This paper revisits the normative properties of search-matching economies when homogeneous workers have concave utility functions and wages are bargained over. The optimal allocation of resources is characterized first when information is perfect and second when search effort is not observable. In the former case, employees should be unable to extract a rent. The optimal marginal tax rate is then 100%. As search effort becomes unobservable, an appropriate positive rent is needed and the optimal marginal tax rate is lower. Moreover, the pretax wage is lower in order to boost labor demand. Finally, in both cases, nonlinear income taxation is a key complement to unemployment insurance