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. To decentralize these optima, employees should be unable to extract a rent when information is perfect. An appropriate positive rent is however needed in the second case. To implement these optima, non-linear income taxation is a key complement to unemployment insurance. According to the level of the workers’ bargaining power, taxation has to be progressive