Wealth Polarization and Pulverization in Fractal Societies

In this paper we study the geometrical properties of the support of the limit distributions of income/wealth in economies with uninsurable individual risk, and how they are affected by technology and preference parameters and by policy variables. We work out two simple successive generation models with stochastic human capital accumulation and with R&D and we prove that intense technological progress makes the support of the wealth distribution converge to a fractal Cantor-like set. Such limit distribution implies the disappearance of the middle class, with a “gap” between two polarized wealth clusters that widens as the growth rate becomes higher. Hence, we claim that in a highly meritocratic world in which the payoff of the successful individuals is high enough, and in which social mobility is strong, societies tend to look highly “fractalized”. We also show that a redistribution scheme financed by proportional taxation does not help cure society’s disconnection/polarization; on the contrary, it might increase it. Finally we show that these results are not confined to our analytically worked out examples but are easily extended to a widely used class of macroeconomic and growth models.