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Existence and uniqueness of steady-state equilibrium in a two-sector overlapping generations model

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  • Li, Jinlu
  • Lin, Shuanglin

Abstract

In his seminal paper Galor [A two-sector overlapping generations-model: a global characterization of the dynamical system, Econometrica 60 (1992) 1351-1386] establishes conditions for the existence of equilibrium in the two-sector overlapping generations (OLG) model. Although appealing theoretically, these conditions are implicit and not easy to apply. This paper develops new theorems on the existence and uniqueness of steady-state equilibrium in the two-sector OLG model. We provide explicit conditions on the utility and production functions for the existence and uniqueness of equilibrium, with which one only needs to check the derivatives of the production and utility functions and their interactions, without requiring solving for the savings function and its derivatives. We present detailed steps to check the existence and uniqueness of equilibrium and provide illustrative examples.

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  • Li, Jinlu & Lin, Shuanglin, 2008. "Existence and uniqueness of steady-state equilibrium in a two-sector overlapping generations model," Journal of Economic Theory, Elsevier, vol. 141(1), pages 255-275, July.
    • Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:255-275
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    1. Galor, Oded & Ryder, Harl E., 1989. "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital," Journal of Economic Theory, Elsevier, vol. 49(2), pages 360-375, December.
    2. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
    3. David Altig, 2001. "Simulating Fundamental Tax Reform in the United States," American Economic Review, American Economic Association, vol. 91(3), pages 574-595, June.
    4. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    5. Galor, Oded, 1992. "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System," Econometrica, Econometric Society, vol. 60(6), pages 1351-1386, November.
    6. Balasko, Yves & Cass, David & Shell, Karl, 1980. "Existence of competitive equilibrium in a general overlapping-generations model," Journal of Economic Theory, Elsevier, vol. 23(3), pages 307-322, December.
    7. Michel, Philippe & de la Croix, David, 2000. "Myopic and perfect foresight in the OLG model," Economics Letters, Elsevier, vol. 67(1), pages 53-60, April.
    8. Boldrin, Michele, 1992. "Dynamic externalities, multiple equilibria, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 198-218, December.
    9. Wang Yong, 1993. "Stationary Equilibria in an Overlapping Generations Economy with Stochastic Production," Journal of Economic Theory, Elsevier, vol. 61(2), pages 423-435, December.
    10. Ronald Wendner, 2003. "Existence, uniqueness, and stability of equilibrium in an OLG economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 165-174, December.
    11. Jones, Larry E. & Manuelli, Rodolfo E., 1992. "Finite lifetimes and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 171-197, December.
    12. Emmanuel Thibault, 2000. "Existence of equilibrium in an OLG model with production and altruistic preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 709-715.
    13. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
    14. Galor, Oded & Ryder, Harl E., 1991. "Dynamic efficiency of steady-state equilibria in an overlapping-generations model with productive capital," Economics Letters, Elsevier, vol. 35(4), pages 385-390, April.
    15. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521001151.
    16. Philippe Weil, 1987. "Confidence and the Real Value of Money in an Overlapping Generations Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(1), pages 1-22.
    17. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
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    Cited by:

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    4. Jean-Paul Barinci & Hye-Jin Cho & Jean-Pierre Drugeon, 2021. "On equilibrium elasticities of substitution in simple overlapping generations economies with heterogeneous goods," SciencePo Working papers Main halshs-03238950, HAL.
    5. Wei-Bin Zhang, 2018. "Business Cycles In A General Equilibrium Dynamic Model With Land Value And Rent," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 63(216), pages 7-34, January –.
    6. Zhang, Jin Shui, 2011. "The analytical solution of balanced growth of non-linear dynamic multi-sector economic model," Economic Modelling, Elsevier, vol. 28(1-2), pages 410-421, January.
    7. Barinci, Jean-Paul & Cho, Hye-Jin & Drugeon, Jean-Pierre, 2021. "On equilibrium elasticities of substitution in simple overlapping generations economies with heterogeneous goods," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 120-137.
    8. Wei-Bin ZHANG, 2015. "Tourism, Trade And Wealth Accumulation With Endogenous Income And Wealth Distribution Among Countries," EcoForum, "Stefan cel Mare" University of Suceava, Romania, Faculty of Economics and Public Administration - Economy, Business Administration and Tourism Department., vol. 4(1), pages 1-1, January.
    9. Prof. Wei-Bin Zhang, 2015. "Economic Oscillations in a Multi-Country Growth Model with Free Trade and Tourism," Eurasian Business & Economics Journal, Eurasian Academy Of Sciences, vol. 2(2), pages 1-19, July.
    10. Li, Jinlu & Lin, Shuanglin, 2012. "Existence And Uniqueness Of Steady-State Equilibrium In A Generalized Overlapping Generations Model," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 299-311, November.
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    12. Wei-Bin Zhang, 2017. "Spatial Agglomeration And Economic Development With The Inclusion Of Interregional Tourism," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 62(213), pages 93-128, April - J.
    13. Ali Khan, M. & Piazza, Adriana, 2012. "On the Mitra–Wan forestry model: A unified analysis," Journal of Economic Theory, Elsevier, vol. 147(1), pages 230-260.
    14. Wei-Bin Zhang, 2014. "Growth and inequality examined by integrating the Walrasian general equilibrium and neoclassical growth theories," International Journal of Business and Economic Sciences Applied Research (IJBESAR), International Hellenic University (IHU), Kavala Campus, Greece (formerly Eastern Macedonia and Thrace Institute of Technology - EMaTTech), vol. 7(1), pages 7-32, April.
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