IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2509.19019.html
   My bibliography  Save this paper

Existence and Calculation of Optimal Equilibria on Overlapping Generations Economies

Author

Listed:
  • Leandro Lyra Braga Dognini

Abstract

A well-known feature of overlapping generations economies is that the First Welfare Theorem fails and equilibrium may be inefficient. The Cass (1972) criterion furnishes a necessary and sufficient condition for efficiency, but does not address the matter of existence of efficient equilibria, and Cass, Okuno, and Zilcha (1979) provide nonexistence examples. I develop an algorithm based on successive approximations of a nonstationary, consumption-loan, prone to savings, overlapping generations economy with finite-lived heterogeneous agents to find elements of its set of equilibria as the limit of nested compact sets. These compact sets are the result of a backward calculation through equilibrium equations that departs from the set of Pareto optimal equilibria of well-behaved tail economies. The equilibria calculated through this algorithm satisfy the Cass (1972) criterion and are used to derive the existence results on efficient equilibria.

Suggested Citation

  • Leandro Lyra Braga Dognini, 2025. "Existence and Calculation of Optimal Equilibria on Overlapping Generations Economies," Papers 2509.19019, arXiv.org.
    • Handle: RePEc:arx:papers:2509.19019
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2509.19019
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benveniste, Lawrence M & Cass, David, 1986. "On the Existence of Optimal Stationary Equilibria with a Fixed Supply of Fiat Money: I. The Case of a Single Consumer," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 402-417, April.
    2. Rao Aiyagari, S. & Peled, Dan, 1991. "Dominant root characterization of Pareto optimality and the existence of optimal equilibria in stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 54(1), pages 69-83, June.
    3. David Cass & Menahem E. Yaari, 1966. "A Re-examination of the Pure Consumption Loans Model," Journal of Political Economy, University of Chicago Press, vol. 74(4), pages 353-353.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. 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.
    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. 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.
    2. Labadie, Pamela, 2009. "Anonymity and individual risk," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2440-2453, November.
    3. Chattopadhyay, Subir, 2018. "The unit root property and optimality with a continuum of states—Pure exchange," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 105-118.
    4. 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.
    5. Mark Pingle & Leigh Tesfatsion, 1993. "``Active Intermediation in a Monetary Overlapping Generations Economy''," Macroeconomics 9312001, University Library of Munich, Germany, revised 04 Dec 1993.
    6. 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.
    7. Tomohiro Hirano & Alexis Akira Toda, 2025. "Bubble Necessity Theorem," Journal of Political Economy, University of Chicago Press, vol. 133(1), pages 111-145.
    8. Ghiglino, Christian & Tvede, Mich, 1995. "No-trade and uniqueness of steady states," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 655-661, April.
    9. Barbie, Martin & Hagedorn, Marcus & Kaul, Ashok, 2000. "Dynamic Efficiency and Pareto Optimality in a Stochastic OLG Model with Production and Social Security," IZA Discussion Papers 209, Institute of Labor Economics (IZA).
    10. Chattopadhyay, Subir & Gottardi, Piero, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Journal of Economic Theory, Elsevier, vol. 89(1), pages 21-67, November.
    11. Gaetano Bloise & Filippo L. Calciano, 2007. "A Note On The Characterization Of Inefficiency In Stochastic Overlapping Generations Economies," Departmental Working Papers of Economics - University 'Roma Tre' 0083, Department of Economics - University Roma Tre.
    12. Philippe Weil, 2008. "Overlapping Generations: The First Jubilee," Journal of Economic Perspectives, American Economic Association, vol. 22(4), pages 115-134, Fall.
    13. Bernhard Felderer & Klaus Ritzberger, 1995. "Family allowances as welfare improvements," Journal of Economics, Springer, vol. 61(1), pages 11-33, February.
    14. Martin F. Hellwig, 2024. "Dynamic efficiency and inefficiency in a class of overlapping-generations economies with multiple assets," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2024_08, Max Planck Institute for Research on Collective Goods.
    15. Bertocchi, Graziella & Kehagias, Athanasios, 1995. "Efficiency and optimality in stochastic models with production," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 303-325.
    16. Pingle, Mark & Tesfatsion, Leigh, 1998. "Active Intermediation In Overlapping Generations Economies With Production And Unsecured Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 2(2), pages 183-212, June.
    17. Bryant, John, 1981. "Bank Collapse and Depression," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 13(4), pages 454-464, November.
    18. Gaetano Bloise & Pietro Reichlin, 2023. "Low safe interest rates: A case for dynamic inefficiency?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 633-656, December.
    19. Ken Urai & Hiromi Murakami, 2017. "Local Independence, Monotonicity, Incentive Compatibility and Axiomatic Characterization of Price-Money Message Mechanism," Discussion Papers in Economics and Business 17-08, Osaka University, Graduate School of Economics.
    20. Pingle, Mark & Tesfatsion, Leigh, 1998. "Active intermediation in a monetary overlapping generations economy1," Journal of Economic Dynamics and Control, Elsevier, vol. 22(10), pages 1543-1574, August.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2509.19019. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.