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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
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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 141 (2008)
Issue (Month): 1 (July)
Pages: 255-275

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Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:255-275

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. 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.
  2. Larry E. Jones & Rodolfo E. Manuelli, 1990. "Finite Lifetimes and Growth," NBER Working Papers 3469, National Bureau of Economic Research, Inc.
  3. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
  4. Galor, Oded, 1992. "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System," Econometrica, Econometric Society, vol. 60(6), pages 1351-86, November.
  5. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521806428, October.
  6. Emmanuel Thibault, 2000. "Existence of equilibrium in an OLG model with production and altruistic preferences," Economic Theory, Springer, vol. 15(3), pages 709-715.
  7. Michel, Philippe & de la Croix, David, 1999. "Myopic and perfect foresight in the OLG model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  8. 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.
  9. Barro, Robert J., 1974. "Are Government Bonds Net Wealth?," Scholarly Articles 3451399, Harvard University Department of Economics.
  10. Boldrin, Michele, 1992. "Dynamic externalities, multiple equilibria, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 198-218, December.
  11. David Altig, 2001. "Simulating Fundamental Tax Reform in the United States," American Economic Review, American Economic Association, vol. 91(3), pages 574-595, June.
  12. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
  13. 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.
  14. Ronald Wendner, 2003. "Existence, uniqueness, and stability of equilibrium in an OLG economy," Economic Theory, Springer, vol. 23(1), pages 165-174, December.
  15. Weil, Philippe, 1987. "Confidence and the Real Value of Money in an Overlapping Generations Economy," The Quarterly Journal of Economics, MIT Press, vol. 102(1), pages 1-22, February.
  16. 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.
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Citations

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Cited by:
  1. 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.
  2. Shuanglin Lin & Wei Zhang, 2009. "The effect of corruption on capital accumulation," Journal of Economics, Springer, vol. 97(1), pages 67-93, May.
  3. 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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