Re: [OPE-L] Okishio Theorem

From: Rakesh Bhandari (bhandari@BERKELEY.EDU)
Date: Tue Oct 30 2007 - 13:24:35 EDT

>I have asked Alan Freeman what he makes of the debate between Fred and Rakesh.
>His reply is below to your information.
>Dear Dogan
>Thank you for drawing my attention to this 
>correspondence and for your interest in the 
>Rakesh, in a post that begins with a very clear 
>statement of the issue of logic surrounding 
>impossibility theorems, goes on to state that we 
>(TSSI) have not "demonstrated that empirically 
>David Laibman's tracking theorem (the money rate 
>of profit tracks the material rate of profit) 
>will not hold in the long term".
>This second point unfortunately subtracts a 
>great deal from the good done by the first 
>point, and highlights a long-standing source of 
>confusion, which I think Laibman's contribution 
>was archetypal in creating and perpetuating. 
>This is the simple issue in mathematical logic 
>of how one refutes an impossibility theorem.
>No TSSI researcher would never seek to do what 
>Rakesh complains we have not done, and nor is it 
>a failing in the TSSI that they do not do so. 
>The idea that the TSSI refutation of the Okishio 
>theorem should be held to account for empirical 
>predictions which it does not make is, I think, 
>based on a residual misunderstanding that never 
>gets cleared up - thus unfortunately making 
>impossible any resolution of the basic issue. 
>The TSSI refutation of the Okishio theorem is an 
>argument about logic: whether Marx's reasoning 
>is logically inconsistent as alleged, or not, as 
>TSSI proves.

I agree with Alan that the critique of 
impossibility theorem should be separated from an 
inevitability theorem.  I meant to underline that 
very distinction.  And while Alan's message is 
lucid and deserving of high level engagement, I 
would say that some TSSI people are also 
interested in the classic inevitability theorem. 
I am thinking here of Kliman's mentor 
Dunayevkskaya and Carchedi in his Frontiers of 
Political Economy. Aren't they both 
catastrophists? Perhaps Alan is not but there is 
plenty of written indication otherwise!

  Neither RD or Carchedi of course has a 
mechanical break down theory (nor did Grossman, I 
would argue).
But I don't think TSSI people have only been 
interested in the purely logical critique of an 
impossibility theorem. And that in my opinion is 
to their credit. Though again I think the 
critique of the impossibility theorem is in 
itself a major intellectual accomplishment.

I do understand that value, money and material 
profit rates may diverge in TSSI framework. 
Laibman's focus is not as I put it on money rate 
of profit tracking material profit rate but the 
value rate tracking the material rate which 
results from his slowing down the rate of 
accumulation. Yes this critique does not speak to 
the critique of the impossibility theorem, but it 
is still interesting for the empirical and real 
world questions it raises.

Now I say all this without having read carefully 
the second half of Alan's message, but I did not 
want to delay my reply.

But of course this second half seems to shown 
again that TSSI people are not scholastic, simply 
engaged in a critique of an impossibility theorem 
for its own sake.


>The actual course of the profit rate is 
>determined empirically, not logically. For this 
>reason, the empirical course of events neither 
>refutes nor confirms the logical argument with 
>which TSSI refutes the Okishio theorem. The 
>money rate of profit may track the 'material 
>rate' or it may not. This depends purely and 
>simply on the course of monetary inflation. If 
>the value of money is set at the corn rate, that 
>is, one unit of money always represents one unit 
>of use-value (whatever this might mean in a 
>multi-product economy) then of course the 
>so-called tracking theorem will hold, since one 
>has chosen the condition that ensures it will 
>hold. If on the other hand the value of money 
>is supposed, as Marx explicitly states, to be 
>such that one unit of money always represents 
>one unit of value (that is, the MELT is always 
>1) , then the money profit rate will follow the 
>value rate - for the same reason, that one has 
>chosen the condition that ensures this outcome 
>will hold.
>Whether the value rate in turn must necessarily 
>decline is a further matter I deal with 
>below. The key point in the immediate context of 
>the so-called 'tracking theorem' is that the 
>material rate and the value rate are different 
>from each other under temporal determination, 
>whereas under simultaneous determination they 
>are the same. Therefore, if the MELT remains 
>constant, the money rate cannot in general track 
>the material rate.
