IDEAS home Printed from https://ideas.repec.org/a/bla/jpbect/v23y2021i4p691-709.html
   My bibliography  Save this article

Existence of equilibrium in an overlapping‐generations model with government debt

Author

Listed:
  • Jinlu Li
  • Shuanglin Lin

Abstract

The Diamond overlapping generations (OLG) model with government debt has been widely utilized in economics, but the existence of the steady‐state equilibrium is either assumed or illustrated numerically. This paper provides easily checkable conditions for the existence and uniqueness of steady‐state equilibrium in this model. By checking the first derivatives of the production and utility functions and their interactions, we can determine whether the model has a nontrivial equilibrium or not. We show that the level of government debt, production technology, individual preference, and the growth rate are important for the existence of equilibrium. If government debt exceeds a certain level, equilibrium will not exist. Given technology, preference, and the growth rate, the upper‐bounds of the government debt‐output ratio in equilibrium can be determined based on our results.

Suggested Citation

  • Jinlu Li & Shuanglin Lin, 2021. "Existence of equilibrium in an overlapping‐generations model with government debt," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(4), pages 691-709, August.
    • Handle: RePEc:bla:jpbect:v:23:y:2021:i:4:p:691-709
    DOI: 10.1111/jpet.12520
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jpet.12520
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jpet.12520?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    2. Torben M. Andersen, 2020. "Taxation of capital income in overlapping generations economies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1245-1261, September.
    3. 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.
    4. Oliver Lorz, 2004. "Time Consistent Optimal Redistribution Policy in an Overlapping Generations Model," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(1), pages 25-41, February.
    5. Shuanglin Lin, 2000. "Government Debt and Economic Growth in an Overlapping Generations Model," Southern Economic Journal, John Wiley & Sons, vol. 66(3), pages 754-763, January.
    6. Ihori, Toshihiro, 2001. "Wealth taxation and economic growth," Journal of Public Economics, Elsevier, vol. 79(1), pages 129-148, January.
    7. Michael Carlberg & Arne Hansen, 2013. "Sustainability and Optimality of Public Debt," Springer Books, Springer, edition 2, number 978-3-642-32967-8, January.
    8. Gaetano Carmeci & Luciano Mauro & Fabio Privileggi, 2021. "Growth maximizing government size, social capital, and corruption," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(3), pages 438-461, June.
    9. Philippe Michel & Pierre Pestieau, 2004. "Fiscal Policy in an Overlapping Generations Model with Bequest‐as‐Consumption," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(3), pages 397-407, August.
    10. Karl Farmer, 2006. "Reducing Public Debt under Dynamic Efficiency: Transitional Dynamics in Diamond's OLG Model," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 34(2), pages 195-208, June.
    11. Thomas Aronsson & Olof Johansson‐Stenman, 2010. "Positional Concerns In An Olg Model: Optimal Labor And Capital Income Taxation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(4), pages 1071-1095, November.
    12. Andrew B. Abel, 2005. "Optimal Taxation when Consumers Have Endogenous Benchmark Levels of Consumption," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 21-42.
    13. Fernando Perera-Tallo & Hideo Konishi, 1997. "Existence of steady - state equium in an overlapping-generations model with production (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 529-537.
    14. Ihori, Toshihiro, 1978. "The Golden Rule and the Role of Government in a Life Cycle Growth Model," American Economic Review, American Economic Association, vol. 68(3), pages 389-396, June.
    15. Lin, Shuanglin, 1998. "Labor income taxation and human capital accumulation," Journal of Public Economics, Elsevier, vol. 68(2), pages 291-302, May.
    16. Farmer Karl & Kuplen Stefan, 2018. "Involuntary Unemployment in a Neoclassical Growth Model with Public Debt and Human Capital," Studia Universitatis Babeș-Bolyai Oeconomica, Sciendo, vol. 63(2), pages 3-34, August.
    17. David Altig, 2001. "Simulating Fundamental Tax Reform in the United States," American Economic Review, American Economic Association, vol. 91(3), pages 574-595, June.
    18. Persson, Torsten, 1985. "Deficits and intergenerational welfare in open economies," Journal of International Economics, Elsevier, vol. 19(1-2), pages 67-84, August.
    19. 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.
    20. 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.
    21. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Jean-Marc Bonnisseau & Lalaina Rakotonindrainy, 2017. "Existence of equilibrium in OLG economies with increasing returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 111-129, January.
    3. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    4. Kevin Reffett & Olivier Morand, 2008. "Isotone recursive methods for Stationary Markov Equilibra in OLG models with stochastic nonclassical production," 2008 Meeting Papers 470, Society for Economic Dynamics.
    5. Smith, Bruce D., 1984. "Money, nonconvex preferences, and the existence of equilibrium: A note," Journal of Economic Theory, Elsevier, vol. 32(2), pages 359-366, April.
    6. Jean-Marc Bonnisseau & Lalaina Rakotonindrainy, 2015. "A note on the characterization of optimal allocations in OLG models with multiple goods," Post-Print halshs-01158117, HAL.
    7. Engineer, Merwan & Esteban, Joan & Sakovics, Jozsef, 1997. "Costly transfer institutions and the core in an overlapping generations model," Journal of Economic Behavior & Organization, Elsevier, vol. 32(2), pages 287-300, February.
    8. Bloise, Gaetano & Calciano, Filippo L., 2008. "A characterization of inefficiency in stochastic overlapping generations economies," Journal of Economic Theory, Elsevier, vol. 143(1), pages 442-468, November.
    9. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    10. James Sprigg & Mark Ehlen, 2007. "Comparative dynamics in an overlapping-generations model: the effects of quasi-rational discrete choice on finding and maintaining Nash equilibrium," Computational Economics, Springer;Society for Computational Economics, vol. 29(1), pages 69-96, February.
    11. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2015. "Local determinacy of prices in an overlapping generations model with continuous trading," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 16-24.
    12. Martin Barbie & Marten Hillebrand, 2018. "Bubbly Markov equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 627-679, October.
    13. Kehoe, Timothy J. & Levine, David K., 1990. "The economics of indeterminacy in overlapping generations models," Journal of Public Economics, Elsevier, vol. 42(2), pages 219-243, July.
    14. 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.
    15. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    16. Molina-Abraldes, Antonio & Pintos-Clapés, Juan, 2008. "Pareto optimality in continuous-time OLG economies," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 933-950, September.
    17. Aiyagari, S. Rao, 1987. "Optimality and monetary equilibria in stationary overlapping generations models with long-lived agents: Growth versus discounting," Journal of Economic Theory, Elsevier, vol. 43(2), pages 292-313, December.
    18. Jean-Marc Bonnisseau & Lalaina Rakotonindrainy, 2015. "A note on the characterization of optimal allocations in OLG economies with multiple goods," Documents de travail du Centre d'Economie de la Sorbonne 15003, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. Zhigang Feng & Matthew Hoelle, 2017. "Indeterminacy in stochastic overlapping generations models: real effects in the long run," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 559-585, February.
    20. N.M. Hung & N.V. Quyen, 2006. "Toward Sustainability: Technology Transition and Endogenous Population Growth," Cahiers de recherche 0601, Université Laval - Département d'économique.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jpbect:v:23:y:2021:i:4:p:691-709. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/apettea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.