  Rising inequalities around the globe bring into question our economic systems
and the origin of such inequalities. Here we propose a toy agent-based model
where each entity is simultaneously producing and consuming indivisible goods.
We find that the system exhibits a non-trivial phase transition beyond which a
market clearing equilibrium exists but becomes dynamically unreachable. When
production capacity exceeds a threshold and adapts too slowly, some agents
cannot sell all their goods. This leads to global price deflation and induces
strong wealth inequalities, with the spontaneous separation of the population
into a rich class and a poor class. We explore ways to alleviate poverty in
this model and whether they have real life significance.