>Actually, the empirical and real behaviour of 
>the money profit rate corresponds to neither of 
>these cases - in general, I would conjecture on 
>the basis of the evidence I have seen that it 
>probably, empirically, to correspond to Marx's 
>assumption of a constant MELT until around the 
>1920s, and since then it has in certain periods 
>rather tended to exceed the 'material rate', 
>with certain reversions from time to time.
>But all this is absolutely neither here nor 
>there as regards the logic of the matter. 
>Neither the TSSI nor simultaneism can be 
>logically disproved by what happens empirically. 
>Empirical reality may confirm or deny whether a 
>theory is true but cannot determine whether it 
>is logically possible.
>This brings us to a fundamental confusion that 
>permeates the whole discussion on what TSSI has 
>actually proven, which I agree Rakesh in this 
>post does state fairly clearly, only then to 
>re-introduce the old confusion.
>Let's begin from basics. An impossibility 
>theorem is refuted by finding one example in 
>which it fails. If for example someone makes the 
>statement 'it never rains in July' then one July 
>rainfall refutes the statement. Furthermore 
>Okishio's statement is even stronger than the 
>above because it does not refer to empirical 
>reality at all: it says in effect that it cannot 
>possibly rain in July - in effect, that there is 
>something about the nature of July which 
>precludes rain falling under any empirical 
>circumstances whatsoever. Such a logical 
>assertion, precisely because it is a logical 
>assertion, can be refuted completely 
>independently of empirical observation by simply 
>demonstrating that the conditions that may bring 
>about rain, may also come to pass in July - that 
>there is nothing special about July above and 
>beyond the days being longer and the sun rising 
>higher (in the Northern hemisphere) than in 
>That logical refutation is what the TSSI has achieved.
>One makes nonsense of what has actually been 
>proven - and in particular, one completely 
>obfuscates the point that the TSSI refutes 
>Okishio's theorem, if one claims (which in 
>effect Laibman did) that the contrary statement 
>to 'it never rains in July' is 'it always rains 
>in July'. This is a very elementary question in 
>logic which one is taught in a Mathematics 
>Bachelor Degree in either the first or the 
>second week at college. It is extraordinary that 
>after five years of our hammering away on this 
>point, I have yet to meet a simultaneist that 
>gets it.
>I conclude that the confusion arises because, in 
>their heads, most if not all of the 
>protagonists are attempting to address a 
>different question from the one that we have 
>raised. I think they read TSSI as if it were an 
>'inevitability theorem', as if what we were 
>saying is that it always rains in July. Not only 
>have we never said this, we have battered away 
>in every available forum from Wikipedia to the 
>published journals, to establish that we never 
>said it, and that explicitly from the very 
>beginning and in extremely plain English we 
>openly stated that we did not advance any such 
>We make no claim that the rate of profit 
>necessarily falls, nor can this conclusion 
>logically be deduced from the TSSI, nor does the 
>TSSI stand or fall on whether the profit rate 
>necessarily falls. TSSI is not an inevitability 
>theorem but the refutation of an impossibility 
>theorem. We never said the profit rate must fall 
>but simply showed that it can fall, under 
>circumstances where according to Okishio, it 
>cannot. That is simply the end of the matter. 
>This debate should have been closed long ago.
>If our opponents were simply to admit, candidly, 
>openly and honestly and without reservation, 
>this single point - that is, to recognise the 
>validity of the first part of Rakesh's post and 
>acknowledge that Okishio's theorem has been 
>definitively proven to be false -  then 90% of 
>the initial rational basis for the heat in the 
>discussion would evaporate. The duty to do this 
>is a duty to logic, not just honour. But our 
>opponents have never have done this, and I do 
>not think they ever will, although nothing would 
>please me more than to be proved wrong on this 
>If it is true that Rakesh has been suspended 
>then I am afraid that my gloomiest suspicions 
>are confirmed. It seems that our friends or our 
>critics, however they like to think of 
>themselves, do not yield to logic. The question 
>is why?
>My belief is that the old generation of Marxists 
>are seeking to use (or refuse to use, or abuse, 
>or choose to refuse, or whatever) the TSSI to 
>resolve a debate about politics instead of a 
>debate about logic. There is a very lively and 
>longstanding debate in politics, still going on, 
>about whether the fall in the rate of profit 
>(and the collapse of capitalism) is inevitable. 
