Urban Scaling and the Benefits of Living in Cities

Abstract

Complexity science offers tools to better understand the processes underlying city development, which is particularly important for building cities that are environmentally, socially, and economically sustainable. Urban scaling laws are empirically observed power-law relationships between population (i.e., city size) and other characteristics of cities in the same country. The theoretical underpinnings of these relationships have been proposed in The Origins of Scaling in Cities model, which derives scaling exponents from fundamental concepts in economic geography and general first principles of physics. The model introduces a parameter called net urban benefit, defined as a city’s social output minus the dissipative costs of infrastructure, representing a new metric relevant to city sustainability. Here we present a new derivation for a functional form of the metric, as well as new derivations that reveal how cities behave when the metric is maximized. We show results for U.S. cities and discuss the implications for the sustainability of the U.S. urban system, including the feedback mechanisms that keep cities on their current trajectories toward maximizing their socioeconomic output while minimizing infrastructure costs.