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The effect of externality on the transitional dynamics: the case of Lucas model

Author

Listed:
  • Constantin Chilarescu

    (University of Lille)

Abstract

The main aim of this paper was to provide a closed-form solution to the model of Lucas with externalities and to prove that this solution is unique. The method we proposed enables us to determine the unknown starting values of the control variables and to obtain the optimal trajectories of all variables of the system.

Suggested Citation

  • Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    • Handle: RePEc:ebl:ecbull:eb-18-00196
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    File URL: http://www.accessecon.com/Pubs/EB/2018/Volume38/EB-18-V38-I3-P157.pdf
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    References listed on IDEAS

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    1. Rodolfo E. Manuelli & Ananth Seshadri, 2014. "Human Capital and the Wealth of Nations," American Economic Review, American Economic Association, vol. 104(9), pages 2736-2762, September.
    2. Bella, Giovanni & Mattana, Paolo, 2014. "Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov–Takens bifurcation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 69-79.
    3. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
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    5. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2012. "Homoclinic Bifurcation and Global Indeterminacy of Equilibrium in a Two-Sector Endogenous Growth Model," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 427-451, Springer.
    6. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
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    9. Manash Ranjan Gupta & Bidisha Chakraborty, 2007. "Uniqueness And Indeterminacy Of The Equilibrium Growth Path In The Uzawa‐Lucas Model With Sector Specific Externalities," The Japanese Economic Review, Japanese Economic Association, vol. 58(3), pages 400-406, September.
    10. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas–Uzawa model," Economic Modelling, Elsevier, vol. 28(1), pages 109-117.
    11. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    12. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    13. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    14. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 28(1-2), pages 109-117, January.
    15. C. Chilarescu & I. Viasu, 2019. "Uniqueness and Multiple Trajectories for the Case of Lucas Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1157-1177, October.
    16. Bella, Giovanni & Mattana, Paolo & Venturi, Beatrice, 2017. "Shilnikov chaos in the Lucas model of endogenous growth," Journal of Economic Theory, Elsevier, vol. 172(C), pages 451-477.
    17. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. Constantin Chilarescu, 2019. "Closed form solutions of Lucas Uzawa model with externalities via partial Hamiltonian approach. Some Clarifications," Papers 1907.12623, arXiv.org.

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    More about this item

    Keywords

    endogenous growth model; externality effect; optimal solution; transitional dynamics.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

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