  We introduce and solve analytically a model for the development of disparate
social classes in a competitive population. Individuals advance their fitness
by competing against those in lower classes, and in parallel, individuals
decline due to inactivity. We find a phase transition from a homogeneous,
single-class society to a hierarchical, multi-class society. In the latter
case, a finite fraction of the population still belongs to the lower class, and
the rest of the population is in the middle class, on top of which lies a tiny
upper class. While the lower class is static and poor, the middle class is
upwardly mobile.
