A Model of Income Distribution

  • Satya R. Chakravarty
  • Subir Ghosh
Part of the New Economic Windows book series (NEW)


This paper determines the distribution of income that maximizes aggregate saving when the economy meets the restrictions that the mean income and level of social welfare are given. Presuming that the aggregate demand in the economy consists of the sectoral demand components, consumption and investment, the determined distribution is the one of a given total, that maximizes the funds that can be generated for investment without any loss of welfare. The saving function is assumed to be of Keynesian type: the marginal propensity to save is less than unity and the average propensity to save is increasing with income. The social welfare function we employ here is the single parameter Gini social welfare function introduced by Donaldson and Weymak (1983). If social welfare is assumed to be measured by the Gini social welfare function, then for a simple saving function, the resulting distribution turns out to be the Pareto. We also present an alternative unrestricted maximization of the aggregate saving function and look for the underlying income density function.We finally demonstrate that the Pareto income distribution is completely identifiable for the prespecified levels of welfare and the mean of the income distribution.


Social Welfare Income Distribution Pareto Distribution Social Welfare Function Inequality Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Becker, G. and Tomes, N. (1979). An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility. Journal of Political Economy 87, 1153–1189CrossRefGoogle Scholar
  2. 2.
    Chakravarty, S.R. (2009). Inequality, Polerization and Poverty: Advancer in Distributional Analysis. Springer, New YorkCrossRefGoogle Scholar
  3. 3.
    Champernowne, D.G. (1953). A Model of Income Distribution. Economic Journal 63, 318–351CrossRefGoogle Scholar
  4. 4.
    Chipman, J.S.(1974). The Welfare Ranking of Pareto Distributions. Journal of Economic Theory 9, 275–282CrossRefGoogle Scholar
  5. 5.
    Courant, R. and Hilbet, D. (1953). Methods of Mathematical Physics, Vol.1. Wiley Inter-Science, New YorkGoogle Scholar
  6. 6.
    Donaldson, D. and Weymark, J.A. (1983). Ethically Flexible Gini Indices of Inequality for Income Distributions in the Continuum. Journal of Economic Theory 29, 353–358CrossRefGoogle Scholar
  7. 7.
    Eckstein, Z., Eichenbaum, M.S. and Peled, D. (1985). The Distribution of Wealth and Welfare in the Presence of Incomplete Annuity Markets. Quarterly Journal of Economics 99, 789–806CrossRefGoogle Scholar
  8. 8.
    Jerison, M. (1994). Optimal Income Distribution Rules and Representative Consumers. Review of Economic Studies 61, 739–771CrossRefGoogle Scholar
  9. 9.
    Loury, G.C. (1981). Intergenerational Transfers and the Distribution of Earnings. Econometrica 49, 843–967CrossRefGoogle Scholar
  10. 10.
    Shorrocks, A.F. (1975). On the Stochastic Models of Size Distributions. Review of Economic Studies 42,631–641CrossRefGoogle Scholar
  11. 11.
    Wold, H.O.A. and Whittle, P. (1957) A Model Explaining the Pareto Distribution of Wealth. Econometrica 25, 591–595CrossRefGoogle Scholar
  12. 12.
    Yoshino, O. (1993). Size Distribution of Workers Household Income and Macroeconomic Activities in Japan: 1963–88. Review of Income and Wealth 39, 387–402CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2010

Authors and Affiliations

  • Satya R. Chakravarty
    • 1
  • Subir Ghosh
    • 2
  1. 1.Economic Research UnitIndian Statistical InstituteKolkataIndia
  2. 2.Department of StatisticsUniversity of CaliforniaRiversideUSA

Personalised recommendations