• Taiji HARASHIMA Department of Economics, Kanazawa Seiryo University, Japan


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.


[1] Aghion, P., Howitt, P. (1998). Endogenous Growth Theory, MIT Press, Cambridge, MA.
[2] Arrow, Kenneth J. (1951). Social Choice and Individual Values, Wiley, New York.
[3] Arrow, Kenneth J. (1962). The Economic Implications of Learning by Doing, Review of Economic Studies, 29: 155–173.
[4] Arrow, Kenneth J., Bert Bolin, Robert Costanza, Partha Dasgupta, Carl Folke, C. S. Holling, Bengt-Owe Jansson, Simon Levin, Karl-Goran Maler, Charles Perrings, and David Pimentel (1995). Economic Growth, Carrying Capacity, and the Environment, Science, 268(28): 520–521.
[5] Barro, Robert J. and Xavier Sala-i-Martin. (1995). Economic Growth, McGraw-Hill, New York.
[6] Becker, Robert A. (1980). On the long-run steady state in a simple dynamic model of equilibrium with heterogeneous households, The Quarterly Journal of Economics, 95(2): 375–382.
[7] Bergson, A. (1938). A Reformulation of Certain Aspects of Welfare Economics, The Quarterly Journal of Economics, 52(2): 310-334.
[8] Black, D. (1958). The Theory of Committees and Elections, Cambridge University Press, Cambridge, UK.
[9] Coase, Ronald H. (1937). The Nature of the Firm, Economica, 4: 386–405.
[10] Dinopoulos, E., Thompson, P. (1998). Schumpeterian Growth without Scale Effects, Journal of Economic Growth, 3: 313–335.
[11] Farmer, Roger E. A. and Amartya, Lahiri. (2005). Recursive Preferences and Balanced Growth, Journal of Economic Theory, 125(1): 61–77.
[12] Ghiglino, C. (2002). Introduction to a general equilibrium approach to economic growth, Journal of Economic Theory, 105(1): 1–17.
[13] Gray, John N. (1998). False Dawn: The Delusions of Global Capitalism, Granta Publications, London.
[14] Grossman, Sanford J. and Hart, Oliver D. (1986). The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration, Journal of Political Economy, 94: 691–719.
[15] Hamilton, W.D. (1964a). The Genetical Evolution of Social Behavior I, Journal of Theoretical Biology, 7(1): 1–16.
[16] Hamilton, W.D. (1964b). The Genetical Evolution of Social Behavior II, Journal of Theoretical Biology, 7(1): 17–52.
[17] Harashima, Taiji. (2009). Trade Liberalization and Heterogeneous Rates of Time Preference across Countries: A Possibility of Trade Deficits with China, MPRA (The Munich Personal RePEc Archive) Paper, 19386.
[18] Harashima, Taiji. (2010). Sustainable Heterogeneity: Inequality, Growth, and Social Welfare in a Heterogeneous Population, MPRA (The Munich Personal RePEc Archive) Paper, 24233.
[19] Harashima, Taiji. (2012). Sustainable Heterogeneity as the Unique Socially Optimal Allocation for Almost All Social Welfare Functions, MPRA (The Munich Personal RePEc Archive) Paper, 40938.
[20] Jacobs, J. (1969). The Economy of Cities, Random House, New York.
[21] Jones, C.I. (1995). Time series test of endogenous growth models, Quarterly Journal of Economics, 110(2): 495–525.
[22] Jones, C.I. (1999). Growth: With or Without Scale Effects?, American Economic Review Papers and Proceedings, 89(2): 139–144.
[23] Kaldor, N. (1961). Capital Accumulation and Economic Growth, Chap. 10 of A. Lutz and D. C. Hague (eds.), The Theory of Capital, St. Martin’s Press, New York.
[24] Klein, N. (2000). No Logo, Flamingo, London.
[25] Lawrance, E.C. (1991). Poverty and the Rate of Time Preference: Evidence from Panel Data, Journal of Political Economy, 99(1): 54–77.
[26] Marshall, A. (1890). Principles of Economics, Macmillan, London.
[27] Moore, J. (1992). The Firm as a Collection of Assets, European Economic Review, 36: 493–507.
[28] Peretto, P. (1998). Technological change and population growth, Journal of Economic Growth, 3: 283–311.
[29] Romer, P.M. (1986). Increasing returns and long-run growth, Journal of Political Economy, 94(5) 1002–1037.
[30] Samuelson, P.A. (1947). Foundations of Economic Analysis, Harvard University Press (Enlarged ed. 1983), Cambridge, MA.
[31] Samwick, A.A. (1998). Discount Rate Heterogeneity and Social Security Reform, Journal of Development Economics, 57(1): 117–146.
[32] Sen, Amartya Kumar. (1976). Real National Income, Review of Economic Studies, 43(1): 19–39.
[33] Soros, G. (2008). The New Paradigm for Financial Markets: The Credit Crisis of 2008 and What It Means, Public Affairs, New York.
[34] Stiglitz, J. (2002). Globalization and Its Discontents, W.W. Norton & Company, New York.
[35] Stiglitz, J. (2009). Moving beyond market fundamentalism to a more balanced economy, Annals of Public and Cooperative Economics, 80(3): 345–360.
[36] Ventura, L. (2003). Direct Measure of Time-preference, Economic and Social Review, 34(3): 293–310.
[37] Williams, G.C. (1966). Adaptation and Natural Selection, Princeton University Press, Princeton, NJ.
[38] Williamson, O.E. (1967). Hierarchical Control and Optimum Firm Size, Journal of Political Economy, 75: 123–138.
[39] Young, Alwyn. (1998). Growth without Scale Effects, Journal of Political Economy, 106: 41–63.
How to Cite
HARASHIMA, Taiji. SUSTAINABLE HETEROGENEITY IN EXOGENOUS GROWTH MODELS. THE SOCIALLY OPTIMAL DISTRIBUTION BY GOVERNMENT’S INTERVENTION. Theoretical and Practical Research in the Economic Fields, [S.l.], v. 5, n. 1, p. 73-100, june 2017. ISSN 2068-7710. Available at: <>. Date accessed: 05 july 2022. doi: