Re: [OPE-L] standard commodity

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Tue Mar 15 2005 - 18:07:38 EST


Taken literally, the above combined with the excerpt below from a
previous post can be interpreted as making one or both of the following

i)  the mathematical techniques employed alter our view of production;

Yes they certainly do

ii) our view of production is that it can be represented by (linear and)
    matrix algebra.

That is the most common formalism used by Marxist economists certainly.
It provides the common basis for most discussions on the theory of

i) seems to me to be arse-backwards: i.e. our view of production
determines (or should determine) what quantitative techniques are
employed to describe that process rather than vice versa.
I don't think you can isolate things in this way. Once you try to
think about something complex, you have to formalize it mathematically.
You can not have a 'view' of a complex subject matter unless you
have a mathematical model of it. 
ii) seems to assert that the production process can be described
as a linear process.  Yet, shouldn't we view production as
part of a non-linear dynamic process?
It may be that one may want to see it as part of a non-linear process,
but in formulating a theory of something it is helpful to use linear
models so long as they give reasonable results. But of course 
Sraffas model is non-linear. A part of the results of Ochoa et all
has been to show that in practice the non-linearities in the Sraffa
model do not seem to be of much practical significance.

You also make a history of thought claim  that Sraffa and
Leontief  "were responsible for the importation of matrix
representations into Marxist economic discourse."   Have you
forgotten about von Bortkiewicz?

I was under the impression the VB just dealt with simultaneous
equations and small numbers of them at that.
The full matrix formalism arose as a result of the development
of socialism and the problems of socialist planning. 
It came from Gosplan, early copies of whose tables became
available to economists at Cambridge - Keynes mentions
having access to them.

The person I should have mentioned was Von Neumann. It
is likely that his facility with the application of matrix
formalisms in his growth model was a combined result of
reflections on what was going on in the USSR along with
his own background in providing a systematic mathematical
basis for Heisenbergs matrix mechanics in his  work
on the mathematical basis for quantum mechanics.

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