  Using a model based on generalised Lotka Volterra dynamics together with some
recent results for the solution of generalised Langevin equations, we show that
the equilibrium solution for the probability distribution of wealth has two
characteristic regimes. For large values of wealth it takes the form of a
Pareto style power law. For small values of wealth, (w less then wmin) the
distribution function tends sharply to zero with infinite slope. The origin of
this law lies in the random multiplicative process built into the model. Whilst
such results have been known since the time of Gibrat, the present framework
allows for a stable power law in an arbitrary and irregular global dynamics, so
long as the market is `fair', i.e., there is no net advantage to any particular
group or individual. We show for our model that the relative distribution of
wealth follows a time independent distribution of this form even thought the
total wealth may follow a more complicated dynamics and vary with time in an
arbitrary manner. In developing the theory, we draw parallels with conventional
thermodynamics and derive for the system the associated laws of `econodynamics'
together with the associated econodynamic potentials. The power law that arises
in the distribution function may then be identified with new additional
logarithmic terms in the familiar Boltzmann distribution function for the
system. The distribution function of stock market returns for our model, it is
argued, will follow the same qualitative laws and exhibit power law behaviour.
