On Tue, 14 Dec 2010, Paul Cockshott wrote:
> I agree that one possible hypothesis is that the disorder we see
> in real profit rates arises from technical change. Another
> possibility is that it arises from variations in the turnover
> and depreciation rates of capital stocks in different industries
> and firms which would mean you have a large number of coupled
> oscillators with different periods which could have a similar
> dispersive effect.
> Your [Ian Wright's] earlier models evolved to a maximal entropy
> distribution which is what you expect of a conservative system
> with high degree of freedom. If your current one does not then
> it is likely to be non conservative in some way. Maxwells daemon
> must be at work somewhere. Dave Z suggested in conversation with
> me that the non conservative element might be the effect of
> price changes on stocks?
Ian's model contains several classical negative-feedback rules,
for instance:
* An increase/reduction in unsold stocks of a firm's output leads
to a fall/rise in price of that output.
* An increase/fall in the price of a firm's output (relative to
cost, i.e. an increase/fall in the firm's rate of profit) leads to
an increase/fall in the firm's output.
* An increase/fall in aggregate employment relative to the (fixed)
labour force leads to an increase/fall in the wage rate.
In that context (and given constant technology and a uniform
"period of production") it's not surprising that the system tracks
towards an equalized finite rate of profit "in principle".
What is noteworthy is the de facto numerical stability of the
system. The mathematical expression of Ian's system is in
continuous time. As Ian and I have discussed offlist, the system
can be simulated effectively in discrete time, but only if the
time-step is chosen to be suitably small. With dt = 1 everything
flies apart pretty fast (negative prices, employment of more than
the entire labour force, and so on, in just a few iterations), but
with dt = 0.001 I can replicate Ian's results fine; his various
elasticities are well chosen.
Allin Cottrell
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Received on Wed Dec 15 22:08:07 2010
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