From: Philip Dunn (pscumnud@DIRCON.CO.UK)
Date: Thu Jun 12 2003 - 08:39:30 EDT
Quoting Ian Wright <ian_paul_wright@HOTMAIL.COM>: > Hello Philip, > > Thanks for the informative reply (and pointing out an error in my > interpretation of an equation -- see below). > > >I simply do not know what the correspondences are > >for Marxian economics. One problem is that economies do not seem to exhibit > >much in the way of ergodicity. Without that there can be no deterministic > >thermodynamic limit. > > Some empirical distributions of capitalism seem to be qualitatively > constant. Here are some candidates: income distributions (exponential > plus Pareto tails), firm size distributions (a Zipf power law), firm > growth rate distributions (double Laplace), and Farjoun and Machover > argue for a right-skewed profit rate distribution, probably a gamma > distribution. I am sure more could be added to this list. The precise > forms of these distributions may change over time (i.e., the parameters > of the distributions), but the distribution types seem to be constant. > Even if capitalism is not be ergodic in the long-run, different processes > occur at different time scales. Therefore some processes may reach > statistical equilibrium before being displaced by non-ergodic processses > that run at a slower rate. The existence of constant empirical distributions > over time suggests that this happens, and therefore analyses based > on statistical equilibrium are appropriate for some questions. > Hello Ian Constant distributions are not enough for ergodicity. In the case of income distribution, aach individual's income needs to time-average to the distribution mean. Similarly, the size of each firm must time-average to the average firm size. And the rate of profit of each firm must time-average to the average profit rate. In the first two cases, it is clear that there is non-ergodicity. In the case of profit rates, Cockshott and Cottrell have presented empirical evidence that profit rates and organic compositions are (negatively) correlated (www.wfu.edu/~cottrell/eea97.pdf). Since differences in organic compositions persist over long periods, this suggests that profit rate differentials persist similarly. So no ergodicity there either. None of this rules out statistical equilibrium but deterministic theories, such price of production theory, are dubious in that they rely on an ergodicity which is not there.
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