RE: [OPE] market socialism

From: Paul Cockshott (
Date: Mon Jun 30 2008 - 16:29:20 EDT

Paul, could you explain this "negative exponential income distribution under market socialism"?


A. Agafonow

Paul replies

It follows from the results of Yakovenko that in any market economy with conservation
of money, the distribution of money holdings between agents will follow a negative
exponential distribution, technically known as the Gibbs-Boltzmann distribution.

This follows from very general statistical mechanics considerations where you
have random 'exchange' processes with a conserved quantity. The arguments for this
were first developed in physics where the conserved quantity is energy, and the
exchange process, collisions between molecules.

In the economic case the conserved quantity is money, and the exchange processes
are commodity trades.

Ian Wright maintains a web page on the Wolfram server
which explains the process and gives references to the literature.

In a negative exponential distribution the number of agents holding an amount of wealth w
is given by k * exp( -aw)
for two parametric constants k and a
thus there are many agents with very little wealth, and a few agents with a larger amount of wealth.

In a market socialist economy, the agents would either be worker owned firms ( Yugoslav model ) or
state owned firms ( Hungarian model ). What one would expect to see is an uneven distribution
of assets between these firms, which, at least in the Yugoslav case will spill over into an
uneven distribution of income between workers owning these enterprises.

When Ian says that the distribution of income would not be extreemely uneven, he is 
comparing it to the power law or 'fat tailed' distribution of income that actually exists
in capitalist economies. Ian has shown that such a fat tailed distribution arises necessarily
once you have the buying and selling of labour power.

In a fat tailed distribution, the probability of finding agents with extreeme wealth ( Bill Gates
for example ) is higher than it would be in a negative exponential distribution.

So technically, in terms of the functional forms of the distributions, Ian is right that 
a market socialist economy would not, at least initially, have as uneven a distribution as a capitalist
economy. However, my judgement of the politics of the situation is that, because the negative
exponential distribution is itself a highly uneven distribution, it will rapidly give rise to
political pressures to allow extensions of the market mechanism, which, if put into practice,
will soon result in a fat tailed wealth distribution.

In particular there will be pressure to allow either:

1. The enterprises which have large surpluses to lend at interest to other firms,

2. An indirect market for labour power in the form of subcontracting. High wealth co-ops
   would hire low wealth ones to do work for them at unfavourable rates.

Either of these would result in a dynamic polarisation process leading to the
formation of a class of rentier co-ops and an exploited class of producer co-ops.

Paul Cockshott
Dept of Computing Science
University of Glasgow
+44 141 330 1629

-----Original Message-----
From: on behalf of Alejandro Agafonow
Sent: Mon 6/30/2008 7:35 PM
To: Outline on Political Economy mailing list
Subject: Re: [OPE] market socialism

----- Mensaje original ----
De: Paul Cockshott <>
Para: Outline on Political Economy mailing list <>
Enviado: lunes, 30 de junio, 2008 17:11:26
Asunto: RE: [OPE] market socialism

DOGAN: «"when everyone's entitled to get as much for himself as he can, all available property, however much there is of it, is bound to fall into the hands of a small minority, which means that everyone else is poor." How are you going to face this challange.»

I think that IAN WRIGHT summarized pretty well the answer:

«If a society had different rules that controlled the distribution of income -- in other words different macro-level constraints -- you would get much more egalitarian distributions of wealth even with markets.»


Depends what you mean by more egalitarian. Ian is right at a technical level, one would expect a negative
exponential income distribution under market socialism rather than a power law distribution. But
a negative exponential distribution can still be very uneven, and this uneveness is the soil
from which pressures for full scale capitalism inevitably grow.


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