transformation problem

To be honest, I can't figure out for the life of me what Marx is trying to say in that passage. I've reread it a million times and I still don't know what he's getting at. He makes bizarre statements like "Now, as we make our calculation the profit of A will not be included in its cost-price, nor will the profits of B, C, D, etc., be included in theirs. Nobody ever includes his own profit in his cost-price." This is entirely obvious, since as he admits in the second sentence "nobody ever includes his own profit in his cost-price." It seems to me that Marx is still trying to work out the relation of values and prices at this point in the manuscript.

In any case, this passage has not been the controversial one, which might come as a surprise since it is clearly related to the controversy. (Perhaps because of how confusing it is, it has been ignored, which seems to me to be the correct procedure since I can't see a debate about this passage going anywhere.)

The infamous passage is actually this one:

"The foregoing statements have at any rate modified the original assumption concerning the determination of the cost-price of commodities. We had originally assumed that the cost-price of a commodity equalled the value of the commodities consumed in its production. But for the buyer the price of production of a specific commodity is its cost-price, and may thus pass as cost-price into the prices of other commodities. Since the price of production may differ from the value of a commodity, it follows that the cost-price of a commodity containing this price of production of another commodity may also stand above or below that portion of its total value derived from the value of the means of production consumed by it. It is necessary to remember this modified significance of the cost-price, and to bear in mind that there is always the possibility of an error if the cost-price of a commodity in any particular sphere is identified with the value of the means of production consumed by it. Our present analysis does not necessitate a closer examination of this point."

According to an interpretation which was advanced by Bortkiewicz and has been dominant ever since (though it is by no means the only way to interpret Marx), in this passage Marx admits to making an error in his tables, because the cost-prices in the price of production table are not transformed into a separate price-of-production-cost-price (i.e. a cost-price which is the sum of the PRICES of the means of production consumed + the PRICE of the means of subsistence consumed). Bortkiewicz "corrects" this error by separating value and price of production into two completely different systems.

In the value system, the value of a commodity is determined by k + s , where k is the VALUE of the means of production consumed in a commodity's production plus the VALUE of the means of subsistence consumed by workers. S is surplus-value.

In the price system, the price of a commodity is determined by k' + r, where k' is the PRICE of the means of production consumed in a commodity's production plus the PRICE of the means of subsistence consumed by the worker, and r is the average rate of profit (rather than the surplus-value actually produced).

As you can see, this means that value and price are now in two entirely distinct systems of equations. In Marx's tables, there are not two distinct cost-prices, there is only ONE cost-price represented by k. Marx says that the value of a commodity is equal to k + s, where k is the cost-price of a commodity and s is the surplus-value produced, and the price of a commodity is k + p, where k is cost-price and p is average profit. I.e. cost-price (k) is identical in both systems.

Once Bortkiewicz has separated the value system from the price system, a number of (in)famous results emerge:

1. Marx claims both that total value equals total price, as well as that total surplus-value equals total profit. This implies that the general rate of profit in the "value system" and the "price system" are identical. Once this is "corrected" in the manner of Bortkiewicz, this cannot be the case: one can stipulate that EITHER total price equals total value, OR that total profit equals total surplus-value, but they cannot BOTH be equal at the same time (excepting some completely unrealistic scenarios, such as equal organic compositions of capital, in which there is no transformation anyway, or where there is no constant capital, etc.).

2. Given the above, the rate of profit of the "price system" and the "value system" MUST be unequal.

3. The general rate of profit is not at all affected by production of luxury goods (goods which do not enter into any production process as constant capital, nor are consumed by workers). This is contrary to Marx's theory in which the general rate of profit is determined by the surplus-value extracted in ALL sectors of production. (This is also a defense of Ricardo, who gave primacy to the conditions of production in the wage-good sector. Marx criticized Ricardo on this point.)

