Social optimum, heterogeneous workers and firms in the labour market with on-the-job-search

This paper develops a search model with heterogeneous workers, firms, and on-the-job search. Employed low-skilled workers are allowed to seek better paid jobs at high productivity firms. Low productivity firms make take-it-or-leave-it wage offers, whereas high productivity firms use Nash bargaining over wages. There are two important sources of inefficiency in the model besides the well-known classical search externality. First, low-skilled workers do not have any bargaining power when they are employed at low productivity firms. Second, the two types of workers are pooled in the same submarket. We demonstrate that lump-sum transfers paid to workers can internalize these inefficiencies. Moreover, both types of firms may benefit from the increase in the supply of low-skilled workers when the productivity difference in the two jobs for these workers is large, as a result the overall wage gap among workers increase. On the contrary, when the productivity difference is small, the effects are reversed. Finally, both types of firms emerge in the equilibrium when firms are allowed to open vacancies in both submarkets. On the one hand, it is attractive for firms to open vacancies in the low productivity submarket since they pay low wages to workers. On the other hand, it is also profitable for firms to open vacancies in the high productivity submarket because the probability of jobs being filled with low-skilled workers increase significantly, even though the bargained wages of high-skilled workers increase.