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Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies

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  • Olivier F. Morand

    (University of Connecticut)

  • Kevin L. Reffett

    (Arizona State University)

Abstract

In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in the the state space is unbounded. Important examples of such economies are single vector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are well known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and also present a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium.

Suggested Citation

  • Olivier F. Morand & Kevin L. Reffett, 2001. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Working papers 2001-02, University of Connecticut, Department of Economics.
    • Handle: RePEc:uct:uconnp:2001-02
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    References listed on IDEAS

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    1. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    2. Crettez, Bertrand & Morhaim, Lisa, 2012. "Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 197-206.
    3. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 505-523, November.
    4. Pierri, Damian Rene & Reffett, Kevin, 2021. "Memory, multiple equilibria and emerging market crises," UC3M Working papers. Economics 32871, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Yu, Meng & Zhang, Junnan, 2019. "Equilibrium in production chains with multiple upstream partners," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 1-10.
    6. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    7. Wozny Lukasz & Growiec Jakub, 2012. "Intergenerational Interactions in Human Capital Accumulation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-47, June.
    8. Morand, Olivier F. & Reffett, Kevin L., 2007. "Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 501-522, April.
    9. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation," Working Papers hal-00294828, HAL.
    10. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    11. Mathieu Taschereau-Dumouchel & Edouard Schaal, 2015. "Coordinating Business Cycles," 2015 Meeting Papers 178, Society for Economic Dynamics.
    12. Meng Yu & Junnan Zhang, 2019. "Equilibrium in Production Chains with Multiple Upstream Partners," Papers 1908.08208, arXiv.org.
    13. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(3), pages 807-835, August.
    14. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    15. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation," Discussion Papers 0803, University of Exeter, Department of Economics.
    16. 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.
    17. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
    18. Manjira Datta & Kevin Reffett & Łukasz Woźny, 2018. "Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 593-626, October.
    19. Kevin Reffett & Olivier Morand, "undated". "On the Existence and Characterization of Markovian Equilibrium in Models with Simple Non-paternalistic Altruism," Working Papers 2133478, Department of Economics, W. P. Carey School of Business, Arizona State University.
    20. 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.
    21. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    22. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    23. Guanlong Ren & John Stachurski, 2018. "Dynamic Programming with Recursive Preferences: Optimality and Applications," Papers 1812.05748, arXiv.org, revised Jun 2020.
    24. Manjira Datta & Leonard Mirman & Kevin Reffett, "undated". "Nonclassical Brock-Mirman Economies," Working Papers 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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