Sequential breakage generates universality lognormal distributions of per capita GDP

The distribution of per capita income and per capita GDP appears lognormal except for a power law high end (e.g., Montroll & Shlesinger, Proc National Academy of Sciences 1982; Garlaschelli et al., European Physics Journal B 2007; Yakovenko & Rosser, Reviews of Modern Physics 2009; Hong, Han & Kim, Empirical Economics, 2020; Hastings & Young-Taft, Proc International Conference on Complex Systems 2021). We observe that these distributions are near universal after suitable rescaling to account for population and GDP growth. We provide an explanation by translating Sugihara’s (American Naturalist, 1980) argument that sequential breakage of niche components causes lognormal distributions of species abundance from ecology into economics, thus explaining these observed empirical distributions at a variety of scales. For example, per capita GDP in Africa, Latin America and the Caribbean, and Asia (US$, IMF data reported in Wikipedia) each appear to follow a similar distribution, as might be expected from expressing the lognormal distribution as a limit of products of random distributions of economic niche components. This generative model for lognormality also implies universality and may help inform efforts to address inequality and poverty around the world.