A circular metropolitan area consists of an inner city and a suburb. Households sort over the two jurisdictions based on public service levels and their costs of commuting to the metropolitan center. Using numerical simulations, we show (1) there typically exist two equilibria: one in which the poor form the majority in the inner city and the other in which the rich form the majority in the inner city; (2) there is an efficiency vs. equity trade-off as to which equilibrium is preferred; and (3) if the inner city contains only poor households, equity favors expanding the inner city to include rich households.