Nested economies of scale in global city mass

TL;DR

This study reveals that larger cities and denser neighborhoods are more efficient in their built environments, with economies of scale emerging from within-city disparities, challenging traditional per-capita assumptions.

Contribution

It uncovers universal sublinear scaling laws of city mass with population at multiple levels and introduces a theoretical framework explaining these patterns from within-city disparities.

Findings

Cities scale sublinearly with population at 0.90

Neighborhoods scale sublinearly at 0.75

Scaling patterns inform urban policy and sustainability

Abstract

A longstanding puzzle in urban science is whether there's an intrinsic match between human populations and the mass of their built environments. Previous findings have revealed various urban properties scaling nonlinearly with population, yet existing models of city built mass are still dominated by per-capita linear thinking. Our analysis of >3,000 cities globally reveals universal sublinear scaling of city mass with population at both the city (\{beta}=0.90) and neighborhood levels ({\delta}=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 city-level scaling emerges naturally from within-city disparities. This multi-scale understanding redefines "over-built" and "under-built" conditions as deviations from expected scaling patterns, implying either excessive environmental impacts or inadequate living standards. Effective urban policy thus requires moving beyond simple per-capita assumptions, adopting scale-adjusted metrics and managing cities as nested, complex systems.