RE: [OPE] value-form theory redux

From: Paul Cockshott <>
Date: Sun Mar 15 2009 - 18:26:49 EDT

In Kantorovichs 1939 paper he used the term resolving multipliers. Later he called them Objectively Determined Valuations.. I did not really understand these until the editors of Intervention Journal of Economics insisted two weeks ago that I give a rigourous mathematical account of Kantorovich's technique. I chose
to do it by writing a program to use the method of resolving multipliers to solve Kantorovichs problem C.
In this he considers the problem of a socialist construction team working on for example a railway cutting.
They have 3 diggers, each of a different design, and have to remove 20,000 meters of each of 3 different soil typpes for example (peat, gravel, boulder clay) as their plan target.
The problem is to find which machines to use on which soil types for how many hours given the
relative 'norms' of each machine for each soil type. A norm seems to have indicated the normal
hourly product of a machine.

In converting his paper and pencil method to be performed by an intelligent mathematician into Pascal
code I realised just how in his system the resolving multipliers were used. One sees that they really
were very like prices but did not require any exchange nor any 'subjective preferences' they arose directly
from the technical constraints on production.

Of course the constraints in his examples are all short term ones. If one considers the long term, then
Kantorovich agrees that labour content is the objectively determined valuation. However I am pretty certain
that as soon as one imposes additional global constraints such as total C02 emissions, then there will be some
deviation of the resolving multipliers from labour values.

The resolving multipliers of K play a very analogous role to the derivative of the Harmony function that
Allin and I proposed in our planning algorithm.

From: [] On Behalf Of Dave Zachariah []
Sent: Sunday, March 15, 2009 4:50 PM
To: Outline on Political Economy mailing list
Subject: Re: [OPE] value-form theory redux

Paul Cockshott wrote:
> I think Kantorovich demonstrated pretty clearly that such commensurability is possible in the absence of commodities and commodity production and that it arises not from anything subjective but from the objective properties of the technology and labour processes that are available at any given instant.

Were his 'objectively determined valuations' multipliers in the
programming problem?

The introduction to your paper is worthwhile quoting in the context of VFT:

    [I]n the 1930s (say) one might have expected the "typical" young
    Marxist intellectual to have a scientific training or at least to
    have general respect for scientific method by the turn of the
    century one would be hard pressed to find a young Marxist
    intellectual (in the dominant Western countries) whose background
    was not in sociology, accountancy, continental philosophy, or
    perhaps some "soft" (quasi-philosophical) form of economics, and who
    was not profoundly sceptical of (while also ignorant of) current
    science. Unlike that Western Marxist tradition we have to treat
    political economy and the theory of social revolution like any other
    science. We must formulate testable hypotheses, which we then assess
    against empirical data. Where the empirical results differ from what
    we expected, we must modify and retest our theories.

//Dave Z
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Received on Sun Mar 15 18:30:17 2009

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