This paper develops a microeconomic model of directed search, where firms are heterogeneous in the number of vacancies advertised, and wages affect workers' choices when both applying for jobs and accepting a job. An aggregate matching function is derived, which incorporates workers' preferences for firms. The aggregate level of matches is shown to be independent of the workers' preferences in the job acceptance stage. When firms' labor demands are heterogeneous, the matching market equilibrium outcome is suboptimal. Matching efficiency is, however, attained in equilibrium, when wages are employed as a rationing device. This results in wage dispersion, despite workers being homogeneous
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