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Regularity of a general equilibrium in a model with infinite past and future

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  • Gorokhovsky, Alexander
  • Rubinchik, Anna
Abstract
We develop easy-to-verify conditions to assure that a comparative statics exercise in a dynamic general equilibrium model is feasible, i.e., the implicit function theorem is applicable. Consider an equilibrium equation, ϒ(k,E)=k of a model where an equilibrium variable (k) is a continuous bounded function of time, real line, and the policy parameter (E) is a locally integrable function of time. The key conditions are time invariance of ϒ and the requirement that the Fourier transform of the derivative of ϒ with respect to k does not return unity. Further, in a general constant-returns-to-scale production and homogeneous life-time-utility overlapping generations model we show that the first condition is satisfied at a balanced growth equilibrium and the second condition is satisfied for “almost all” policies that give rise to such equilibria.

Suggested Citation

  • Gorokhovsky, Alexander & Rubinchik, Anna, 2018. "Regularity of a general equilibrium in a model with infinite past and future," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 35-45.
    • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:35-45
    DOI: 10.1016/j.jmateco.2017.10.006
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    1. 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.
    2. d'Albis, Hippolyte, 2007. "Demographic structure and capital accumulation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 411-434, January.
    3. 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.
    4. Burke, Jonathan L., 1990. "A benchmark for comparative dynamics and determinacy in overlapping-generations economies," Journal of Economic Theory, Elsevier, vol. 52(2), pages 268-303, December.
    5. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
    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.
    7. S. Demichelis & H. Polemarchakis, 2007. "The determinacy of equilibrium in economies of overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 461-475, September.
    8. Jochen Mierau & Stephen Turnovsky, 2014. "Demography, growth, and inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 29-68, January.
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    Cited by:

    1. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).

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    More about this item

    Keywords

    Overlapping generations; Implicit function theorem; Determinacy; Time-invariance; Comparative statics;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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