Urban scaling and the geographic concentration of inequalities by city size

Urban scaling laws summarise how socio-economic behaviours of urban systems may be predicted from city size. While most scaling analysis rests on using aggregate quantities (total incomes, GDP, etc.), examining distributions of these aggregate quantities (e.g. income distributions) could shed light on how socio-economic inequalities may correlate or be causally linked to city size. In this direction, this paper examines how geographic distributions and spatial inequalities of income and housing costs vary by city size. The paper presents three principal results. First, it brings out qualitative implications of quantitative scaling by relating scaling of the distributions of income and housing costs to their specific geographic concentrations. Second, it shows that some small and medium sized cities are clear outliers, showing behaviour similar to the largest cities and starkly different from the behaviours of the bulk of small and medium sized cities. Third, this above observation explains why heteroscedasticity, or large and heterogeneous fluctuations, are frequently observed in urban indicator data when plotted as a function of city size. Putting together these three results, overall, it is shown that income distributions and housing costs scale and concentrate in cities by size in a predictable way, where the largest cities superlinearly/disproportionately agglomerate the highest income earners and the highest housing costs, and show relatively lower concentrations of low-middle income earners and low-medium housing costs. In contrast, most of the smaller and medium sized cities show a ‘flipped’ opposite trend. A few small and medium sized cities are outliers: they show trends that match those of the largest cities, due to specialisations of economic functions or concentrations of high-paying occupations in these cities. The empirical findings lead to a discussion on the objective and normative relationships between city size and urban inequalities. It is suggested that due to the concentrations of high income and high housing costs, largest cities may have a resulting housing market structure that will push out lower and medium income earners, thereby making affordability, diversity, and socio-spatial justice emerge as important urban policy issues.