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Behavior of Stabilized Trajectories of a Two Factor Economic Growth Model Under the Changes of a Production Function Parameter

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1881))

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Abstract

Based on a two-factors economic growth model with a production function of a constant elasticity of substitution, the paper considers a control problem with the infinite time interval and analyzes its stabilized solutions, when the elasticity parameter changes. A qualitative analysis of a Hamiltonian system reveals an existence of a saddle steady state, which continuously depends on the elasticity coefficient. In the domain containing the steady state, the stabilization of a Hamiltonian system is performed, and solutions of the stabilized system are numerically constructed. Varying the elasticity coefficients of CES-production function, these solutions undergo changes. The paper shows that for a limit value of the elasticity parameter, when a production function turns into the Cobb-Douglas production function, corresponding stabilized solutions converge to the limit case associated with the Cobb-Douglas function. Numerical experiments support the theoretical conclusions.

The research of the first author, Anastasiia A. Usova, is supported by the Russian Science Foundation (Project No. 19-11-00105), https://rscf.ru/project/19-11-00105/.

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Acknowledgements

The research of the first author, Anastasiia A. Usova, is supported by the Russian Science Foundation (Project No. 19-11-00105), https://rscf.ru/project/19-11-00105/.

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Authors and Affiliations

  1. N.N. Krasovskii Institute of Mathematics and Mechanics UbRAS, 16 S.Kovalevskaya str., Yekaterinburg, 620990, Russia

    Anastasiia A. Usova & Alexander M. Tarasyev

  2. Ural Fedelal University, 19 Mira str., Yekaterinburg, 620002, Russia

    Alexander M. Tarasyev

Authors
  1. Anastasiia A. Usova
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  2. Alexander M. Tarasyev
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Corresponding author

Correspondence to Anastasiia A. Usova .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. Sobolev Institute of Mathematics, Omsk, Russia

    Anton Eremeev

  4. Melentiev Energy Systems Institute, Irkutsk, Russia

    Oleg Khamisov

  5. Institute of Applied Mathematical Research, Petrozavodsk, Russia

    Vladimir Mazalov

  6. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Usova, A.A., Tarasyev, A.M. (2023). Behavior of Stabilized Trajectories of a Two Factor Economic Growth Model Under the Changes of a Production Function Parameter. In: Khachay, M., Kochetov, Y., Eremeev, A., Khamisov, O., Mazalov, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2023. Communications in Computer and Information Science, vol 1881. Springer, Cham. https://doi.org/10.1007/978-3-031-43257-6_25

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  • DOI: https://doi.org/10.1007/978-3-031-43257-6_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43256-9

  • Online ISBN: 978-3-031-43257-6

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