Do the rich and poor colocate in large cities?

This paper focuses on colocation rather than segregation in the context of Japanese large cities. Using the time cost of commuting from traditional urban economic theory, we analyze how different income households are sorted according to the distance from the city center. By examining microdata on housing prices and rents in Tokyo metropolitan area, we find that the rich and poor tend to colocate and are sorted by income near the city center for detached-housing prices. This is predicted if the income differential is large enough. We also find that different income groups coexist in the same location for condominium prices. This is predicted if the income elasticity of demand for space is close to one and the pecuniary cost of commuting is zero.