4. Marx's theory of the tendential fall in the rate of profit is untenable. The rate of profit actually rises with any increase in productivity (unless the increase in productive occurs in a sector producing luxury goods, which would leave the general rate of profit unchanged, as I noted above). In fact this result was not noticed immediately but was a result of the way Bortkiewicz "corrected" Marx. I don't believe it was explicitly noticed for at least a few years. Bortkiewicz wrote a paper dealing with this but I believe to this day it's never been translated into English. Okishio's theorem is the most famous of the theorems to have made this claim.

As you can probably see, all 4 of these things cast serious doubt on major aspects of Marx's theory.

If it is assumed that total value and total price are equal, then total surplus-value and total profit must be unequal. Thus, there seems to be a source of profit different from surplus-labor. Or, alternatively, if one assumes that total surplus-value equals total profit, then total value and total price must be unequal. There thus seems to be a source of value different from living labor.

Pecularity 3 has been discussed less frequently, but in my opinion this only reinforces the point that in Bortkiewicz' correction, profit cannot come from living labor, since the living labor performed by workers that produce luxury goods becomes entirely irrelevant.

The theory that the rate of profit RISES with increases of productivity casts doubt on (what is arguably) Marx's theory of periodic crises.

Fortunately for Marx's theory, and unfortunately for its critics, Bortkiewicz' critique has a number of serious problems, the most serious of which, in my opinion is the following:

The reason Bortkiewicz claims that value and price must be separated into two separate systems is because of an attempted proof he gave which is supposed to show that if values and prices are left in the same system, there can be no reproduction of the capitalist system: reproduction breaks down spuriously. His proof was disproved in 1988 by Kliman and McGlone, who showed that it is possible to keep value and price in the same system, as Marx did, without any spurious breakdown of reproduction. Thus, Bortkiewicz' argument about the necessity of separating the systems falls down. Bortkiewicz' "correction", then, is not at all a correction but in fact an entirely different theory of profit determination.

In my opinion the best book on the "transformation problem" is Andrew Kliman's "Reclaiming Marx's Capital", which was published at the beginning of this year. It's quite intelligible for anyone who has read through Marx's discussion of the transformation of values into prices of production as well as the law of the tendential fall in the rate of profit. There is some arithmetic but no algebra accept in appendices which are optional and one can skip without affecting the line of argument. It clearly and intelligibly explains Bortkiewicz' critique as well as subsequent ones as well as the debates that have taken place since then.

There is also an interesting paper by Alejandro Ramos-Martinez which examines the parts of Vol. 3 of Capital that Engels didn't include in the finished version, which help clarify what Marx was doing. His perspective on the "transformation problem" is the same as that of Andrew Kliman. (As a brief summary: there is no transformation problem. Marx's explanation of the transformation of values into prices of production is logically consistent.) I can send this as a PDF file if you private message me. (This also has no complex math.)

I hope this helps you understand what the critique of Marx is.

Mike

sorry if i skipped any bit that explained this, but what would be such a (macro level) source?

To be clear, I do think that Marx was correct to view the basis of profit as the surplus-labor of the working class. So these are not my views.

In the theory implied in the models used to criticize Marx, the basis of profit is not surplus-labor but is surplus-product, in the literal sense of "things." For this reason the theory is frequently referred to as "physicalism", which is basically synonymous with Sraffianism, neo-Ricardianism, or the surplus approach (which is the term most generally accepted by its proponents).

Take a very basic example:

A farmer plants 10 bushels of corn at the beginning of the year and harvests 11 at the end of the year. The only capital investment is the 10 bushels of corn, no living labor is used, and no wage is paid.

In the physicalist theory, which is implied in Bortkiewicz' critique of Marx, the profit rate of this example is 10%. Price is irrelevant. The price of corn could be anything and the rate of profit will remain 10 percent. Why? Because in this theory, input prices must equal output prices. The price of a single bushel of corn planted at the beginning of the year must equal the price of 1 bushel of corn planted at the end of the year.

So let's represent the price of corn by PC, and let the rate of profit be R. An equation which would depict the economy would be:

10PC (1+R) = 11PC

In other words, the cost-price (10PC) plus the profit on the costprice (1+R) is equal to the value of the output, which is 11PC.

