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

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We develop easy-to-verify conditions assuring that comparative statics in a general equilibrium model where time is a real line is feasible, i.e., the implicit function theorem is applicable. Consider an equilibrium equation, $Upsilon(k,E)=k$ 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 the equilibrium map $Upsilon$ and the requirement that the Fourier transform of the derivative of the map $Upsilon$ with respect to the equilibrium variable 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.

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  • Rubinchik, Anna & Gorokhovsky, Alexander, "undated". "Regularity of a general equilibrium in a model with infinite past and future," Working Papers WP2017/1, University of Haifa, Department of Economics.
  • Handle: RePEc:haf:huedwp:wp201701
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    1. 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.
    2. d'Albis, Hippolyte, 2007. "Demographic structure and capital accumulation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 411-434, January.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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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