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The Fractal Nature of Inequality in a Fast Growing World

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  • Guido Cozzi
  • Fabio Privileggi

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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Bibliographic Info

Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2007_45.

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Date of creation: Dec 2007
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Handle: RePEc:gla:glaewp:2007_45

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Related research

Keywords: Wealth Inequality; Growth; Technological Change; Fractal; Cantor Set; Invariant Distribution; Polarization; Pulverization;

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References

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  1. Cecilia Garcia-Penalosa & Eve Caroli & Philippe Aghion, 1999. "Inequality and Economic Growth: The Perspective of the New Growth Theories," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1615-1660, December.
  2. 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.
  3. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  4. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-51, July.
  5. Guido Cozzi & Fabio Privileggi, 2002. "Wealth Polarization and Pulverization in Fractal Societies," ICER Working Papers - Applied Mathematics Series 39-2002, ICER - International Centre for Economic Research.
  6. Abhijit V. Banerjee & Andrew F. Newman, 1990. "Occupational Choice and the Process of Development," Discussion Papers 911, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Oded Galor & Joseph Zeira, 2013. "Income Distribution and Macroeconomics," Working Papers 2013-12, Brown University, Department of Economics.
  8. Benhabib, Jess & Rustichini, Aldo, 1996. " Social Conflict and Growth," Journal of Economic Growth, Springer, vol. 1(1), pages 125-42, March.
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  10. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June.
  11. Mitra, Tapan & Privileggi, Fabio, 2005. "Cantor Type Attractors in Stochastic Growth Models," POLIS Working Papers 43, Institute of Public Policy and Public Choice - POLIS.
  12. Mitra, Tapan & Privileggi, Fabio, 2003. "Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty," Working Papers 03-09, Cornell University, Center for Analytic Economics.
  13. Piketty, Thomas, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," Review of Economic Studies, Wiley Blackwell, vol. 64(2), pages 173-89, April.
  14. Alberto Alesina & Dani Rodrik, 1991. "Distributive Politics and Economic Growth," NBER Working Papers 3668, National Bureau of Economic Research, Inc.
  15. Roland Benabou, 2000. "Unequal Societies: Income Distribution and the Social Contract," American Economic Review, American Economic Association, vol. 90(1), pages 96-129, March.
  16. Barro, Robert J, 2000. " Inequality and Growth in a Panel of Countries," Journal of Economic Growth, Springer, vol. 5(1), pages 5-32, March.
  17. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-58, May.
  18. Andreoni, James, 1989. "Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1447-58, December.
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