The PC on both sides of the equation cancel out. We are thus left with:

10 (1+R) = 11

= 10 + 10R = 11

= 10R = 1

= R= 0.1, or 10%

As you can see, the price of corn is immediately canceled out. The rate of profit is 0.1, or 10%, no matter what the price of corn is, and is in fact determined by the relation of the physical input to the physical output. (The rate of physical surplus is also 10%. 1 bushel of corn surplus divided by 10 bushels invested.)

Surplus-value and profit have arisen without any labor being performed. The basis of profit cannot be surplus-value. Instead, it is physical quantities of use-values, and the relation between the input and output of use-values is what determines the rate of profit. (It is no surprise, then, that on the basis of this theory Marx's theory that the rate of profit falls with increasing productivity has been "refuted".)

In Marx's theory, on the other hand, this is what would occur:

10 bushels would be planted, so the input price would be 10PC. No living labor would be used, so the total price of output would be equal to the price of the input (which in this case consists only of CONSTANT capital, which adds no new value to the final product), no matter how much physical output was produced. So if 11 bushels were harvested at the end, their total value would be equal to the price 10 bushels of corn as an input. NO profit would arise, because the price at the end of the process only allows the capitalist to recover the investment made at the beginning. No surplus-labor, and no profit.

Think of this empirically as well. If there were methods of producing commodities at no cost, prices would immediately fall. Think of the constant struggles over patents with software, for example, where because the cost of reproduction is virtually zero once the software has been created, since the software can be pirated at virtually no cost. The only way to counter this is to crack down on pirating and enforce copyright restrictions. (I'm currently writing from a country where the price of software, movies, music, is generally less than a dollar because of the possibility of reproducing the commodities almost for free.) According to the physicalist understanding of capitalism, on the other hand, one might expect that the infinite reproducibility of software would lead to higher and higher rates of profit, since the price of the output would not fall but remain constant.

Just quickly:

Two things:
1. this example is used by Henry George in "Progress and Poverty" - written almost at the same time as Capital. It's a pretty interesting book (ends up arguing for a tax on the full rental value of land).

2.

Planting is labour, as is harvesting.

SIMCP,

It's hard to follow this for me unless you give a simple numerical example. What you say seems to be an accurate rephrasing of what Marx said, but I'm still not clear on what Marx said, so I'm not entirely clear on what you said.

How are you suggesting that value is formed? (I.e. by what components.) My impression is that you are saying that the value of a commodity is represented by k+s , where k is the sum of the VALUE of means of production plus the VALUE of means of subsistence consumed by workers, and s is surplus-value? And the price of production of a commodity is k'+p, where k' is the sum of the PRICE of the means of production plus the WAGE paid to workers (i.e. the PRICE of the means of subsistence) plus the average rate of profit (p)? Or is this a misrepresentation?

If that's not a misrepresentation, then I think you run into problems if you'd wish to retain Marx's theory of the transformation of values into prices of production. As I noted above, Bortkiewicz showed that if you disconnect values from prices in this way, by making values depend only on values and prices depend only on prices, you cannot have the two aggregate equalities together (total surplus-value= total profit and total value=total price), and the rate of profit in terms of value is different from the rate of profit in terms of price (the same is also true of the rate of surplus-value).

In this case, you have to choose: does total price equal total value, or does total surplus-value equal profit (since both cannot hold true simultaneously)? If the former, then total surplus-value and total profit cannot be equal, and we must ask where the excess profit above surplus-value comes from, if profit is greater than surplus-value, or if profit is less than surplus-value, where does the surplus-value greater than profit go? If, on the other hand, you say that total surplus-value equals total profit, then total price and total value cannot be equal. Where does the excess of price above value come from (provided that total price is greater than total value), or if total price is less than total value, where does the excess value go? There is a problem of appearing and disappearing surplus-/value.

