Re: [OPE-L] a paper on Marx's transformation problem and Ricardo's problem of an invariable measure of value

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Wed Jul 18 2007 - 18:21:56 EDT

I am making two points

1. That no growth is implied in dated labour values, what is implied is a diminishing fraction of the total labour of past time intervals being necessary for the current output.

2. This diminishing fraction terminates within a finite time horizon because all units of means of production are integers not real numbers. 0.3 of a hydraulic press is not a means of production. Note that Kantorovich certainly realised this and was careful to present all his quantities as integers. So yes, this integral analysis of linear production processes has been in the literature since 1938.

The example you give from electrostatics is classical electro mechanics which is cast in Newtonian form with continuously differentiable fields. This has been rejected by physicists as only an approximation since Einsteins 1905 paper on the photo electric effect. All physical quantities are quantised - thus integer rather than real.

Paul Cockshott

-----Original Message-----
From: OPE-L on behalf of Ian Wright
Sent: Wed 7/18/2007 10:02 PM
Subject: Re: [OPE-L] a paper on Marx's transformation problem and Ricardo's problem of an invariable measure of value
> I am describing an alternative, and what seems quite straight forward
> interpretation of the series representation. This is the way I have
> always understood the standard dated labour interpretation.

There is not just one dated labour interpretation (I have already
mentioned two).

Are there any references in the literature to your finite
interpretation? It seems hard to imagine given that the series
representation is infinite.

> If you formulate the series representation as an infinite series it is
> obviously wrong as an economic argument, since no actual process can
> involve infinities - this was established long ago by Aristotle

Of course no economic process starts from nothing and takes an
infinite number of steps. That's obvious, which is why I state that
the process of replacement is "hypothetical" (a  point you previously
objected to).

But note that standard labour-values by definition are equal to an
infinite series. There is no choice in the matter.

Do these infinites imply absurdity? Not at all. For example, the
electrostatic potential energy of a charged particle is defined as the
work that must be done to move it from an infinite distance away to
its present location. This is a way of understanding potential energy.
It does not imply that the particle was actually moved through an
infinite distance.

Labour-values and potential energy are very similar in this respect:
both are instantaneous properties of "objects" in a "field" that have
mathematical representations in terms of infinite series.

Or should we reject the physicists interpretation of potential energy too?

> processes see the paper
> joint paper with Greg
> Michaelson and Lewis Mackenzie,
> and
> ( Cantor
> diagonalisation and planning), by Greg Michaelson, Allin Cottrell and me
> attacking the use of infintistic arguments by the Austrian school of
> economists.
> Any real economic process must have variables that are integers and
> coefficients that are rationals, and the resulting time series have a
> finite horizon.

You use the standard formula for labour-values in your own empirical
work. So you are already using quantities that are the sum of an
infinite series of terms, whether you like it or not.

These rather straightforward labour-cost accounting issues can be
resolved without introducing the red-herring of constructive vs.
non-constructive mathematics.

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