  Understanding cities is central to addressing major global challenges from
climate and health to economic resilience. Although increasingly perceived as
fundamental socio-economic units, the detailed fabric of urban economic
activities is only now accessible to comprehensive analyses with the
availability of large datasets. Here, we study abundances of business
categories across U.S. metropolitan statistical areas to investigate how
diversity of economic activities depends on city size. A universal structure
common to all cities is revealed, manifesting self-similarity in internal
economic structure as well as aggregated metrics (GDP, patents, crime). A
derivation is presented that explains universality and the observed empirical
distribution. The model incorporates a generalized preferential attachment
process with ceaseless introduction of new business types. Combined with
scaling analyses for individual categories, the theory quantitatively predicts
how individual business types systematically change rank with city size,
thereby providing a quantitative means for estimating their expected abundances
as a function of city size. These results shed light on processes of economic
differentiation with scale, suggesting a general structure for the growth of
national economies as integrated urban systems.
