The Area and Population of Cities: New Insights from a Different Perspective on Cities

TL;DR

This paper constructs cities from high-resolution data to analyze their population and area distributions, revealing Zipf's law applies to cities of various sizes and proposing a model consistent with these findings.

Contribution

It introduces a bottom-up clustering method to define cities and demonstrates Zipf's law applies across a wide range of city sizes, providing new insights into urban scaling.

Findings

Zipf's law holds for cities with as few as 12,000 inhabitants in the USA.

City area distributions also follow Zipf's law.

A parsimonious model with endogenous city area explains the observed distributions.

Abstract

The distribution of the population of cities has attracted a great deal of attention, in part because it sharply constrains models of local growth. However, to this day, there is no consensus on the distribution below the very upper tail, because available data need to rely on the "legal" rather than "economic" definition of cities for medium and small cities. To remedy this difficulty, in this work we construct cities "from the bottom up" by clustering populated areas obtained from high-resolution data. This method allows us to investigate the population and area of cities for urban agglomerations of all sizes using clustering methods from percolation theory. We find that Zipf's law (a power law with exponent close to 1) for population holds for cities as small as 12,000 inhabitants in the USA and 5,000 inhabitants in Great Britain. In addition the distribution of city areas is also close to a Zipf's law. We provide a parsimonious model with endogenous city area that is consistent with those findings.