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Wealth Polarization and Pulverization in Fractal Societies

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Author Info
Guido Cozzi ()
Fabio Privileggi ()

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Abstract

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.

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Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 39-2002.

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Length: 49 pages
Date of creation: Sep 2002
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Handle: RePEc:icr:wpmath:39-2002

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Related research
Keywords: Inequality and Growth Education Technological Change Wealth Polarization/ Pulverization Iterated Function System Attractor Fractal Cantor Set Invariant Distribution

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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References listed on IDEAS
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  3. Benhabib, Jess & Rustichini, Aldo, 1996. " Social Conflict and Growth," Journal of Economic Growth, Springer, vol. 1(1), pages 125-42, March.
  4. Barro, Robert J, 2000. " Inequality and Growth in a Panel of Countries," Journal of Economic Growth, Springer, vol. 5(1), pages 5-32, March. [Downloadable!] (restricted)
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  9. Kristin J. Forbes, 2000. "A Reassessment of the Relationship between Inequality and Growth," American Economic Review, American Economic Association, vol. 90(4), pages 869-887, September. [Downloadable!] (restricted)
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  11. Alesina, Alberto & Rodrik, Dani, 1994. "Distributive Politics and Economic Growth," The Quarterly Journal of Economics, MIT Press, vol. 109(2), pages 465-90, May. [Downloadable!] (restricted)
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  12. Robert J. Barro, 1999. "Inequality, Growth, and Investment," NBER Working Papers 7038, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  16. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June. [Downloadable!] (restricted)
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  18. Peter Howitt, 1999. "Steady Endogenous Growth with Population and R & D Inputs Growing," Journal of Political Economy, University of Chicago Press, vol. 107(4), pages 715-730, August. [Downloadable!] (restricted)
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  20. Piketty, Thomas, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," Review of Economic Studies, Blackwell Publishing, vol. 64(2), pages 173-89, April. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research. [Downloadable!]
  2. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
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  3. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
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  4. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
  5. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
  6. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research. [Downloadable!]
  7. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research. [Downloadable!]
  8. Guido Cozzi & Fabio Privileggi, 2007. "The Fractal Nature of Inequality in a Fast Growing World," Working Papers 2007_45, Department of Economics, University of Glasgow. [Downloadable!]
  9. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  10. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research. [Downloadable!]
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