>The inevitability of capitalist collapse was, I 
>think, the essential content of the debate 
>between the Luxemburgists (the Russian left, 
>that is) and the Bukharinites in Russian in 
>1924. Richard B Day's excellent book 'The Crisis 
>and the Crash' deals with this extremely 
>clearly. This inevitabilist trend continued in 
>existence, in my view, as a strand of Marxist 
>thinking which wished to claim or prove that, 
>either as a result of problems of reproduction 
>(Grossman etc), or as a result of the decline in 
>the rate of profit (Yaffe, Shaikh, etc), in some 
>way or other, purely economic mechanisms of 
>capitalism will bring about its inevitable 
>In the debate around TSSI, most simultaneists 
>have (wrongly) stuck to the belief, without any 
>critical interrogation, that the 'inevitable 
>decline of the profit rate ' arises as a 
>conclusion from the TSSI. Basically, they group 
>the TSSI with the 'catastrophist' (or as Ben 
>Fine abusively labelled it 'fundamentalist') 
>school of thinking in Marxist thought.
>In fact one can read Laibman's alleged 
>refutation, through his tracking theorem, as the 
>outcome of this quite simple confusion. 
>He treats the TSSI refutation of Okishio's 
>theorem as if it were an 'inevitability' 
>theorem. The TSSI antidote to the Okishian 
>impossibility theorem, his reading goes (as with 
>many others), is a TSSI inevitability theorem. 
>He may have departed from this view since, but 
>if so, I have not seen this in any forum I am 
>acquainted with, least of all one in the public 
>Of course, if TSSI claimed, or concluded, that 
>the profit rate's decline was inevitable, then 
>mutatis mutandis it could be refuted by finding 
>one temporal case in which the profit rate does 
>not decline. This, Laibman (by an argument I 
>find unnecessarily complicated) did demonstrate. 
>As far as I know, he believes to this day that 
>this refutes TSSI. Certainly Rakesh, I do think, 
>in the post that you copied to me perpetuates 
>this primal confusion by writing as if there was 
>any case to answer. But there is no case to 
>answer. Laibman's problem is Laibman's problem. 
>We are very sad he has a problem. But it is not 
>our problem and Rakesh, by fustigating us for 
>failing to solve it, merely perpetuates this 
>fundamental confusion and thereby I fear 
>risks undoing all the good he does in the first 
>part of his contribution.
>Since the TSSI refutation of Okishio makes no 
>prediction about the actual course of the profit 
>rate, it cannot possibly be in turn refuted by 
>the profit rate's empirical course.
>What the profit rate actually does is entirely 
>another matter. The whole point about the TSSI 
>is that it is merely the starting point. It 
>frees the mind and research from the dead hand 
>of Platonic simultaneism, at which point honest 
>research can replace dogmaticised schematics as 
>the mode of investigation. Precisely because 
>within the TSSI the profit rate is 'free' to 
>fall or rise, there are a variety of hypotheses 
>about its actual course, all of them compatible 
>with the method itself. In this, the TSSI is no 
>different from, say, the law of gravity. The law 
>of gravity does not inform us that objects 
>necessarily fall or necessarily rise. It simply 
>states the mathematical conditions governing 
>their motion. This, I think, the TSS 
>interpretation of Marx (that is, Marx himself) 
>definitely does do.
>Hence one may, within TSSI, that is, compatibly 
>with Marx's value theory, frame an entire range 
>of conjectures and hypotheses about the actual 
>movement of not only the profit rate but many 
>other variables (for example national 
>inequality, which I personally study, the 
>business cycle, and so on). The difference from 
>simultaneism is that logic does not dictate in 
>advance which of these theses are true or false. 
>Instead, we have to go and test them. But what 
>we test is not the TSSI as a whole nor indeed 
>Marx's theory of value, to call it by what we 
>have established as its proper name. We test a 
>particular hypothesis framed within [the TSSI 
>of] Marx's theory of value.
