Income Inequalities Increase with City Size: Evidence from French Data

We analyse the income distributions of cities in France and the scaling of the income of different deciles as a function of the population. We find a significant difference in the scaling exponents for the richer and poorer parts of the population, implying an unequivocal rise in inequalities in larger cities, made worse by living costs that are disproportionately higher for the poor. We find that the distribution of revenues of cities in France has a universal, Gumbel-like form, with mean and variance growing with the logarithm of population. We show how this result directly implies different income scaling exponents as a function of decile. We also study the spatial correlations of income and population, which decay exponentially with distance. We find that large cities are not more income-segregated than small cities. Finally, we search for couplings between social and economic factors, like age and income, and propose a toy model that reproduces some of our observations.