Title: Superlinear scaling in the urban system of England of Wales. A comparison with US cities,
Abstract: According to the theory of urban scaling, urban indicators scale with city
size in a predictable fashion. In particular, indicators of social and economic
productivity are expected to have a superlinear relation. This behavior was
verified for many urban systems, but recent findings suggest that this pattern
may not be valid for England and Wales (E&W), where income has a linear
relation with city size. This finding raises the question of whether the cities
of E&W exhibit any superlinear relation with respect to quantities such as the
level of education and occupational groups. In this paper, we evaluate the
scaling of educational and occupational groups of E&W to see if we can detect
superlinear relations in the number of educated and better-paid persons. As E&W
may be unique in its linear scaling of income, we complement our analysis by
comparing it to the urban system of the United States (US), a country for which
superlinear scaling of income has already been demonstrated. To make the two
urban systems comparable, we define the urban systems of both countries using
the same method and test the sensitivity of our results to changes in the
boundaries of cities. We find that cities of E&W exhibit patterns of
superlinear scaling with respect to education and certain categories of
better-paid occupations. However, the tendency of such groups to have
superlinear scaling seems to be more consistent in the US. We show that while
the educational and occupational distributions of US cities can partly explain
the superlinear scaling of earnings, the distribution leads to a linear scaling
of earnings in E&W.