[OPE-L:4219] Re: Re: Re: Part Two of Volume III of Capital

From: Steve Keen (s.keen@uws.edu.au)
Date: Sun Oct 22 2000 - 09:05:46 EDT


This may read like a "flame", but I am going to try to communicate to you
why you do not have the knowledge (of mathematics) you need to make the
claims you are making.

For instance, you say to Allin that you introduce "one (count it: ONE)
complicating. albeit utterly realistic, assumption to your non complex but
utterly unrealistic simple reproduction tableau", and conclude with the
comment that "Anybody with an 8th grade education in math could understand
what I did to your simple reproduction scheme."

Both statements are true. But equally, only someone with the equivalent of
an 8th grade education (which I here define to be anyone who has not done
university subjects in pure mathematics) could believe that this one
"complicating assumption" has only a minor impact on the complexity of the
issues involved.

Your one complicating assumption--and the entire TSS endeavour--moves the
issue of the transformation problem from the realm of linear algebra to
that of ordinary differential equations (and strictly speaking, to
open-dimensional nonlinear stochastic partial differential equations). That
shift moves the subject from a realm in which, effectively, definitive
proofs are easy, to one in which definitive proofs are not just difficult,

To repeat, it is not just that the solutions of ordinary differential
equations are difficult: even for the vast majority of one-dimensional
systems, they are technically impossible (this is proven to most
mathematics students in week 3 or 4 of a subject on ordinary differential

Those who go on to higher level subjects (some third year subjects) learn
that three or higher dimensional systems of nonlinear differential
equations are also insoluble--a proof which dates back to Poincare in 1899.

So Allin is quite right in what he said to you.

Now I'm not saying that the move is not in some senses justified. I am
willing to concede the TSS point that the analysis of Marx on this front
should be dynamic, and I also know that the "simultaneist" equilibrium long
run solutions will only apply if the eigenvalues of the Jacobian of the
resulting dynamic model have negative dominant real parts (I'm using the
jargon here deliberately--anyone who's been trained in this area knows what
I'm saying, those that don't won't have a clue--and that is my point).

But I also concur with Allin (and, if I'm reading him correctly in recent
posts, also Duncan--though I could be wrong there) that Marx expected his
system would work even with the constraint of a stable equilibrium.

With that belief, I feel no need to do the incredibly hard work actually
needed to establish the truth, one way or the other, of the TSS
propositions. And,of course, since I reject your initial premise that labor
is the only source of value, there's no need for me to undertake a far more
difficult disproof.

There is also a "burden of proof" issue here. You might give academic
conspiracy theories as the main reason for why Marxist economics has been
marginalised (and I'm not about to deny that they have any influence: they
most certainly have!). But there are also many genuine radicals who have
expressed disquiet with how the TSS approach has attempted to eliminate the
transformation problem.

In my not so humble opinion, the burden of proof of its claims lies with
you and its adherents in general. If you really want to prove that the TSS
approach is correct--rather than simply provide numerical couter-examples
to the "simultaneist" approach--then you have to equip yourself with the
technical knowledge needed.

This includes at least introductory first-year courses in linear algebra,
calculus and ordinary differential equations. To really do what you need to
do, you should also consider at least 2nd year courses in the same, as well
as a subject or two in dynamics (preferably treating both difference and
differential equations, as well as an introduction to chaos).

Once you have done all that, then try to build a full TSS model, and see
whether its specifications are internally consistent.

Until you have that level of knowledge, you are fighting well outside your
weight class in trying to engage in these arguments with myself, Allin,
Ajit, Paul, Gil, Duncan and others.


