# Re: value and labour

From: Andrew Brown (Andrew@LUBS.LEEDS.AC.UK)
Date: Tue May 13 2003 - 08:14:28 EDT

```Hi,

I agree Sraffa is a genius to be taken extremely seriously.

Now, the exchange value of a good is the amount of another for
which it exchanges. In fact there are there are really as many
exchange values of the good as there are other goods. To say 'the'
exchange value implies something else, a third thing. Still, we
might say that exchange value is short hand for exchangeability. If
so then the expression of exchange value of a good by one other
good is simply a short hand for expressing the exchangeability of
the good by the vector of all other exchange values, i.e. the
quantities of all other goods for which the good in question
exchanges. We simply use one good as a numeraire. All of this is
true regardless of any notion of 'the standard commodity'.

Now, you explain to me that the Sraffian system works by
establishing exchange relationships between vectors, i.e. different
bundles of commodities. The standard commodity is a special
such vector, in that its exchange ratios with other vectors are
independent of income distribution (we are assuming profit rate
equalisation). But then surely what is of economic interest is how
much of each individual commodity exchanges with every other
commodity? This is still what exchange value must boil down to, is
it not? In which case the interesting commodity vectors are those
where every entry but one is equal to zero. Let me explain. You
mention the car unit vector as follows:

> 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
> vector >

Here I would like to take the standard commodity vector to be a
(composite) 'commodity' and its scalar to be the exchange value of
the car expressed in this commodity. If this is valid then my
original expression of the issue was valid. If it is not valid then
please explain why not.

>
> > 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 argument is formal because the standard commodity is formal.
You must be presupposing that something is being measured by
exchange value (expressed in terms of the standard commodity),
otherwise why expect anything other than a formal argument? Until
you state what it is that is being measured, then all we have are
formal propositions. That is the whole point: without value (the third
thing, that which is being measured) how can economics, Sraffian
or otherwise, make any sense?

>
> 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.
>

We have incommensurability, and until you tell us what is being
measured by the standard commodity, i.e. what you mean by
'value' above, there is no more to say. Perhaps I did not make this
clear enough in my previous post.

Many thanks,

Andy

>
> > 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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