We exploit the power of the Alonso-Mills-Muth (AMM) urban economics model and show that various utility functions and plausible conditions offer alternative explanations of households' location by income within a city. These include the existence of a "rich" center and more complex socio-spatial urban forms for instance alternating a rich center, poor suburbs and a rich outer ring, which have not yet been derived from the AMM model to our knowledge. In doing so we combine analytical ideas and illustrations by the means of an agent-based model. The hypothesis of a central or non-central amenity is also studied, leading to different insights on the issue.