  The agent-based Yard-Sale model of wealth inequality is generalized to
incorporate exponential economic growth and its distribution. The distribution
of economic growth is nonuniform and is determined by the wealth of each agent
and a parameter $\lambda$. Our numerical results indicate that the model has a
critical point at $\lambda=1$ between a phase for $\lambda < 1$ with economic
mobility and exponentially growing wealth of all agents and a non-stationary
phase for $\lambda \geq 1$ with wealth condensation and no mobility. We define
the energy of the system and show that the system can be considered to be in
thermodynamic equilibrium for $\lambda < 1$. Our estimates of various critical
exponents are consistent with a mean-field theory (see following paper). The
exponents do not obey the usual scaling laws unless a combination of parameters
that we refer to as the Ginzburg parameter is held fixed as the transition is
approached. The model illustrates that both poorer and richer agents benefit
from economic growth if its distribution does not favor the richer agents too
strongly. This work and the accompanying theory paper contribute to
understanding whether the methods of equilibrium statistical mechanics can be
applied to economic systems.
