Do good workers hurt bad workers - Or is it the other way around?

I study the effect of worker heterogeneities on wages and unemployment in a directed search model. A worker's productivity in a given firm depends both on his type and on a worker-firm specific component. Firms advertise unconditional wage offers only. The resulting equilibrium is inefficient, with a too high wage premium for high-type workers, and too few high-type jobs. This reduces the welfare of high-type workers. My findings contrast with the findings in the literature on labor market segmentation, where it is argued that the existence of high-type workers forces down wages and reduces welfare for low-type workers.