Heterogeneous Firms in a Finite Directed Search Economy

We consider a directed search model for a finite economy with heterogeneous firms in two informational environments. In the first, the productivity of all firms is publicly observed. We prove existence of equilibria in pure posting strategies by firms and show that wage dispersion is driven by fundamentals. That is, more productive firms post higher wages and wage dispersion is absent when firms are homogeneous. When firms have heterogeneous productivities the equilibrium is not constrained efficient. In the second environment the productivity level of each firm is private information. The main results extend to this environment: Equilibria in pure strategies exist; strategies are increasing in productivity; and constrained efficiency does not obtain. When the productivity level of all firms is drawn from the same distribution, symmetric equilibria exist and the ranking of wages equals that of productivity.