On the possibility and optimality of positive rent gradients

The assertion that externalities from low density can create positive residential rent gradients is examined in several cases: optimal externality internalization (zoning), excessive and insufficient restriction, and no internalization. In all cases positive rent gradients are unlikely (i.e., require land to be an inferior good), unstable, or impossible. In addition, easily interpretable welfare conditions are found as a result of consumer and social welfare maximization. The Alonso-Muth-Mills model is found to be quite robust.