Sarkar, S., Phibbs, P., Simpson, R. and Wasnik, S., 2016, The scaling of income distribution in Australia: Possible relationships between urban allometry, city size, and economic inequality, *Environment and Planning B: Urban Analytics and City Science*, Online First: http://journals.sagepub.com/doi/abs/10.1177/0265813516676488.

Cities, like many other complex systems, appear to follow scaling laws. By "scaling", we mean that socio-economic attributes of a city (like GDP, income, wealth, crime, congestion etc.) and physical attributes (like lengths of roads, other infrastructure, etc.) show predictable variations with city size (or population). We have written about the scientific findings earlier here, here and here, and some of the results were were covered by national and regional newspapers, links here.

In this visualisation, the attempt is to demonstrate the idea through an extremely simple infographic, wihtout explicitly invoking the mathematics of scaling theory. Let's compare, very roughly, the number of people in the middle and highest income categories, and a rough estimate of the income earned by them, again broken down and visualised by category. The data used comes from the 2011 Census of Australia, provided by the Australian Bureau of Statistics (ABS). We use the TableBuilder facility provided by the ABS to extract the income distribution by Significant Urban Areas (SUAs) of Australia, which provides the number of people in each income category. The ABS also provides an Income Fact Sheet which provides us with imputed median incomes per week for each of the income categories.

The differences between the middle and highest categories come out to be quite stark: the larger the city, the larger the proportion of the highest income earners in that city, and disproportionately larger the income earned in that category. Thus, reinforcing the result: the larger the city, the higher the likelihood of more unequal distribution of income and wealth.

The X-axis shows the 20 largest SUAs of Australia, ordered by highest to lowest populations. The middle income category corresponds to all people earning between $400-$599 per week, or $20,800 to $31,199 per annum. The y-axis shows the number of these people in each of the 20 largest population SUAs (in red). The top income category corresponds to all people earning more than $2000 per week, or more than $104,000 per annum. The y-axis shows the number of these people for the 20 largest SUAs (in grey). The values are stacked, which means the red and grey portions represent complete counts of members in each category. Note the quick growth of the number of people in the grey region as city size increases.

The X-axis shows the 20 largest SUAs of Australia, ordered by highest to lowest populations. The middle income category corresponds to all people earning between $400-$599 per week, or $20,800 to $31,199 per annum. The y-axis shows the imputed total income of these people in each of the 20 largest population SUAs, by multiplying the number of people in this category with the imputed median weekly income per capita provided by the ABS Income Fact Sheet, which is $487 (in red). The top income category corresponds to all people earning more than $2000 per week, or more than $104,000 per annum. The y-axis shows the imputed total income of these people for the 20 largest SUAs, by multiplying the number of people in the category with the imputed income provided by the ABS Income Fact Sheet, which is $2579 (in grey). The values are stacked, which means the red and grey portions represent complete estimates of incomes in each category. Note the dispropotionately high income in the grey region as city size increases.