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Sustainable Heterogeneity as the Unique Socially Optimal Allocation for Almost All Social Welfare Functions

  • Harashima, Taiji

The socially optimal allocation has been regarded to be unspecifiable because of utility’s interpersonal incomparability, Arrow’s general possibility theorem, and other factors. This paper examines this problem by focusing not on the social welfare function but instead on the utility possibility frontier in dynamic 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.

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File URL: http://mpra.ub.uni-muenchen.de/40938/1/MPRA_paper_40938.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40938.

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Date of creation: 29 Aug 2012
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Handle: RePEc:pra:mprapa:40938
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  1. Harashima, Taiji, 2010. "Sustainable Heterogeneity: Inequality, Growth, and Social Welfare in a Heterogeneous Population," MPRA Paper 22521, University Library of Munich, Germany.
  2. Samwick, Andrew A., 1998. "Discount rate heterogeneity and social security reform," Journal of Development Economics, Elsevier, vol. 57(1), pages 117-146, October.
  3. Prescott, Edward C, 1998. "Needed: A Theory of Total Factor Productivity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 525-51, August.
  4. 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.
  5. Harashima, Taiji, 2009. "Endogenous Growth Models in Open Economies: A Possibility of Permanent Current Account Deficits," MPRA Paper 19385, University Library of Munich, Germany.
  6. Taiji Harashima, 2004. "A New Asymptotically Non-Scale Endogenous Growth Model," Development and Comp Systems 0412009, EconWPA, revised 20 Dec 2004.
  7. Farmer, Roger E A & Lahiri, Amartya, 2003. "Recursive Preferences and Balanced Growth," CEPR Discussion Papers 3949, C.E.P.R. Discussion Papers.
  8. Ghiglino, Christian, 2002. "Introduction to a General Equilibrium Approach to Economic Growth," Journal of Economic Theory, Elsevier, vol. 105(1), pages 1-17, July.
  9. Harashima, Taiji, 2009. "A Theory of Total Factor Productivity and the Convergence Hypothesis: Workers’ Innovations as an Essential Element," MPRA Paper 15508, University Library of Munich, Germany.
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