This paper analyses the efficiency of the equilibrium allocation in a matching model with two types of workers and jobs. The basic assumption is that high-skill workers can perform both skilled and unskilled jobs, while low-skill workers can only perform unskilled jobs. Our first result shows that the equilibrium with ex-post bargaining is never efficient. Second, under Hosios? (1990) condition we show that high-skill workers are under-valued in equilibrium, while the opposite holds for low-skill workers. Firms therefore tend to create too few unskilled jobs, resulting in a suboptimally high unemployment rate for low-skill workers. We show that these results generalize to environments with more types of agents and different production technologies. Finally, in an extension we derive a tax scheme that restores efficiency and we show how workers? bargaining strength affects unemployment and skill-mismatch.