDP is amount of goods, and, valued at US price levels, this amount of goods has a certain price.

Total amount of work is embodied in total amount of goods, which has a certain price, valued at US price levels.

But to evaluate this amount of goods at US price levels is arbitrary: only the amount of goods counts.

To know the value of a particular commodity, it is sufficient for us to know the ratio of prices, since the values ratio and the prices ratio are identical by definition.

The prices ratio is given by the price index. Ideally, we should use a price index calculated from the average prices of all goods globally, but since such an index does not exist, we use the US price index which is an acceptable approximation.

I'm not sure I'm very clear. Let's summarize:

  1. the entire work is incorporated into the whole product,
  2. the prices ratio allows us to calculate the value of each commodity in the gross product (because prices ratio = values ratio)
  3. if not better, the US prices ratio is an acceptable approximation of the world prices ratio.

--Ascax (talk) 01:39, 16 December 2016 (UTC)

Empirical Marxism[edit]

An unidentified user added this to the article, which more properly belongs here in the talk page: "The claim in this sentence that the 'empirical' Marxists simply state that the transformation problem is irrelevant because there is a correspondence between prices and labor values is completely untrue. First, they do not claim that individual prices and labor values ever correspond but actually that individual prices and values of necessity never correspond. The correspondence they show is one of aggregate prices and aggregate value or aggregate profit and aggregate surplus value. It is not the empirical correspondence as such orrespondence in itself is not the claim, but the fact that the deviation of value from price or profit from surplus value is itself only explainable through Marx's labor theory of value (not Smith or Ricardo) - this deviation is NOT explainable either in Sraffian or Newhich they focus on, but the theoretical consistency of Marx's claim of value transfer in exchange with this correspondence. The coclassical traditions. This is actually the solution of the transformation problem, ironically the same solution of the labor commanded theory of value. The transformation problem is one of neoclassical theory, which they ignore because they choose to focus on fictional market equilibrium instead of the actual relationship between what profit should be in their theory (the aggregate costs of production, ie. the return to all factors) and what it really is in reality. There is no way to explain this in neoclassical theory, because neoclassical theory has no theory of value but a theory of prices; it is tautological to say that there are 'price transfers' on the market."

In fact, Cockshott, Shaikh, et al do indeed say that individual values and prices correspond highly. I will add some article references to that effect. James Haughton (talk) 12:59, 11 April 2011 (UTC)

They must of necessity, because the claim that the aggregate amount of labour corresponds to aggregate prices is meaningless. One is measured in hours, the other in money. The substance of the theory can only be meaningful if (at least at some point) there is a set relationship between hours and money across different individual instances. This logic seems to escape people.--Jack Upland (talk) 08:42, 25 April 2011 (UTC)

Rework[edit]

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)

I agree that the introduction of Sraffa et. al. in the Overview section is premature. To resolve this, I'm moving those paragraphs into the "Implications" section. The logic of that section is a continuation of the argument started in the overview, and as such I think it more properly belongs there. I am also renaming that section from "Implications" to "Critics of the theory" for POV reasons. The previous title gives the article a tone of accepting these claimed proofs presented by Marx's critics. Ejrd1993 (talk) 00:20, 29 May 2011 (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)

More rework of the overview. The first paragraph was a long description of the labor contained in a commodity, and didn't tie into the remainder of the overview, and I didn't think it was necessary for understanding the theory, so I deleted it. I've expanded the second paragraph to present a still brief but somewhat more thorough description of Marx's theory. Finally, I changed the title of the section to "Marx's Theory" since that is in fact what the section is about. Ejrd1993 (talk) 03:59, 10 June 2011 (UTC)

Moved the section "Critics of the Theory" lower in the article for NPOV reasons. As it was, there was a brief introduction to the theory, then a long discussion of attempts to refute the theory, then more exposition of the theory, then more refutation, then "Marxian reply to mainstream views". It reads as a fight back and forth, not an objective discussion of the theory, followed by elaborators and criticisms. Ejrd1993 (talk) 04:51, 10 June 2011 (UTC)

Numeric Example Rework[edit]

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)
Re Cplot's comments on the "non-transformation problem" question, there is a fallacy in the reasoning in that sub-section. It purports to show that “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.” (my emphasis) But to show what happens using concrete numbers, assume this starting condition:
Average deer production: 6 hours plus 5 arrows
Average beaver production: 10 hours plus 3 arrows
Average arrow production: 2 hours
From these we get:
Average deer embodies 16 hours
Average beaver embodies 16 hours
Therefore one deer exchanges for one beaver, on the basis that both have an equal amount of total labor embodied in them.
Now assume that arrow production goes from 2 hours to 1 hour, but everything else stays the same.
Average deer embodies 11 hours
Average beaver embodies 13 hours
Now one deer exchanges for 11/13 beaver, since that is the ratio of the labor they have embodied in them.
Obviously, for most other arbitrary numbers, the exchange ratio will also change. In certain special cases the exchange rate really will be unaffected. One example is where direct labor producing deer and direct labor producing beaver are the same, and the same number of arrows are used. A little imagination will show a few more special cases.
That said, the sub-section detracts from the overall article. First, it has nothing to do with the transformation problem, but instead is an erroneous discussion of how exchange based on embodied labor is affected by changes in the production of inputs. Secondly, it is a poor argument in any case, since it simply asserts what it is purporting to prove. Therefore I'm deleting it. Ejrd1993 (talk) 07:15, 1 September 2011 (UTC)

