Directed search with multi-vacancy firms

I construct a directed search model in which firms decide whether to enter a market and how many positions to create. Within this framework, the number of firms and the size of each firm are determined endogenously, wages play an allocative role in the matching process, and the frictions inherent in this process derive from the equilibrium behavior of workers and firms. I characterize the (unique) equilibrium. Comparative statics generate testable implications for cross-sectional variation in matching efficiency, as well as the dynamic behavior of vacancies and unemployment. Moreover, allowing for ex-ante heterogeneity across firms, the model can easily and naturally generate the observed relationship between firm size, wages, profitability, and hiring.