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Regularity and stability of equilibria in an overlapping generations model with exogenous growth

Author

Listed:
  • MERTENS, Jean-François

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • RUBINCHIK, Anna

Abstract

In an exogenous-growth economy with overlapping generations (OG) we analyse local stability of the balanced growth equilibria with respect to perturbations of consumption endowments, thought of as the "monetised" value of a government policy to individuals. We show that perturbed economies have a unique equilibium in the neighbourhood, that the equilibrium allocation expressed in terms of efficient labour units is Fréchet differentiable in L? with derivatives given by kernels, and that the equilibrium is stable in the sense that if perturbations converge to 0 at ±?, the corresponding equilibria converge back to the unperturbed equilibrium at ±?. As a corollary this implies a proof of non-vacuity of the main result in Mertens and Rubinchik (2006).

Suggested Citation

  • MERTENS, Jean-François & RUBINCHIK, Anna, 2009. "Regularity and stability of equilibria in an overlapping generations model with exogenous growth," LIDAM Discussion Papers CORE 2009005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2009005
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2009.html
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    Citations

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    Cited by:

    1. 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.
    2. Mertens, Jean-François & Rubinchik, Anna, 2019. "Regularity And Stability Of Equilibria In An Overlapping Generations Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 23(2), pages 699-729, March.
    3. Mertens, Jean-François & Rubinchik, Anna, 2012. "Intergenerational Equity And The Discount Rate For Policy Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 16(1), pages 61-93, February.
    4. Mertens, Jean-Francois & Rubinchik, Anna, "undated". "Banach Families And The Implicit Function Theorem," Working Papers WP2011/6, University of Haifa, Department of Economics.
    5. Mertens, Jean-François & Rubinchik, Anna, 2014. "Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 187-196.
    6. Jean-François Mertens & Anna Rubinchik, 2013. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 537-595, November.

    More about this item

    Keywords

    regularity of infinite economies; policy evaluation; overlapping generations; exogenous growth; intergenerational fairness; utilitarianism; relative utilitarianism;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • H43 - Public Economics - - Publicly Provided Goods - - - Project Evaluation; Social Discount Rate

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