  We study a stochastic $N$-particle system representing economic agents in a
population randomly exchanging their money, which is associated to a class of
one-dimensional kinetic equations modelling the evolution of the distribution
of wealth in a simple market economy, introduced by Matthes and Toscani
\cite{matthes-toscani2008}. We show that, unless the economic exchanges satisfy
some exact conservation condition, the $p$-moments of the particles diverge
with time for all $p>1$, and converge to 0 for $0<p<1$. This establishes a
qualitative difference with the kinetic equation, whose solution is known to
have bounded $p$-moments, for all $p$ smaller than the Pareto index of the
equilibrium distribution. On the other hand, the case of strictly conservative
economies is fully treated: using probabilistic coupling techniques, we obtain
stability results for the particle system, such as propagation of moments,
exponential equilibration, and uniform (in time) propagation of chaos with
explicit rate of order $N^{-1/3}$.
