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Optimal Economic Growth Problem

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We study the optimal economic growth model based on the controlled Kaldor businesscycle model and formulated as an infinite-horizon optimal control problem. We show that the original problem is approximated by standard problems on finite intervals and obtain conditions guaranteeing that the Pontryagin maximum principle for the problem under consideration holds in the normal form with explicitly given adjoint variable.

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References

  1. A. S. Aseev, “Optimal stationary regimes in Kaldor’s business cycle controlled model,” Math Models Comput. Simul. 11, 750-758 (2019). https://doi.org/https://doi.org/10.1134/S2070048219050028

    Article  MathSciNet  MATH  Google Scholar 

  2. H.-W. Lorenz, Nonlinear Dynamical Economics and Chaotic Motion, Springer, Berlin etc. (1993).

    Book  MATH  Google Scholar 

  3. A. F. Filippov, Differential equations with Discontinuous Right-Hand Sides, Kluwer, Dordrecht (1988).

    Book  MATH  Google Scholar 

  4. D. Acemoglu, Introduction to Modern Economic Growth, Princeton Univ. Press, Princeton (2008).

    MATH  Google Scholar 

  5. R. J. Barro and X. Sala-i-Martin, Economic Growth, McGraw Hill, New York (1995).

    MATH  Google Scholar 

  6. M. J. Weitzman, Income, Wealth, and the Maximum Principle, Harvard Univ. Press, Cambridge, MA (2003).

    Book  MATH  Google Scholar 

  7. D. A. Carlson, A. B. Haurie, and A. Leizarowitz, Infinite Horizon Optimal Control: Deterministic and Stochastic Systems, Springer, Berlin (2011).

    MATH  Google Scholar 

  8. A. F. Filippov, “On some questions of optimal control” [in Russian], Vestn. Mosk. Univ., Ser. Matr. Mekh. Astron. Fiz. Khim. 14, No. 2, 25–32 (1959).

  9. L. Cesari, Optimization — Theory and Applications. Problems with Ordinary Differential Equations., Springer, New York etc. (1983).

  10. S. M. Aseev and A. V. Kryazhimskii, “The Pontryagin maximum principle and optimal economic growth problems,” Proc. Steklov Inst. Math. 257, 1–255 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  11. L. S. Pontryagin, V. S. Boltyanskij, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Pergamon Press, Oxford etc. (1964).

    MATH  Google Scholar 

  12. F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York (1983).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, 1 Leninskie Gory, Moscow, 119991, Russia

    A. S. Aseev

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  1. A. S. Aseev
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Correspondence to A. S. Aseev.

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Translated from Problemy Matematicheskogo Analiza 125, 2023, pp. 37-45.

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Aseev, A.S. Optimal Economic Growth Problem. J Math Sci 276, 37–47 (2023). https://doi.org/10.1007/s10958-023-06723-4

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  • DOI: https://doi.org/10.1007/s10958-023-06723-4

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