How urban scaling and resource distribution shape social welfare and migration dynamics

TL;DR

This paper models how urban scaling laws and resource distribution influence migration patterns and social welfare, revealing conditions that lead to city convergence or divergence in size and inequality.

Contribution

It introduces a mathematical framework linking urban scaling laws with resource allocation, highlighting their effects on migration and social welfare dynamics.

Findings

Superlinear resources promote city size convergence and social welfare equality.

Sublinear resources lead to megacity growth and increased inequality.

Policy implications for resource distribution to manage urban growth.

Abstract

Many outputs of cities scale in universal ways, including infrastructure, crime, and economic activity. Through a mathematical model, this study investigates the interplay between such scaling laws in human organization and governmental allocations of resources, focusing on impacts to migration patterns and social welfare. We find that if superlinear scaling resources of cities -- such as economic and social activity -- are the primary drivers of city dwellers' utility, then cities tend to converge to similar sizes and social welfare through migration. In contrast, if sublinear scaling resources, such as infrastructure, primarily impact utility, then migration tends to lead to megacities and inequity between large and small cities. These findings have implications for policymakers, economists, and political scientists addressing the challenges of equitable and efficient resource allocation.