# [OPE-L:1468] Re: Math and numbers

Paul Cockshott (wpc@clyder.gn.apc.org)
Tue, 12 Mar 1996 16:40:39 -0800

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Alan
----
You want output stocks, add output stocks. You want fixed capital,
add fixed capital. You want desynchronised production, desynchronise
production. You want etcetera, add etcetera. You want it, you got it.

If these same numbers can be interpreted differently without
contradiction, then do it. Any way you like. But when you've
done it, you won't have anything recognisable as simultaneous.

Paul
----
I have included all these things in the model I posted
on the web a couple of days back. I was responding to the
claims that it was not possible, using a simulaneous
definition of value to handle effects like the depreciation
of capital stocks. It seems to me, to be pretty simple
to do.

You say, appropos the conventional formalisation of
how to compute labour values from an I/O matrix:

&lt;&lt;A is a *flow* matrix. Where is fixed capital in the *flow*
relation v = vA+L?>>

Clearly it is not there. It does not have to be if
what one is wanting to do is compute the labour time
socially necessary to reproduce a commodity, which
is how value is defined in the first chapters of Capital.

Levels of analysis
--------------------
It is important to recognise different levels of
abstraction in analysis. Attempting to pose problems
proper to a lower level of abstraction using the
conceptual tools proper to a higher level of abstraction
is, I believe, uninformative. As I see more postings
on the TSS theory I think that a lot of what appear
to be problems from the standpoint of TSS, are actually
the result of using concepts at the wrong level of
abstraction. As we move from the abstract to the
concrete I think that we should go through roughly
the following levels:

1. Value analysis: relates to the structure of the social
division of labour. It is the most abstract level of
analysis of the social metabolism, as a process of human
co-operative labour. As such, it pertains to several
different forms of economy, including some non-commodity
producing forms.

2. Exchange value analysis: pertains to how the
properties of this social division of
labour are fetishistically projected or mapped onto
the products of labour in a commodity producing society.
As such, it pertains to commodity production in
general, including barter.

3. Formal price analysis: pertains to how exchange value is
represented in monetary economies. As yet, it makes
no assumption about the specific mechanism by which
labour values are mapped onto prices.

4. Formal analysis of capital at the level m-c-m',
this is specific to that subset of monetary economies
in which there is a circuit of capital. It includes,
as Gil has argued those economies in which merchant
or usurers capital exists without capitalist production.

5. Analysis of the production of surplus value under
the specifically capitalist mode of production, where
the c phase of the circuit takes the form of (c+v).

6. Analysis of the general process by which the
specifically capitalist mode of production engenders
technical progress - the production of relative
surplus value. This encompasses the general tendancy
of values to decline under capitalism.

7. Price of production theory: this relates to how
a highly abstract capitalist economy in which profit
rates are equalised, and how this produces a specific
form of price formation. This analysis, necessarily
presupposes for the moment a technically static
system of production, since in the presence of
technical change no equalisation of profit rates
occurs.

The above levels of abstraction are an order preserving
sub-sequence of the topic sequence presented in Capital.

I consider that there are a number of more concrete
levels that we have to deal with, which were not
extensively dealt with in Capital.
Some of these more concrete levels pertain to questions
that also concern TSS proponents.

I would suggest as subsequent levels:

8. Market price analysis: this would look at how the
fact that the profit rate is not actually equalised
affects prices. It would handle the movement from
a deterministic model at level 7, to a stochastic
statistical model. I would suggest that Farjoun and
Machover have started this work.

9. Realisation analysis: this would look at how
actual monetary profits are determined by conditions
outside of production. This was pioneered by Luxemburg
and Kalecki.

There are then a parallel set of levels that have
to be gone through a second time to construct a
thoroughly dynamic analysis:

D1. Dynamic value analysis. This is the counterpoint
to simple value analysis and handles the effect of
continuous change in the technical conditions of
production.

D4. Analysis of stock appreciation and depreciation.
This can be performed at level 4, since this pertains
to the simple circuit of capital m-c-m'. It is for
the purpose of this analysis irrelevant what the
c phase is materialised in, provided the commodity
can appreciate or depreciate.

D6. Analysis of how profits relative surplus value
are affected by the depreciation of constant capital
stocks.

D7..8 Analysis of the extent to which technical change
impedes/hinders the formation of a general rate of
profit, and the consequent effect on the dispertion
of profit rates. This relates to both levels 7 and
8.

Conflation of levels
--------------------
My objection to the TSS theory is that it attempts to
answer D8 level problems with the level 1 category value.
It does it moreover, using mathematical techniques
that a proper to levels 1 or 7. By this I mean
fixed synchronised production cycles with no fixed
capital. These are just not appropriate tools for
handling dynamic problems, which should be cast as
differential equations. So long as one was using them
to answer the static questions of levels 1 and 7,
rather than the dynamic ones of levels D1. and D8, then
they are informative. Applied outside of that context,
I find them uninformative because one can not tell if
the 'contradictions' that the TSS proponents claim to
see ( though I dont yet have a clue as to what these