I do think that these pose serious, even fatal, problems for any Marxist who would like to say that values depend only on values and prices depend only on prices. If profit is not determined by surplus-labor then a huge part of Marx's theory falls down. (For example, the bulk of Vol, 1, which deals with this surplus-labor and its importance, large parts of Vol. 2, which deals with the circulation of this product of surplus-labor, and of course large parts of Vol. 3 which deal with the supposed distribution of this surplus-labor among the different sections of the capitalist class.)

Also, it is not Marx's supposed "admission of error" that is presented as a killer blow to Marxism, but rather what happens once the "error" is "corrected". Notice the 4 peculiarities I pointed out in an above post about just what happens once the supposed error is "corrected." These are what are presented as a blow to Marx.

BTW, I think the "solution" is rather simple: values and prices have the same cost-price, which depends on the prices of the means of production consumed, plus the wage paid to workers. In other words, value itself depends partly on past prices. This is why Marx represents the value of a commodity as k+s, and the price of production of a commodity as k+p : cost-price is the same in both equations.

Once this is accepted, then Marx's conclusions about total price and total value, and total profit and total surplus-value, hold true, as does his claim that the aggregate rate of profit is equal both in terms of value and price. (The paper I'm going to send you gives quite a bit of textual evidence that this was in fact Marx's solution to the conundrum that previously faced the law of value.)

Regards,
Mike

SIMCP,

I went through the chapter again and I have a preliminary answer to what I think Marx is doing in that passage.

But first a response to this statement:

This is a response that many Marxists gave to the Sraffian critique of Marx (most notably Paul Mattick, Sr. in his critique of Paul Samuelson). I don't think it can be sustained. First of all, Marx himself gave quite a few numbers in his transformation procedure, so as an interpretation of Marx it doesn't really make sense. Even in the specific passage you quote Marx uses variables to represent certain mathematical relations between quantities of surplus-value, profit and cost-price.

Secondly, central to Marx's theory are the claims that in the aggregate, surplus-value equals profit and price equals value. This is a definite quantitative claim. And since cost-price is equal to price minus profit, given the two aggregate equalities we should be able to ascertain aggregate cost-price.

This is not to say that Marx's theory can be reduced to quantitative equalities but it is undeniable that these aggregate equalities are very important in Marx's theory (since it is only by means of them that Marx is able to reconcile the law of value with the appearances of capitalist production).

As for the passage and its relation to the rest of the chapter, I've come to the conclusion that in the passage you refer to at the top, Marx going through one possible way of separating values and prices. Marx first tries to separate the profit which lies within the cost-price of commodities from the rest of the cost-price. In other words, he is going in the direction of trying to ascertain two distinct cost-prices: one which presents itself to the capitalist, as a sum of prices, and a distinct value-cost-price which is based on the value (rather than the price) of the means of production and subsistence consumed.

But later Marx comes to the conclusion that cost-price cannot be treated in this way, it must be taken as a given money magnitude (i.e. the wage paid to the worker plus the money paid to attain the means of production):

Notice that the statement that "the cost-price of a commodity is always smaller than its value" would NOT be true if there were two separate cost-prices. Imagine a case where the value of the means of production consumed plus the value of the means of subsistence consumed were $50, while the price of the means of production consumed plus the wage paid to the workers were $100 (the difference of $50 being due to divergence of value from production price, such that value was significantly less than production price for these commodities).

Now suppose that 1 hour of labor produces $1 of value. 10 hours of labor are used, so $10 of value are produced.

In this case, the value of the commodity ($50 value of means of subsistence/production + $10 living labor) would NOT be greater than the cost-price of the commodity ($100). It would be $40 less.

Since this simply doesn't make sense, and Marx would have contradicted himself if he had assumed that there were two different cost-prices, we must conclude that he is saying that the two cost-prices are identical: the value of a finished commodity (partly) depends on the price of the means of production being used in its production. (This, of course, isn't the only evidence for this interpretation. There is much more presented in the article I sent you as well as the Kliman essays I posted above, as well as the Kliman book.)

