The scaling of income inequality in cities

Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with city size. We study scaling of per capita incomes for separate census defined income categories against population size for the whole of Australia. Across several urban area definitions, we find that lowest incomes grow just linearly or sublinearly ($\beta = 0.94$ to $1.00$), whereas highest incomes grow superlinearly ($\beta = 1.00$ to $1.21$), with total income just superlinear ($\beta = 1.03$ to $1.05$). These findings support the earlier finding: the bigger the city, the richer the city. But, we also see an emergent metric of inequality: the larger the population size and densities of a city, higher incomes grow more quickly than lower, suggesting a disproportionate agglomeration of incomes in the highest income categories in big cities. Because there are many more people on lower incomes that scale sublinearly as compared to the highest that scale superlinearly, these findings suggest a scaling of inequality: the larger the population, the greater the inequality. Urban and economic planning will need to examine ways in which larger cities can be made more equitable.