  We study the model of interacting agents proposed by Chatterjee et al that
allows agents to both save and exchange wealth. Closed equations for the wealth
distribution are developed using a mean field approximation. We show that when
all agents have the same fixed savings propensity, subject to certain well
defined approximations defined in the text, these equations yield the
conjecture proposed by Chatterjee for the form of the stationary agent wealth
distribution. If the savings propensity for the equations is chosen according
to some random distribution we show further that the wealth distribution for
large values of wealth displays a Pareto like power law tail, ie P(w)\sim
w^{1+a}. However the value of $a$ for the model is exactly 1. Exact numerical
simulations for the model illustrate how, as the savings distribution function
narrows to zero, the wealth distribution changes from a Pareto form to to an
exponential function. Intermediate regions of wealth may be approximately
described by a power law with $a>1$. However the value never reaches values of
\~ 1.6-1.7 that characterise empirical wealth data. This conclusion is not
changed if three body agent exchange processes are allowed. We conclude that
other mechanisms are required if the model is to agree with empirical wealth
data.