You said:

This isn't correct, it you mean this to show the impossibility of adding value (due to living labor) to a cost-price which itself includes profit. The cost-price (which includes profit) is taken as a given precondition. It does depend on past prices. But this doesn't actually cause any problems. All theories depend on given preconditions. In Marx's theory, past prices are one of his given preconditions. There is no reason to rule out past value-distribution affecting future value-distribution.

Regards,
Mike

John,

I disagree with what you say about value, at least as it pertains to Marx's own understanding of his solution to the problem. In Marx's theory already from Ch. 1 of the first Volume, and for the rest of all 3 volumes, value is treated as an actual magnitude which can be expressed by both in terms of labor-time and in terms of money. This also is certainly the case in Part II of Vol. 3 of Capital, in which Marx's claim that in the total surplus-value equals total profit and total value equals total price presupposes that both value and price can be expressed in the same units (namely, money).

So the claim that they are simply in two different dimensions, so to speak, cannot stand as a legitimate interpretation of Marx's theory.

That said, I am not saying that the theory cannot stand on its own terms. It may be able to. But it must make entirely different predictions and have an entirely different theoretical basis from Marx's.

I should note that I think Saad-Filho's attempt to solve the so-called transformation problem is a roundabout way of doing nothing. Saad-Filho (whose position is shared by Ben Fine, as far as I'm aware) basically says that Marx took the first step to solving the transformation procedure (by transforming the outputs), and what needs to be done is to complete it by transforming the inputs through a further process. But once this process is completed, the same inconsistencies that had always been alleged pop back up: total price does not equal total value, and total profit does not equal total surplus-value (or, rather, the two cannot be equal simultaneously). Thus the critique of Marx turns out to be correct, it's just that a different method of arriving at the critique is proposed. But the method of arriving at the critique was never at issue. Saad-Filho arrives at the exact same conclusion as Bortkiewicz, except that he refuses to acknowledge it.

Examine the first quote you provided more closely:

The second sentence admits that Marx's procedure is incapable of arriving at the calculation of actual prices of production. But once Saad-Filho makes a proposal that does suffice to calculate actual prices of production, it is seen that value is not the basis of price and surplus-value is not the basis of profit. This then makes his third sentence, which claims that value is the cause of prices of production, absolutely false, since on Saad-Filho's own interpretation this is not the case!

I don't see how this is anything more than a Marxist dodge of the real issue of the debate with the Sraffians: does labor-time determine value, and surplus-labor time determine profit, or do physical quantities?

If one wants to say that the answer is labor-time, one needs a better answer than Saad-Filho's.

Regards,
Mike

hi Mike,

I prefer to think of it in a different way:

1) was Marx right to use the idea of value to illustrate the way in which the amount of energy expended by the workers is less than that which is necessarily received by the workers, in order to provide a basis for the idea of profit being exploitative. I think the answer is yes - if we just stick in the realm of wages, prices, profits, there is no basis upon which to portray the employment of wage-labour and the production of profit through it as something which creates a transfer of power from workers to capital-owners.

2) do we need to include the idea of prices in a theory of capitalism in order to make it more concrete-complex - I think the answer to this is also yes. We need to understand how prices/wages/profits relate to value/surplus-value - i.e. that they are referring to the same things, but never necessarily in the same quantities.

3) does the tendency of the rate of profit to fall exist? I think the answer to this is yes, if we accept the logical conditions existent in Marx's theory - that competition equalizes prices, that the pursuit of increasing particular profits for individual capitals creates a general process which reduces the overall amount of labour employed in production, and therefore reduces the overall rate of exploitation.

4) does it matter for any of this whether price = value (or whether it has been shown to do so incorrectly by Marx).? I don't think so.

For me, Marx is working with so many different levels of abstraction that Capital inevitably contradicts itself. The transformation problem is just one example.

So John, since you say that Capital contradicts itself, are you saying that we should leave communist political economy a mass of contradictions or that we should work out a more consistent approach?