>If this were accepted, some progress would be 
>possible. My personal view (which I think Andrew 
>does not share and which also, I must insist, I 
>do not pretend to share with Marx) is that there 
>are periods of history when we do in fact 
>observe protracted long declines in the rate of 
>profit, which are in turn actually brought about 
>by the process of mechanisation, coupled with 
>accumulation (the logic if the matter is that 
>actually, the rate of profit declines only if 
>accumulation is taking place, so that the stock 
>of capital - the denominator in the rate of 
>profit - is rising without limit. Hence mere 
>mechanisation is insufficient to drive the rate 
>of profit down unless the profit that arises is 
>re-invested and not merely consumed idly). Then 
>there are offsetting factors, discussed by Marx, 
>as for example raising the rate of exploitation 
>(this is, I think, the main offsetting mechanism 
>now at work). However there are simple 
>mathematical limits on these. Even if one 
>reduces the wage to nothing at all (Kliman's 
>scandalously notorious 'v=0') the rate of profit 
>will continue to decline if accumulation 
>proceeds at a rate that exceeds the rate of 
>growth of the labour force.
>Given the normal parameters of the capitalist 
>economy as it really exists, this will be the 
>case unless the rate of accumulation (in value 
>terms, which is not the same as physical terms) 
>slows to a point where it calls into question 
>the reproduction of capitalism. Note that this 
>can occur by 'non-physical' means - for example 
>it would take place if, during mechanisation, 
>the capitalists merely replaced existing stock 
>in use-value terms and did not expand it. In 
>that case, the physical (use-value) size of the 
>invested or advanced capital would remain 
>constant, but as a result of the declining value 
>of this use-value, in value terms there would be 
>disaccumulation. This is more or less the 
>function of slumps. A very important issue is 
>whether a single slump suffices to devalue the 
>stock of capital sufficiently to restore the 
>profit rate. My answer to this is 'no' - but, as 
>with Mandel who first broached this question, my 
>answer is informed centrally by empirical 
>reality, and the theory has to run to catch up. 
>Long-term declines happen, but as yet we do not 
>I think know why. What we do definitely know is 
>that these declines are accompanied by (and it 
>seems reasonable to conjecture, caused by) a 
>long-term decline of the profit rate stretching 
>across several cycles.
>My conjecture is that a full restoration of the 
>profit rate sufficient to launch a phase of 
>accelerated accumulation is conditional inter 
>alia on a political outcome. This was what 
>Ernest thought. The failure of accumulation 
>provokes a 'systemic' or structural crises such 
>as what is now happening in the world, in which 
>the weaknesses arising from the slow pace of 
>capitalist accumulation are such that 
>they summon conscious, political forces into 
>action. I give the name 'market breakdown' to 
>this endogenous process of the capitalist 
>market. Market breakdown does not bring about 
>the collapse of capitalism. It simply means that 
>the invisible hand becomes visible. The social 
>and institutional factors which sustain the 
>market are undermined by the process, and 
>conscious political forces are brought into 
>action. On the one side this produces action by 
>the non-property-owning classes to defend 
>themselves against the increasing depradation of 
>their living conditions. On the other it calls 
>forth increasingly frenetic action by the 
>capitalists - increased use of force in 
>international relations, increased 
>intercapitalist competition, imperialist 
>adventures, at home attempts to dramatically 
>undermine the defences against increased 
>exploitation afforded by the state, conscious 
>nurturing of racism and islamophobia, etc). This 
>is all complicated by the shape that it is given 
>by the existence of the nation-state which pits 
>cross-class national coalitions against each 
>other in such a way as to rupture the intrinsic 
>material identity of interest of the 
>non-property-owning classes. The bourgeoisie of 
>course always attempts to secure that these 
>national state struggles replace and subsume the 
>underlying class 
>antagonism. The non-property-owning classes in 
>their turn succeed only if, as Marx himself 
>noted, they heed the warning that no nation 
>which oppresses another can ever itself be free.
>Trotsky in 1924 , as Day records, concluded that 
>the conditions for the restoration of the 
>stability of capitalism, and for the resumption 
>of accumulation on an accelerated scale, are 
>political rather than economic. He noted that 
>the phases of accelerated accumulation in 
>capitalism are marked by global political 
>convulsions in which the territories and markets 
>of the world are completely re-organised - wars, 
>revolutions, capitalist dictatorships, etc. Not 
>surprising then that the last phase of rapid 
>growth followed on from the second world war. 
