[OPE-L:1308] Re: Labor and Language

Paul Cockshott (wpc@clyder.gn.apc.org)
Mon, 4 Mar 1996 14:01:36 -0800

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In the case of constant capital that lasts more than one period, I
Marx (e.g., Vol. I, p. 318 Vintage) as saying that a fractional share of
the pre-production reproduction cost of the capital is transferred to
value of the product.

I think that I understood this was what you meant for discrete time
periods, but if we cast it as a continuous system with differential
equations, which is what I have done, it is unclear as to what is
meant by pre-production. Production does not really go on in fits
and starts except in particular industries like shipbuilding, it
is ususally continuous.

For example, imagine a machine that lasts 4 periods
and which has the following values: Vo = 40, V1 = 28, V2 = 16, V3 = 12.
Then the value transferred to the products that emerge at times 1, 2,
and 4 is VT1 = 40/4 = 10, VT2 = 28/4 = 7, VT3 = 16/4 = 4, and VT4 = 12/4
3. In sum, a value of 24 has been transferred through "regular"
tion. The remaining value of 40 - 24 = 16 is moral depreciation which,
I interpret Marx, the firm does not recoup in sales (cet. par.), i.e., a
capital loss.

If we take your example above, there is an implicit deltaT between
the time steps, what I am concerned to get is your account of what
happens as deltaT -> 0, i.e., as you move to continuous time. In
the simultaneous model, it is no problem because there exists at
each timestep a vector of values. I am assuming that in the continuous
time limit you would be using some set of lagged values in computing
the moral depreciation. What would be a satisfactory definition of
the lags from your point of view?

I can post the model to Ope if you want, it is written in LaTeX, which
is undoubtedly the best mathematical typesetting system around, and
has the added virtue of being all ascii and thus uncorrupted in going
through the mail, but to print it out you would need a copy of LaTeX.
Alternatively I could generate a Postscript version, which again would
be Ascii, and would print out on most good laser printers.

The model is currently all synchronous, but is fully dynamic. I have
so far only defined the value level, I intend to go on to define the
price/monetary level.

At the value level, it produces the result, which surprised me a bit,
that even taking moral depreciation into account, your example of a
uniform change of labour inputs by 'k' produces no change in the
rate of profit. I had anticipated this for the case of flow profit
rates, but was not expecting it for the stock rates taking into
account moral depreciation.