Figure 1.

Illustration comparing two methodologies—scaling obtained from grouping by income bracket (a,c) and that by decile (b,d). Using simulated log-normal income distributions in two scenarios—log-mean increases with city size while log-variance remains the same (a,b), and log-mean and log-variance both increases with city size (c,d). The income distributions are illustrated on a log-scale. The income-bracket grouping (a,c) leads to differences in the groups’ income scaling for both scenarios, and fails to distinguish whether larger cities have more dispersion in their income distributions. The decile grouping (b,d) leads to the differences in the groups’ scaling observed only when the dispersion increases with the population. The insets show how scaling exponent (β) varies with income groups (bracket or decile).