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Sustainable Heterogeneity in Exogenous Growth Models: The Socially Optimal Distribution by Government’s Intervention


  • Harashima, Taiji


This paper examines the socially optimal allocation by focusing not on the social welfare function but instead on the utility possibility frontier in exogenous growth models with a heterogeneous population. A unique balanced growth path was found on which all of the optimality conditions of all heterogeneous households are equally and indefinitely satisfied (sustainable heterogeneity). With appropriate government interventions, such a path is always achievable and is uniquely socially optimal for almost all generally usable (i.e., preferences are complete, transitive, and continuous) social welfare functions. The only exceptions are some variants in Nietzsche type social welfare functions, but those types of welfare functions will rarely be adopted in democratic societies. This result indicates that it is no longer necessary to specify the shape of the social welfare function to determine the socially optimal growth path in a heterogeneous population.

Suggested Citation

  • Harashima, Taiji, 2013. "Sustainable Heterogeneity in Exogenous Growth Models: The Socially Optimal Distribution by Government’s Intervention," MPRA Paper 51653, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:51653

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    References listed on IDEAS

    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Peretto, Pietro F, 1998. "Technological Change and Population Growth," Journal of Economic Growth, Springer, vol. 3(4), pages 283-311, December.
    3. Ghiglino, Christian, 2002. "Introduction to a General Equilibrium Approach to Economic Growth," Journal of Economic Theory, Elsevier, vol. 105(1), pages 1-17, July.
    4. Farmer, Roger E.A. & Lahiri, Amartya, 2005. "Recursive preferences and balanced growth," Journal of Economic Theory, Elsevier, vol. 125(1), pages 61-77, November.
    5. Moore, John, 1992. "The firm as a collection of assets," European Economic Review, Elsevier, vol. 36(2-3), pages 493-507, April.
    6. Samwick, Andrew A., 1998. "Discount rate heterogeneity and social security reform," Journal of Development Economics, Elsevier, vol. 57(1), pages 117-146, October.
    7. Oliver E. Williamson, 1967. "Hierarchical Control and Optimum Firm Size," Journal of Political Economy, University of Chicago Press, vol. 75, pages 123-123.
    8. Harashima, Taiji, 2010. "Sustainable Heterogeneity: Inequality, Growth, and Social Welfare in a Heterogeneous Population," MPRA Paper 22521, University Library of Munich, Germany.
    9. Alwyn Young, 1998. "Growth without Scale Effects," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 41-63, February.
    10. Harashima, Taiji, 2009. "Trade Liberalization and Heterogeneous Rates of Time Preference across Countries: A Possibility of Trade Deficits with China," MPRA Paper 19386, University Library of Munich, Germany.
    11. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    12. Lawrance, Emily C, 1991. "Poverty and the Rate of Time Preference: Evidence from Panel Data," Journal of Political Economy, University of Chicago Press, vol. 99(1), pages 54-77, February.
    13. Harashima, Taiji, 2012. "Sustainable Heterogeneity as the Unique Socially Optimal Allocation for Almost All Social Welfare Functions," MPRA Paper 40938, University Library of Munich, Germany.
    14. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375-382.
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    More about this item


    Sustainability; Heterogeneity; Social Optimality; Social welfare; Social welfare function; Inequality; Evolution;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • F40 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - General
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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