The major cities of the world have attracted a flurry of out-of-town (OOT) home buyers. Such capital inflows affect housing affordability, the spatial distribution of residents, construction, labor income, wealth, and ultimately welfare. We develop a spatial equilibrium model of a city with substantial heterogeneity among residents. We calibrate the model to the New York and Vancouver metro areas. The observed increase in OOT purchases is associated with 1.1% (5.0%) higher house prices and a 0.1% (0.34%) welfare loss in New York (Vancouver). Taxing OOT buyers can turn welfare losses into gains when tax revenues finance a local public good.