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This paper explores the efficiency of the equilibrium allocation in a matching model with heterogeneous workers and jobs. In the basic setup there are two types of workers with different skill levels. Both types can perform the simple tasks of unskilled jobs, while the complex tasks of skilled jobs require a high-ability worker. We demonstrate that the equilibrium outcome with random search and ex-post bargaining is never efficient. Under the Hosios condition, the average wage is correct, but bargaining compresses the wage distribution relative to workers' shadow values. This feature distorts the relative profits of jobs, making it too attractive for firms to create skilled jobs. Furthermore, due to the low-skill premium, the high-ability workers may accept too many jobs. Finally, in an extension, we show that the introduction of separate markets for the two types of jobs is not sufficient to guarantee efficiency.