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From the cited paper [1]:

> We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent

> For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase

> we find that mean, variance, skewness and kurtosis of income distributions all increase with city size.

> the Kullback–Leibler divergence between a city’s income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population

> Our results show that the increasing benefits of city size are not evenly distributed to people within those cities.

> our analysis including housing cost demonstrates that despite agglomeration effects on income, bigger cities are less affordable for people of all deciles in the sense that they spend proportionally more of their income on housing; this is especially true for lower income people

IMO this presents evidence that dense and well developed cities attract wealthy individuals and businesses. Perhaps this attraction can be attributed to the diversity in food, entertainment, transportation, and labor force. The paper does not attempt to explain why the poorest income deciles do not scale with city population - but take a look at the other comments here for plenty of speculation on the dynamics of income inequality.

[1] Scaling of urban income inequality in the USA https://arxiv.org/pdf/2102.13150.pdf

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