How does imperfect competition in the labor market affect unemployment policies?

We consider a continuum of workers ranked according to their abilities to acquire education and two firms with different technologies that imperfectly compete in wages to attract these workers. The education cost to be borne by workers is higher in the high-technology firm. In equilibrium, we show that the unemployed workers are those with the lowest initial abilities. We then study different policies that subsidize either education cost or wages. We found that the first-best allocation can only be implemented by selective policies. We analyze second-best nonselective policies and show that, in terms of welfare, subsidizing education costs or wages is strictly equivalent.