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We use an urban model to describe the local labour market by a search and matching process with heterogeneous workers and jobs. Our aim is to study the incidence of a large spectrum of public policies. Various measures – such as lowering transport costs, intensifying training programmes and densifying housing – can reduce unemployement, shorten its duration and lessen social inequality. But such policies cannot combat urban segregation. On the other hand, developing social housing could diminish spatial inequality but its effects on employment are negative. A policy mix is thus required to reduce unemployment and spatial inequality.