Nested economies of scale in global city mass

Abstract A long-standing puzzle in urban science is whether there is an intrinsic match between human populations and the mass of their built environments. Existing models assume proportionality: each additional resident demands the same amount of building material. Our analysis of more than 3,000 cities worldwide challenges this linear assumption. Built mass grows more slowly than population (that is, sublinear scaling), across cities ( β = 0.90) and across neighborhoods within a city ( δ = 0.75). This means that larger cities and denser neighborhoods achieve economies of scale with less per capita built mass. Our theoretical framework further shows that the across-city scaling pattern emerges from the uneven within-city distribution of people. These findings caution against well-meaning interventions, such as height and building-size limits, that artificially flatten cities’ natural density gradients. Effective urban policy should instead move beyond per capita linear thinking, adopting scale-adjusted metrics and managing cities as nested complex systems.