Re: [OPE-L] statistical mechanical equilibrium

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Sun Apr 22 2007 - 17:35:19 EDT


Agreed. Just saw Murray Milgate's entry on equilibrium in the
Palgrave which he edited. Will have to copy it later.

Equilibrium as supply and demand balance, as absence of internal or
spontaneous source of change, as the outcome position towards which
the system moves (eg equalized returns for capital, labor and land)


The above is a fair summary of the classical mechanical idea
of equilibrium. The Boltzman idea is different, instead of the
system in equilibrium being static, it is undergoing constant
change, but macroscopic probability density functions that describe
the system remain constant. Particles in the gas under go constant
random motion but the PDF of particle energies remains
constant. The distribution takes the form of the Gibbs-Boltzman PDF.

Applied to political economy, it implies

1. That there is no one price for a commodity, but a random spread
   of prices at which individual sales take place
2. That the mean price of the commodity sold in any time interval
   will itself be randomly distributed.
3. That   individual prices in equilibrium are governed by a
   stable PDF , typically the ratio P/L (price/Labour value) will
   have a log-normal distribution with mean of 0
4. The temporal means will also have a log-normal distribution, with
   mean 0, but with narrower standard deviations than shown by 
   individual prices

As Jurrian implied the same concept can be applied to income distribution.
A given set of production relations will induce a characteristic PDf for
incomes, empirical work and Ians simulations indicate that for capitalist
relations of production these take the form of a power law distribution.

For simple commodity production Ians work and that of Yakovenko 
indicate that the characteristic PDF is the Gibbs-Boltzman one.

or a stable centre of gravity around which price moves--these are
themselves quite different meanings of equilibrium and each of them
has multiple meanings too.

Which aspects of equilibrium does Marx accept, if any? We of course
need clarity here.

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