A quantitative model of two-sided search with ex-ante heterogeneity in both worker and entrepreneurial skills is proposed. It is possible to characterize both the competitive equilibrium and the optimal solution numerically. The competitive equilibrium is shown to be suboptimal. Less-skilled workers and firms are too selective, not matching with their comparable counterparts. High-types, on the other hand, are not selective enough. The model shows promise as a tool for evaluating the effects of labor policies (and other changes in the economy) on the composition of unemployment and on unemployment duration, as well as on wage distributions. The effect of introducing a simple unemployment insurance scheme is then twofold. First, it increases unemployment by allowing a greater proportion of low types not to match, which decreases output. Second, it decreases mismatch, which has a positive effect on output. It is possible to have a positive effect of unemployment insurance on productivity and find the optimal level of unemployment insurance. Finally, it is shown that assuming risk-neutral workers in this model is not innocuous.