The Fractal Nature of Inequality in a Fast Growing World
AbstractIn 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.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoPaper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2007_45.
Date of creation: Dec 2007
Date of revision:
Wealth Inequality; Growth; Technological Change; Fractal; Cantor Set; Invariant Distribution; Polarization; Pulverization;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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.:
- Alesina, Alberto & Rodrik, Dani, 1994.
"Distributive Politics and Economic Growth,"
The Quarterly Journal of Economics,
MIT Press, vol. 109(2), pages 465-90, May.
- Alberto Alesina & Dani Rodrik, 1991. "Distributive Politics and Economic Growth," NBER Working Papers 3668, National Bureau of Economic Research, Inc.
- Rodrik, Dani & Alesina, Alberto, 1994. "Distributive Politics and Economic Growth," Scholarly Articles 4551798, Harvard University Department of Economics.
- Alesina, Alberto F & Rodrik, Dani, 1991. "Distributive Politics and Economic Growth," CEPR Discussion Papers 565, C.E.P.R. Discussion Papers.
- 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.
- Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-58, May.
- Barro, Robert J, 2000. " Inequality and Growth in a Panel of Countries," Journal of Economic Growth, Springer, vol. 5(1), pages 5-32, March.
- Garcia-Penalosa, Cecilia & Aghion, Philippe & Caroli, Eve, 1999.
"Inequality and Economic Growth: The Perspective of the New Growth Theories,"
Economics Papers from University Paris Dauphine
123456789/10091, Paris Dauphine University.
- 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.
- Aghion, Philippe & Caroli, Eve & Garcia-Penalosa, Cecilia, 1999. "Inequality and economic growth: the perspective of the new growth theories," CEPREMAP Working Papers (Couverture Orange) 9908, CEPREMAP.
- 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.
- 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.
- Esteban, Joan & Ray, Debraj, 1994.
"On the Measurement of Polarization,"
Econometric Society, vol. 62(4), pages 819-51, July.
- Esteban, J.M. & Ray, D., 1992. "On the Measurement of Polarization," UFAE and IAE Working Papers 171.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Joan-Maria Esteban & Debraj Ray, 1991. "On the Measurement of Polarization," Boston University - Institute for Economic Development 18, Boston University, Institute for Economic Development.
- Esteban, J. & Ray, D., 1993. "On the Measurement of Polarization," UFAE and IAE Working Papers 221.93, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Benhabib, Jess & Rustichini, Aldo, 1996. " Social Conflict and Growth," Journal of Economic Growth, Springer, vol. 1(1), pages 125-42, March.
- Banerjee, Abhijit V & Newman, Andrew F, 1993.
"Occupational Choice and the Process of Development,"
Journal of Political Economy,
University of Chicago Press, vol. 101(2), pages 274-98, April.
- 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.
- Oded Galor & Joseph Zeira, 2013.
"Income Distribution and Macroeconomics,"
2013-12, Brown University, Department of Economics.
- Roland Benabou, 2000. "Unequal Societies: Income Distribution and the Social Contract," American Economic Review, American Economic Association, vol. 90(1), pages 96-129, March.
- Mitra, Tapan & Privileggi, Fabio, 2005. "Cantor Type Attractors in Stochastic Growth Models," POLIS Working Papers 43, Institute of Public Policy and Public Choice - POLIS.
- 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.
- Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jeanette Findlay).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.