The scaling of income distribution in Australia: Possible relationships between urban allometry, city size, and economic inequality

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 (β = 0.94 to 1.00), whereas highest incomes grow superlinearly (β = 1.00 to 1.21), with total income just superlinear (β = 1.03 to 1.05). These findings show that as long as total or aggregate income scaling is considered, the earlier finding is supported: the bigger the city, the richer the city, although the scaling exponents for Australia are lower than those previously reported for other countries. But, we find an emergent scaling behavior with regard to variation in income distribution that sheds light on socio-economic inequality: the larger the population size and densities of a city, while lower incomes grow proportionately or less than proportionately, higher incomes grow more quickly, 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 an empirical observation on inequality: the larger the population, the greater the income agglomeration in the highest income categories. The implications of these findings are qualitatively discussed for various income categories, with respect to living costs and access to opportunities and services that big cities provide.