Where Do the Rich Live in a Big City?

We reveal the spatial distribution of income classes in a big city by examining housing prices and rent microdata, which increase with income. Traditional urban economic theory of a monocentric city predicts that the suburbs tend to house high income households relative to the central cities, which is often observed in U.S. cities. However, we find that the rich and poor collocate and are sorted by income near the central cities while the middle class locates almost everywhere according to the microdata of detached house prices in the Tokyo metropolitan area. By introducing the time cost of commuting to the traditional urban economic theory, we show that this international difference in the spatial distribution is attributed to the pecuniary commuting cost and the income elasticity of demand for housing space. We then show that any condominium resident locates almost everywhere in the Tokyo metropolitan area. This is because the income elasticity of demand for condominium space is close to 1 and the pecuniary cost of commuting is zero in Japan.