  In Hopenhayn's (1992) entry-exit model productivity is bounded, implying that
the predicted firm size distribution cannot match the power law tail observable
in the data. In this paper we remove the boundedness assumption and, in this
more general setting, provide an exact characterization of existence of
stationary equilibria, as well as a novel sufficient condition for existence
based on treating production as a Lyapunov function. We also provide new
representations of the rate of entry and aggregate supply. Finally, we prove
that the firm size distribution has a power law tail under a very broad set of
productivity growth specifications.