>Reaganism, Thatcherism, and now the neocon 
>programme are all IMO attempts to bring about 
>such a radical reorganisation of the 
>constellation of forces on a world scale.
>The interesting thing, about which there is now 
>some debate on the British left and to some 
>extent in the US, is that one might have 
>expected the defeat of the USSR to have laid the 
>conditions for a renewed phase of accelerated 
>accumulation. This does not seem to have 
>occurred, or perhaps to be more precise, it has 
>not solved the specific problem of the hegemonic 
>imperialist power, namely the USA. Hence Bush 
>must come back 'for another go', hence there 
>seems now to be a near-consensus for an 
>intervention in Iran, etc.: it is that capital, 
>at least US capital, has no other way out. It is 
>trapped in the simultaneous confluence of the 
>general decline in the rate of profit 
>(insufficiently, and only at the expense of its 
>co-imperialists and funders) offset by the 
>increase in the rate of exploitation, the rising 
>resistance of the non-property-owning classes of 
>the dependent world, and the reaction of its 
>rival. The only instruments it has left are 
>financial and political, and the financial 
>resources of the US have now reached the point 
>where the present crisis is the first modern 
>financial crisis to strike into the heart of the 
>USA itself. Not since the great depression has 
>the US been unable to displace the outcome of 
>global financial turbulence onto the rest of the 
>capitalist world. The first sign of its new 
>hegemonic power was 1947 when it forced the 
>devaluation of the pound. Now with supreme irony 
>sixty years later, it is the dollar itself that 
>is in retreat. What is left? Only force, only 
>the naked expression of military and political 
>Which brings us back to the question of 
>inevitability. My view is that whilst the 
>decline in the profit rate is not inevitable, 
>nevertheless it is economically a very powerful 
>mechanism. Otherwise the defeat of the USSR 
>would have been sufficient to bring about the 
>recovery of the USA, This is the reason that for 
>example I conclude, at least empirically, that 
>it persists over several cycles and is not a 
>simple cyclic mechanism, It is at least strong 
>enought that the whole 20 years of Reaganism, 
>the fall of the USSR, etc, were not strong 
>enough to offset it in any permanent way - or 
>were at the very least insufficient to launch a 
>new phase of accelerated growth.
>I insist that this is a purely empirical matter 
>and has no direct bearing on whether or not TSSI 
>has refuted Okishio. The actual logical point is 
>this: within TSSI we are not forced to choose 
>between inevitability and impossibility. TSSI is 
>a framework in which all movements of the profit 
>rate are theoretically possible: this for the 
>first time since Marx allows us to research 
>without prior prejudice which of these 
>theoretical possibilities actually occurs. 
>Within the simultaneist, Okishio framework there 
>is no such luxury. If works with simultaneous 
>valuation, there is no choice. A declining rate 
>of profit is logically impossible, just as 
>mountains on the moon were logically impossible 
>in the time of Galileo. Therefore, we get the 
>psychpathological reaction of inventing an 
>endless cornucopia of bizarre explanations for 
>something that everyone can see is going on: it 
>must be unproductive labour, the regulatory 
>regime, the low intelligence of the bankers, 
>24-hour shifts, irrational capitalist innovatory 
>behaviour - anything and everything is offered 
>as an explanation for why the market refuses to 
>behave as Okishio predicts. But the actual 
>explanation is that no explanation is needed 
>because Okishio's theorem is wrong: driving down 
>the profit rate as an outcome of accumulation is 
>what the capitalist market does, completely 
>unaided by any external condition or any 
>additional presupposition, and though many 
>things offset this, technical progress does not.
>There are of course other mechanisms of market 
>breakdown other than the pure decline in the 
>profit rate , not least the persistent secular 
>trend towards the inequality of 
>nations. Increased economic competition between 
>the dominant capitalist powers also enters the 
>equation, something Brenner points to. But here 
>again we find that an archetypal confusion about 
>value theory, caused by his unfounded rejection 
>of Marx, leads to a fundamental confusion of 
>cause and effect. The value-theoretic confusion 
>is that, in value terms, intercapitalist 
>competition cannot affect the profit rate. It 
>merely redistributes profit between the 
>competitors. Therefore, it cannot be a causal 
>mechanism in the decline of the profit rate, 
>which Brenner seems to believe that it is. 
