Suppose that n buyers each want one unit and m sellers each have one or more units of a good. Sellers post prices, and then buyers choose sellers. In symmetric equilibrium, similar sellers all post one price, and buyers randomize. Hence, more or fewer buyers may arrive than a seller can accommodate. We call this frictions. We solve for prices and the endogenous matching function for finite n and m and consider the limit as n and m grow. The matching function displays decreasing returns but converges to constant returns. We argue that the standard matching function in the literature is misspecified and discuss implications for the Beveridge curve.We have benefited from the input of many people at many conferences and workshops, including

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The paper develops a model of directed search on the job in which transitions of workers between unemployment and employment and across employers are driven by heterogeneity in the quality of firm-worker matches. The equilibrium is such that the agents’ value and policy functions are independent of the endogenous distribution of workers across employment states. Hence, the model can be solved outside of the steady state and used to measure the effect of cyclical productivity shocks on the labor market. Productivity shocks are found to generate large fluctuations in workers’ transitions, unemployment, and vacancies when matches are experience goods, but not when matches are inspection goods.

In this paper I analyse the directed search/matching problem in an economy with heterogeneous skills and skill-biased technology. A unique symmetric equilibrium exists and is socially efficient. Matching is partially mixed in the equilibrium. A high-tech firm receives both skilled and unskilled applicants with positive probability, and favours skilled workers, while a low-tech firm receives only unskilled applicants. The model generates wage inequality among identical unskilled workers, as well as between-skill inequality, despite the fact that all unskilled workers perform the same task and have the same productivity in the two types of firms. Inequality has interesting responses to skill-biased technological progress, a general productivity slowdown, and an exogenous increase in the skill supply elasticity.