Wage announcements with a continuum of worker type

We present models of labor-market discrimination in which identical employers choose among job applicants according to a continuous characteristic such as skin color or worker height. The characteristic in question is assumed to be unrelated to worker productivity. Firms are required to announce wage offers that are not conditioned on the characteristic. Workers apply to firms on the basis of those announcements. Firms rank all applicants with respect to the characteristic and select the most desirable one. We show that in equilibrium all firms will offer the same wage, and workers will apply to each firm with equal probability. All employed workers will receive the same wage, but lower ranked workers will have a higher rate of unemployment than higher ranked workers and will thus have a lower expected income. These results differ from those of directed-search models characterized by a finite number of worker types.