Your whole approach seems to take the "it's close enough to work as plausible propaganda" position. I think that contradicts working towards a situation where the proletariat is able to reason about itself.

Red

Edited for typos

Well, aside from the point about the proletariat reasoning about itself (which I won't say I agree or disagree with, since I didn't say it and am not exactly sure what is meant by it), incompleteness is not at all a form of contradiction. Incompleteness is incompleteness. I may only know some things about the computer I'm writing on, but it does not follow that my knowledge of it is contradictory.

The problem is that you have no evidence that workers are exploited unless you use value-theory. But the validity of value-theory is precisely what it in question. You are begging the question by assuming what you are trying to prove, and then using this as a premise in your argument in order to derive the conclusion that value-theory is necessary. Circular arguments cannot prove anything, since they amount to assertions rather than deductions. See this.

No, it is not unavoidable. Any valid deduction avoids it, by allowing the conclusions to be deduced from premises rather than including the conclusion itself in one of the premises. The link I provided above should make my problem with it fairly clear.

What I was trying to say was that the Sraffians already claim to have disproved your argument. If their disproof is correct, then profit is not derived from the "exchange [of] more value for less", but rather from physical quantities.

You seem to be going in the direction of saying "okay, that is how profit is determined but not surplus-value." But the problem with this is that if surplus-value has no relation to profit, your theory of surplus-value and exploitation is going to be purely Platonic. Surplus-value will be a hidden essence behind profit but there is no way this theory can be either verified nor falsified. It cannot be observed, nor can its effects. It is no different than claims for the existence of God.

I respond to this idea immediately above. If you don't care about the relation of surplus-value to profit, neither should anyone else, but I don't think most people will stick to surplus-value as against profit. Most people will just reject it as irrelevant, since even if true (and there is not even any evidence for this) there would be no way to know that. Even as far as the "plausible propaganda" goes (which Red mentioned), I think this falls far short.

I'm going to hold off on this for now, since it seems that the real basis of our difference is not this and I'm not clear of the relevance of this to the debate. But I will just say that I don't think that these things falsify value-theory as an explanation of concrete phenomenon.

I tried to explain Bortkiewicz's objection to Marx's transformation procedure in my first couple of posts above. I'm afraid I don't think I can do much better than that, it is admittedly a difficult topic at first, and the only way to understand why what Bortkiewicz says must be true (so long as values and prices are held in two separate systems) is to look at his mathematical proof.

Yes, some people have taken this response, but I don't think it's valid. The problem with this is that the appearance and disappearance of value and price in Bortkiewicz' proof occurs in a case of no technical change and no accumulation of capital. So the falling rate of profit and contradictory accumulation cannot explain why value and price seem to appear and disappear, since they can only function as explanation once technical change is introduced as well as the accumulation of capital.

Yes, I misinterpreted you before, but I still think there is a problem here insofar as you still hold to Marx's theory of the law of the tendential fall in the rate of profit. This absolutely presupposes Marx's value theory, particularly his theory that living labor in production (which produces values) determines price magnitudes. Otherwise, there is no way to suggest that a decline in living labor in production has any effect whatsoever on the rate of profit (which is a ratio of prices). So if you give up the quantitative aspects of Marx's theory of value you also give up Marx's explanation for the tendential fall in the rate of profit.

This makes debating anything pointless, since you can believe whatever you want. Why did you consider it worthwhile to take up this discussion/debate if you can believe anything you want based on purely subjective criteria?

Also, perhaps I'm stepping over my bounds by analyzing your personal psychology, but I doubt you actually believe this. Do you believe that Earth orbits the Sun? If so, what are your purely subjective reasons for believing this? I think living life on the basis of purely subjective criteria would be quite difficult, nay impossible.

This response supposes that I want to "capture reality in its entirety". Since I'm not a dialectical materialist, I see no need to try to capture reality in its entirety. I only see the need to capture the object of my studies. Which admittedly still gives headaches, but genuine research is at least possible.

Take care,

Mike