This paper adapts a framework à-la Hotelling to an urban context in order to study the impact of public housing on the level of segregation in a fixed-size city where consumers differ both in income and taste. In this city, the market allocation of the population is characterized by partial segregation: both rich and poor consumers can be found in both neighborhoods. Public authorities replace a fraction of the housing stock with public housing. This policy will not decrease segregation if applicants are not screened according to their income level. Any departure from the optimal level of screening has to be compensated for by a larger program. The final policy mix will then be determined by the extent to which public authorities have the ability, either to screen applicants, or to fund more public units. However, this trade-off will be softened when taking neighborhood externalities into account, thanks to a snowball effect of public housing on neighborhood quality.