How urban scaling laws shape welfare and migration patterns

Many outputs of cities scale in universal ways, including infrastructure, crime, disease burden, and economic activity. Through a mathematical model, this study investigates the interplay between scaling laws pertaining to public costs and needs and governmental allocations of resources, focusing on impacts to migration patterns and social welfare. We find that if the primary driver of city dwellers' utility are needs that scale superlinearly, then cities tend to converge to similar sizes and social welfare through migration. In contrast, if utility is primarily determined by sublinearly scaling needs, then migration tends to lead to megacities and inequity between large and small cities. Varying preferences, however, driven by differing city sizes can stabilize coexistence of variable city sizes. These findings have implications for policymakers, economists, and political scientists addressing the challenges of equitable and efficient resource allocation.