Updated References[edit]

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)

Previous Talk Header[edit]

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)

Formatting Math[edit]

Dear Mario, <math> </math> are the basic tags for indicating maths. Within these tags you use a 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)

from FifelFoo's talk page[edit]

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.

Let’s start from the beginning.[edit]

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)

Problem number 2.[edit]

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 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)

Solution for r[edit]

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)

"Econometric" interpretations of Marx?[edit]

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)

"Supposedly" ?[edit]

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)

Which prices ?[edit]

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)

Reply to Mario[edit]

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)

I agree with Jurriaan that "Obviously you can start talking about beavers & deers and suchlike when the problems get difficult" -- the deer and beaver material is more appropriate for the wiki article on Adam Smith, rather than here. The main problem with its use here is that it considers a very different economy than the one Marx was discussing when he raised the transformation problem. In the D&B example, the economy is some sort of hybrid hunter-gatherer and early-capitalist economy. There is very minimal mention of constant capital, arrows being the only thing passing for such. The assumption that all constant capital "goes away" after one use is also very different from the fully-developed capitalism which Marx is considering. Since Marx is discussing a macro-economic question which only occurs under developed capitalism, spending so much time on the D&B example detracts from the article. Finally, there is no notion as far as I can tell of different organic compositions in different industries. Since this is the key question in the transformation problem, I'd argue that this is a fatal flaw for the D&B example.

As Juriaan says, "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." And D&B gets us no farther toward clarifying that matter. Furthermore, the formulas given in that example are opaque.
I plan to judiciously shorten and move that example into the "Critics of the theory" section. I will leave the outline of the D&B argument, but since it is used mainly as a leadup to refuting Marx under "Marx's error and its correction" and "The non-transformation problem", I think it belongs collected there. I'll be making these changes gradually over the next weeks.Ejrd1993 (talk) 07:47, 17 July 2011 (UTC)

Good idea. Since Marx doesn't discuss "deers and beavers" it's (at best) a distortion to portray his argument in this way. Marx described such arguments as "Robinsonades" (in reference to Robison Crusoe). The economy portrayed in these examples is one that has never generally existed (a hybrid of hunter-gatherer and early capitalist) but which has had an inordinate influence on economic theory.--Jack Upland (talk) 10:24, 4 August 2011 (UTC)

kudos[edit]

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).

Non-Sraffian interpretations of Marx?[edit]

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)

POV[edit]

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)

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

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)

Simplified Version[edit]

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!!!!!!!!!!

Simplified Version of Transformation Problems[edit]

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.

Marxism label[edit]

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)

Old elaboration material[edit]

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)

I've deleted the duplication here of an earlier version of the article. It was mainly repetition of what appears in the article today, and it was a huge block of non-discussion text which made it very difficult to find your way around in the discussion.

references moved from main article[edit]

References[edit]

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. [1]
  • 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.
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  • Freeman, Alan and Guglielmo Carchedi (1996). Marx and non-equilibrium economics. Cheltenhaum, UK ; Brookfield, US, Edward Elgar.
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  • 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.
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  • Marx, Karl. (1971 [1861-63]). Theories of Surplus-Value. Moscow, Progress Publishers.
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  • 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.
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on the recent revert[edit]

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)

2 Objections to the methematical rendering[edit]

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 can be reduced to labor, which would make it possible to solve for in terms of . 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)

Dualistic Monism and Labor Theory of Value[edit]

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.


One - Positive - Yang[edit]

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:

Dt ≡ GP ≡ Lt

and the mathematical relation:

Dt = Lt

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

This link doesn't work anymore. --Alex1011 (talk) 19:53, 22 May 2011 (UTC)

Two - Negative - Yin[edit]

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)

Bias[edit]

This article is biased and editors are resistant to any suggested improvements.--Jack Upland (talk) 09:11, 29 December 2007 (UTC)