At 17:41 21/10/00 -0400, you wrote:
>On Sat, 21 Oct 2000, Rakesh Narpat Bhandari wrote:
>> Re Steve's 4189
>> >A more technical statement of my frustration with your approach is that
>> >appeal to a system which, if stated in the form of dynamic equations,
>> >have more unknowns than equations.
>I agree with Steve: the problem I have with your mode of
>argument is not that you're dodging empirical refutation, but
>that you're dodging theoretical refutation, by introducing
>complicating assumptions as the argument goes along so that your
>opponent (e.g. me) is unable to pin you down to any particular
>proposition and is eventually forced to give up.
>You are kidding, right?
>I introduced one (count it: ONE) complicating. albeit utterly realistic,
>assumption to your non complex but utterly unrealistic simple reproduction
>tableau--that productivity would be 5% greater in this period than in the
>last. I followed out the logic of this one UTTERLY REALISTIC modification
>to your scheme. Then I showed that this implied completely realistic
>interperiodic changes in prices of production, s/v, total value/price even
>if we kept r constant. I then suggested that the ability to demonstrate
>such realistic change should, if anything, count in favor of Marx's
>transformation procedure which necessarily implies all variables must be
>time subscripted. (If we don't keep r constant, then the other variables
>change less.) How this is not a realistic time path for the system you have
>not explained. Why the completely unrealistic, anachronistic system of
>simple reproduction should be preferred over this you have not explained. 
>How someone as smart as you has not been able to keep track of the original
>situation, i.e. simple reproduction, is truly beyond me as I only suggested
>one simple, reasonable change and then examined its consequences.  My ideas
>are difficult only insofar as you don't want to follow them. Anybody with
>an 8th grade education in math could understand what I did to your simple
>reproduction scheme. 
>Allin wrote:
>As regards the transformation, I have this diagnosis.  One
>coherent view of the issue is that stemming from Bortkiewicz.  
>I reply:
>This is not coherent. The average rate of profit should have no place in
>simple reproduction.  See my response to Paul C. 
>Allin wrote:
>There is a clear argument showing that Marx's two equalities
>cannot both be sustained.  This argument is usually developed in
>relation to a simple tableau showing simple reproduction.  Now
>it would be weird and wonderful if one could show that while
>Marx's two equalities don't hold in *that* case, they
>nonetheless *do* hold in the case of extended reproduction with
>ongoing technical change. 
>I reply:
>They do, you are doubtless an unmeasurably better economic model builder 
>than I; so go ahead and construct such a case if you don't like how I
>modified your original situation. Don't be scared; see where it leads you. 
>Allin wrote:
> I don't believe you've shown anything
>of the sort. 
>I reply:
>So are you not denying that someone smarter than me could do such a thing? 
>Allin wrote:
> You've just complexified the example to the point
>where we lose track of the original situation we're trying to
>transform, then "anything goes".
>I reply:
>Allowing for interperiodic increases in labor productivity is
>overcomplexification? You cannot seriously believe this. 
>Allin wrote:
>  You've said several times that some
>further adjustment is called for due to the fact that Marx's
>inputs are assumed to be priced at value, but you refuse to
>follow out the logic of that admission.  Well then, consider the
>I reply:
>Have you yet even tried to meet my challenge that Marx never called for the
>inputs to be transformed into the same prices of production as the outputs?
>Once you remove that constraint to a solution--exactly because labor
>productivity is increasing interperiodically so unit values cannot be
>constant--then the transformation problem disappears, while all the
>variables must necessarily be time subscripted. It's truly that simple. I
>am confident that you understand exactly what I am saying.
>All the best, Rakesh
Dr. Steve Keen
Senior Lecturer
Economics & Finance
University of Western Sydney Macarthur
Building 11 Room 30,
Goldsmith Avenue, Campbelltown
PO Box 555 Campbelltown NSW 2560
s.keen@uws.edu.au 61 2 4620-3016 Fax 61 2 4626-6683
Home 02 9558-8018 Mobile 0409 716 088
Home Page: http://bus.macarthur.uws.edu.au/steve-keen/

This archive was generated by hypermail 2b29 : Tue Oct 31 2000 - 00:00:11 EST