IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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

Listed author(s):
  • Guido Cozzi
  • Fabio Privileggi

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.gla.ac.uk/media/media_126649_en.pdf
Download Restriction: no

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

as
in new window

Length:
Date of creation: Jul 2009
Handle: RePEc:gla:glaewp:2009_30
Contact details of provider: Postal:
Adam Smith Building, Glasgow G12 8RT

Phone: 0141 330 4618
Fax: 0141 330 4940
Web page: http://www.gla.ac.uk/schools/business/research/

More information through EDIRC

References listed on IDEAS
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.:

as
in new window


  1. Mitra, Tapan & Privileggi, Fabio, 2005. "Cantor Type Attractors in Stochastic Growth Models," POLIS Working Papers 43, Institute of Public Policy and Public Choice - POLIS.
  2. Alberto Alesina & Guido Cozzi & Noemi Mantovan, 2012. "The Evolution of Ideology, Fairness and Redistribution," Economic Journal, Royal Economic Society, vol. 122(565), pages 1244-1261, December.
  3. Edward N. Wolff, 2007. "Recent Trends in Household Wealth in the United States: Rising Debt and the Middle-Class Squeeze," Economics Working Paper Archive wp_502, Levy Economics Institute.
  4. James Heckman & Flavio Cunha, 2007. "The Technology of Skill Formation," American Economic Review, American Economic Association, vol. 97(2), pages 31-47, May.
  5. Alberto Alesina & George-Marios Angeletos, 2004. "Fairness and Redistribution," NajEcon Working Paper Reviews 122247000000000306, www.najecon.org.
  6. 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).
  7. Robert J. Barro, 1999. "Inequality, Growth, and Investment," NBER Working Papers 7038, National Bureau of Economic Research, Inc.
  8. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-358, May.
  9. Alberto Alesina & Dani Rodrik, 1991. "Distributive Politics and Economic Growth," NBER Working Papers 3668, National Bureau of Economic Research, Inc.
  10. Flavio Cunha & James J. Heckman, 2009. "The Economics and Psychology of Inequality and Human DEvelopment," Journal of the European Economic Association, MIT Press, vol. 7(2-3), pages 320-364, 04-05.
  11. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-867, June.
  12. Alesina, Alberto F & La Ferrara, Eliana, 2002. "Preferences for Redistribution in the Land of Opportunities," CEPR Discussion Papers 3155, C.E.P.R. Discussion Papers.
  13. Dilip Mookherjee & Debraj Ray, 2000. "Persistent Inequality," Boston University - Department of Economics - The Institute for Economic Development Working Papers Series dp-108, Boston University - Department of Economics, revised Oct 2002.
  14. 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 274-298, April.
  15. James J. Heckman, 2008. "Schools, Skills, and Synapses," Working Papers 200833, Geary Institute, University College Dublin.
  16. Roland Benabou, 2000. "Unequal Societies: Income Distribution and the Social Contract," American Economic Review, American Economic Association, vol. 90(1), pages 96-129, March.
  17. 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.
  18. Mattias Lundberg & Lyn Squire, 2003. "The simultaneous evolution of growth and inequality," Economic Journal, Royal Economic Society, vol. 113(487), pages 326-344, 04.
  19. 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 1447-1458, December.
  20. Aghion, Philippe & Caroli, Eve & García-Peñalosa, Cecilia, 1999. "Inequality and Economic Growth: The Perspective of the New Growth Theories," Scholarly Articles 12502063, Harvard University Department of Economics.
  21. 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.
  22. Dilip Mookherjee & Debraj Ray, 2002. "Is Equality Stable?," Boston University - Department of Economics - The Institute for Economic Development Working Papers Series dp-121, Boston University - Department of Economics.
  23. David Card & John E. DiNardo, 2002. "Skill-Biased Technological Change and Rising Wage Inequality: Some Problems and Puzzles," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 733-783, October.
  24. Galor, Oded & Zeira, Joseph, 1988. "Income Distribution and Macroeconomics," MPRA Paper 51644, University Library of Munich, Germany, revised 01 Sep 1989.
  25. Thomas Piketty, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," Review of Economic Studies, Oxford University Press, vol. 64(2), pages 173-189.
  26. Mitra, Tapan & Privileggi, Fabio, 2009. "On Lipschitz continuity of the iterated function system in a stochastic optimal growth model," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 185-198, January.
  27. Benhabib, Jess & Rustichini, Aldo, 1996. "Social Conflict and Growth," Journal of Economic Growth, Springer, vol. 1(1), pages 125-142, March.
  28. Alesina, Alberto & Giuliano, Paola, 2009. "Preferences for Redistribution," IZA Discussion Papers 4056, Institute for the Study of Labor (IZA).
  29. Flavio Cunha & James J. HECKMAN, 2009. "Investing in our Young People," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 117(3), pages 387-418.
  30. Wu, Ximing & Perloff, Jeffrey M., 2005. "China's Income Distribution, 1985-2001," Institute for Research on Labor and Employment, Working Paper Series qt0zd6m0sf, Institute of Industrial Relations, UC Berkeley.
  31. Benhabib, Jess & Spiegel, Mark, 1997. "Cross-Country Growth Regressions," Working Papers 97-20, C.V. Starr Center for Applied Economics, New York University.
  32. Rajiv Sethi & Rohini Somanathan, 2001. "Inequality and Segregation," Microeconomics 0108005, EconWPA.
  33. Daron Acemoglu, 2000. "Technical Change, Inequality, and the Labor Market," NBER Working Papers 7800, National Bureau of Economic Research, Inc.
  34. Bénabou, Roland, 1996. "Inequality and Growth," CEPR Discussion Papers 1450, C.E.P.R. Discussion Papers.
  35. repec:dau:papers:123456789/10091 is not listed on IDEAS
  36. Mitra, Tapan & Montrucchio, Luigi & Privileggi, Fabio, 2001. "The Nature of the Steady State in Models of Optimal Growth Under Uncertainty," Working Papers 01-04, Cornell University, Center for Analytic Economics.
  37. Roland Bénabou, 1996. "Equity and Efficiency in Human Capital Investment: The Local Connection," Review of Economic Studies, Oxford University Press, vol. 63(2), pages 237-264.
  38. Dilip Mookherjee & Debraj Ray, 2005. "Occupational Diversity and Endogenous Inequality," Boston University - Department of Economics - Working Papers Series WP2005-022, Boston University - Department of Economics.
  39. X. Zhang & R. Kanbur, 2001. "What Difference Do Polarisation Measures Make? An Application to China," Journal of Development Studies, Taylor & Francis Journals, vol. 37(3), pages 85-98.
  40. Perotti, Roberto, 1996. "Growth, Income Distribution, and Democracy: What the Data Say," Journal of Economic Growth, Springer, vol. 1(2), pages 149-187, June.
  41. 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.
  42. Barro, Robert J, 2000. "Inequality and Growth in a Panel of Countries," Journal of Economic Growth, Springer, vol. 5(1), pages 5-32, March.
  43. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658, December.
  44. 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.
  45. L. Montrucchio & F. Privileggi, 1999. "Fractal steady states instochastic optimal control models," Annals of Operations Research, Springer, vol. 88(0), pages 183-197, January.
  46. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723, December.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:gla:glaewp:2009_30. See general information about how to correct material in RePEc.

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.