(response to updated comment at 07:51, 14 October 2009 (UTC)). Blank, rewrite from academic review articles in peer reviewed journals, SOFIXIT? I'm too fatigued to read the literature to comment, and as repeatedly commented above, this is tangental to my involvement in Marxism, but the article hasn't improved since 2007. Fifelfoo (talk) 07:51, 14 October 2009 (UTC)
I'm just flagging the issue for the benefit of readers and future editors.--Jack Upland (talk) 09:12, 15 October 2009 (UTC)
I don't see that any challenges to the objectivity of this article have been made for a year and a half, but I agree that the article is biased. I would like to see it flagged as such. Before simply editing the page to add the flag, I hope to generate some discussion here first.
Here are three of the most clear ways it is biased:
First, and most obvious, the Samuelson “eraser algorithm”. A sophomoric snipe like this has no place in a serious encyclopedia article on a complex economic matter. It only muddies the question. This subsection should be deleted.
Second, in the second to last paragraph of the Overview section there is a survey of some schools of Marxist thought arising since the 1970's on the question. Three schools are listed, described as holding the following three conclusions:
a) that the transformation problem disproves the labor theory of value.
b) that since we can see that values and prices correspond, the transformation problem is irrelevant.
c) that there is no difference between value and price, so there is nothing to transform.
This list doesn't include those modern-day Marxists who hold that the labor theory of value is an accurate description of capitalist economics; that values and prices do differ; and that they do so in an understandable, systematic way. As an example of a modern article taking this position, see On the non-naturalness of value: A defense of Marx and Engels on
 the transformation problem. The position of such Marxists should be summarized clearly in the article.
Third, the article contains phrases such as: “It then offers a simple proof of the general lack of solution for the transformation problem ...”, and “All the above formal conclusions have ceased to be controversial since more than a generation ago”. Whether or not there is a solution to the transformation problem is still a matter of debate, yet the page states the opposite, leaving a reader who is not familiar with the subject in the dark. The article should be edited throughout to remove phrases which suggest that the question is settled when it is not.
Some of these points have been made previously on the discussion page, but it hasn't resulted in the problems being fixed. I think that by flagging the article as biased, it might result in needed changes being accepted. Ejrd1993 (talk) 21:43, 2 May 2011 (UTC)
Given that no one has responded to my comment posted 2 weeks ago that this article is biased, I'm taking the next step and flagging it as biased. I do see that some of the worst examples of bias have been cleaned up since then, but these fixes only represent a start. Ejrd1993 (talk) 06:34, 17 May 2011 (UTC)
Deleting the following subsection on NPOV grounds:
==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 critics of Marx, 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, controversy still remains, as many Marxist theorists contend that there is no logical failure.
It contains nothing but two unsupported assertions: 1) that it has been uncontroversial that there is no solution the transformation problem for more than a generation, and 2) that controversy only remains because Marxist theorists contend there is no failure. First, the subsection fails to present any reasons why Marxist theorists maintain this contention, and second, the two assertions are in direct contradiction with each other: the question is no longer controversial, but there remains controversy on the subject.Ejrd1993 (talk) 07:15, 20 May 2011 (UTC)

That passage is pompous and patronising and deserves to go.--Jack Upland (talk) 10:13, 4 August 2011 (UTC)

So many views...[edit]

Is it really necessary to have "Marxist views", "other Marxist views", "Mainstream Views" and "Marxist response"? Can't it just be Marxist views and mainstream views, or even better just "views"? —Preceding unsigned comment added by 82.27.250.249 (talk) 19:19, 9 September 2008 (UTC)

On Mainstream Views[edit]

No names, no cites, "Mainstream scholars[who?] question the assumption that the basic nature of capitalist production and distribution can be gleaned from unrealistic special cases." Economics as a discipline functions out of the creation of special case models? Fifelfoo (talk) 02:07, 19 May 2009 (UTC)

The examples of hunting beavers and deer do not involve surplus value or profit[edit]

At least as far as Marx is concerned, it would be questionable to use the example of hunting beavers and deer in discussing surplus value and profit, since without the buying and consumption of labor in capitalism there is neither surplus value nor profit in the sense Marx is discussing these. The example might be interesting as a contrast to capitalist production, but it makes little sense to use this as the basis for the entire article. It puts the reader on a path Marx is not on. Also, I completely agree with some comments above regarding the use of mathematics. Quine spoke of the principle of shallow analysis - analyze only what is crucial to the point at hand, so as to not obfuscate things. Use simple math when possible (as Marx did), no math at all when ordinary language suffices. The use of variables is okay for a specialized article or for your private documents, but becomes difficult for the reader to keep straight (even one with good math skills). Write to accommodate the educated reader, not the specialist. Variables can be left out entirely or put in a footnote to remind people you are skilled in that area. — Preceding unsigned comment added by 208.91.176.144 (talk) 03:30, 14 August 2013 (UTC)

Yes, the discussion is skewed against Marx. Hunting beavers and deer is a false presentation of the issue, what he called a "Robinsonade" after Robinson Crusoe, a presentation which takes the issue out of its socio-economic context. The mathematics is also misleading because it was not how Marx presented the problem, and it gives a false impression of the resolution. The transformation problem only exists (at least in Marx's intrerpretation) because the real world does not strictly conform to a mathematical model. Mathematics cannot confirm or deny this point.--Jack Upland (talk) 10:51, 18 June 2014 (UTC)