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The fractal nature of inequality in a fast growing world: new version

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Author Info
Guido Cozzi
Fabio Privileggi

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Abstract

In this paper we investigate wealth inequality/polarization properties related to the support of the limit distribution of wealth in innovative economies characterized by uninsurable individual risk. We work out two simple successive generation examples, one with stochastic human capital accumulation and one with R&D, and 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 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 become unequal and polarized. We also show that a redistribution scheme financed by proportional taxation does not help cure society’s inequality/polarization – on the contrary, it might increase it – whereas random taxation may well succeed in filling the gap by giving rise to an artificial middle class, but it hardly makes such class sizeable enough. Finally, we investigate how disconnection, a typical feature of Cantor-like sets, is related to inequality in the long run.

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Paper provided by Department of Economics, University of Glasgow in its series Working Papers with number 2009_30.

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Date of creation: Jul 2009
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Handle: RePEc:gla:glaewp:2009_30

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Related research
Keywords: Wealth Inequality; Growth; Fractal; Polarization; Pulverization.;

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
O33 - Economic Development, Technological Change, and Growth - - Technological Change - - - Technological Change: Choices and Consequences; Diffusion Processes

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