This paper studies labor-market mismatch, or the coexistence of unemployment and vacancies, in a competitive market equilibrium in which jobs are assigned to heterogeneous workers, an assignment model. Jobs are assigned under uncertain and sequential trade hence a worker-job match only takes place in markets where trade takes place. This gives rise to a competitive market equilibrium with unemployed workers and vacant jobs as equilibrium assignments to markets where trade is expected but not realized. The first and second welfare theorems hold and the assignment can be decentralized through contingent wages that 'seem rigid.' The model is integrated with a typical real business cycle model and with models of equilibrium search unemployment. In response to neutral productivity shocks, the model produces a Beveridge curve --a negative co-movement between unemployment and vacancies during the business cycle.
