Re: value and labour

From: Paul Cockshot (wpc@DCS.GLA.AC.UK)
Date: Tue May 13 2003 - 07:11:02 EDT

On Tue, 2003-05-13 at 11:15, Andrew Brown wrote:
> Hi,
> This relates to our previous exchange regarding the nature or
> substance of value. You suggested the standard commodity was a
> contender for this position.
The first point to note is that I am not an advocate of
sraffian economics per se, I generally defend the marxist
approach. However, I think that Sraffas book is quite
a remarkable intellectual achievement and very
subtle and pioneering, and it has to be treated with
great seriousness. One should not assume that the
general approach it puts forward is incapable to
being developed to meet criticisms.

My feeling is that if the sraffian system falls it is
because it assumes profit rate equalisation which emprically
is not the case, it therefore underestimates the directly
controlling influence that values have on prices.

> The problem I have is that in comparing the standard commodity of
> two different systems you are not really comparing like with like. In
> each respective system the exchange value expressed in terms of
> the standard commodity is an index for exchange value as such, or
> exchangability, where the quantity of exchagability of a particular
> good can only be defined by the whole vector of exchange values of
> that particular good, i.e one car = 2 standard commodities = three
> televisions = 10 computers =.....
This is surely a misrepresentation of the standard commodity
approach. This involves establishing exchange relationships
between general vectors, or bundles of commodities. Thus one
can say that given vectors A, B, C etc one can say
A exchanges for nB, mC etc for scalars n,m.

A particular vector - the standard vector has the property that
the exchange ratio of all other commodity vectors with it are
independent on the distribution of income - assuming equalisation
of the rate of profit for the moment.

But the one car in your example is, in vector representation the
unit basis vector on the car axis, and is a special case of the
more general vector equivalence relation. But what you give
when you say one car = 2 standard commodities = three
> televisions = 10 computers =.....
is not the correct Sraffian formulation which should be
something like
[0,0,0,1,0,0 ....]                  : the car unit vector
exchanges with
0.00935[ 2.1, 1.78, 99.2. 1.1, ....]: a scaled version of the standard

> In different systems there are different sets of goods, so in general,
> exchange value is incommensurable between systems. The whole
> gamut of conlusions reached in Sraffian economics are thereby
> conditional upon how the above issue is resolved.

Yes but this begs the question of accuracy. It is a very formal
argument which strikes me as similar to those put forward for the
impossibility of constructing socialist plans - there the argument
was the to invert a matrix of 1million by 1million was impossible.
Well that may be true of you want an analytic solution, but there
are perfectly tractable techniques for obtaining approximate solutions.

The question you have to ask is : to how many digits precision do we
need to know values?

If we only need to know relative values to say 3 significant digits,
then the presence or absence of a single commodity between two national
economies makes very little difference. If you have a million
commodities, then the specific weight of the additional commodity
in the standard commodity will be vanishingly small, and thus
the fractional error involved with setting it to zero when
using the standard commodity to estimate values will also be
very small. Suppose the additional commodity makes up
one thousandth part of the standard commodity, then the
errors in prices arising from using the old standard commodity
(missing this additional component ) will be at most
one part in a thousand.

> As I recall I thought our subsequent exchange made clear you had
> in mind the standard commodity as an index of productive capacity
> or some such. Is this so? If so then it raises questions about the
> meaning of such an index, and how this is captured by the
> standard commodity. Can productive capacity meaningfully be
> reduced to a single dimension? Probably we then end up with
> 'energy', or 'abstract labour' as a meaningful variable in this context.
What I mean by the index of productive capacity is the
von Neumann maximal growth rate given by the i/o matrix.
The von Neumann growth path requires input and output to
be in the same proportions - same thing as the standard

This von neumann growth rate is also the maximal sraffian
profit rate. The scalar here is not labour or energy, but
the maximal self expansion rate of the economy.

> Could you clarify?
> Andy
> Date sent:              Tue, 13 May 2003 10:53:31 +0100
> Send reply to:          OPE-L <OPE-L@SUS.CSUCHICO.EDU>
> From:                   Paul Cockshott <wpc@DCS.GLA.AC.UK>
> Organization:           University of Glasgow
> Subject:                Re: value and labour
> To:                     OPE-L@SUS.CSUCHICO.EDU
> > Andrew Brown wrote:
> >
> > >
> > > Ajit has also argued (not on OPE-L though) that Sraffian theory is
> > > fundamentally limited due to the fact that any two Sraffian systems
> > > are incommensurable. The difference between the two systems need
> > > only be the presence of a commodity in one system but not in the
> > > other, that is enough to disallow any comparison of value betwen the
> > > two. No doubt I have Ajit's argument wrong, but the above argument
> > > regarding commensurability is what I think, at least. Such
> > > incommensurability severely limits Sraffian economics in two
> > > respects: at a more abstract level, the nature of value is
> > > presupposed but not elaborated upon; at a more concrete level, it is
> > > difficult to work out how Sraffian analysis can be developed to
> > > enable concrete explanation.
> >
> > I think this overstates the incomessurability. I am pretty confident
> > that if someone chose to work on it, you could establish approximate
> > metrics relating closely similar i/o matrices. One would proceed by a
> > process of aggregation forming composite commodities until one had a
> > one to one mapping between outputs of the two tables.
> >
> >  --
> > Paul Cockshott
> > Dept Computing Science
> > University of Glasgow
> >
> > 0141 330 3125
> >
> >
> >

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