>Second and for this reason, it is the decline in 
>the profit rate that produces the competition, 
>not the other way around. The competition is a 
>response to a declining pot, not the cause of 
>the pot's decline.
>This said, it may well be that there are factors 
>independent of the decline in the rate of profit 
>which determined whether intercapitalist 
>compeition takes place more or less intensively. 
>For example the 'Belle Epoque' expansion of 
>1893-1914 was accompanied by an intensification 
>of intercapitalist competition, not a reduction. 
>Hence I now tend to think, one must avoid 
>hypothesising any narrow causal relation between 
>the speed of expansion and the presence or 
>absence of competition. Actually these are two 
>autonomous dimensions. Now we are perhaps in a 
>period of continuing decline accompanied by 
>increased formal competition.
>This thinking is somewhat conjectural. But this 
>is well and good, since within TSSI, the freedom 
>exists to consider all such options. It is only 
>within simultaneist thinking that such 
>conjectures become mutually exclusive. Brenner 
>unnecessarily impales himself on his own 
>rejection of Marx. If he did not exclude the 
>very simple value-theoretic approach from the 
>outset, he would have no need to seek mutual 
>causality between competition and the decline of 
>the profit rate, because he would not need to 
>invoke competition to 'explain' the falling 
>profit rate. The declining profit rate would 
>have a simple and basic explanation independent 
>of the extent of competition, namely, it arises 
>from accumulation tout court
>This merely highlights how ridiculous and 
>obstructive it is, in theoretical terms almost 
>prehistorical, to be discussing in the way so 
>many discussants do on OPE-L. I do not read its 
>posts often, in fact only when someone such as 
>yourself draws attention to them. But when I do, 
>it find it striking how little progress has been 
>made. The participants themselves, except for 
>the temporalists on the list, seem impaled on 
>the logic of their own rejection of Marx. It is 
>a kind of dreadful irony that the Greeks would 
>have appreciated, somewhat akin to the fate of 
>The causal connections that they seek in 
>political life are not available to them within 
>the narrowly circumscribed universe of their 
>theory. So they go around and around and around 
>in the same circles like an army of hamsters 
>pursing each other around a treadmill of 
>futility, and I despair that any of them will 
>ever exit from it. The most peculiar thing is 
>that this is completely self-inflicted. Anyone 
>can get off the treadmill at any time, simply by 
>adopting temporal determination. They don't even 
>have to swallow the TSSI whole. All they have to 
>do is abandon simultaneous determination in all 
>its dogmatic manifestations. Empirically, they 
>never do, and so I am highly pessimistic that 
>they ever will.
>It is however interesting and encouraging that a 
>growing number of people outside the treadmill 
>are approaching this discussion with an open 
>mind. I hope some good will come of that.
>Take care now
>-----Ursprüngliche Mitteilung-----
>Von: Rakesh Bhandari <bhandari@BERKELEY.EDU>
>Verschickt: So., 28. Okt. 2007, 5:46
>Thema: [OPE-L] Okishio Theorem
>Fred you write:
>"I agree that TSSI initially claimed
>to "refute the Okishio theorem on its own terms" (i.e. not that
>Okishio's "terms" were different from Marx's "terms").  But in Kliman's
>book (Chapter 7), the main argument is that the rate of profit in the
>Okishio theorem is determined in a different way from the rate of
>profit in Marx's theory.  There is one paragraph that argues that the
>Okishio theorem "also fails on its own terms", but this claim is
>emphasized much less than before.
>What I think is the contribution of the TSSI is the argument that the
>Okishio theorem is based on a different theory of the rate of profit
>than Marx's theory."
>But TSSI a refutation on Okishio Theorem on its own terms--for all
>practical purposes. Okishio Theorem is according to standard
>interpretation an impossibility theorem--it's impossible for viable
>technical change in itself to depress the profit rate. TSSI did the
>impossible; it showed that viable techical change can depress the profit
>rate. But...TSSI has not demonstrated that empirically David Laibman's
>tracking theorem (the money rate of profit tracks the material rate of
>profit) will not hold in the long term. But TSSI did the impossible, and I
>can understand why they are so damn excited about it. Doing the impossible
>is a large part of what intellectual progress is, no?
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