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An Economic Model for OECD Economies with Truncated M -Derivatives: Exact Solutions and Simulations

Author

Listed:
  • Luis A. Quezada-Téllez

    (Departamento de Física y Matemáticas, Universidad Iberoamericana, Mexico City 01219, Mexico)

  • Guillermo Fernández-Anaya

    (Departamento de Física y Matemáticas, Universidad Iberoamericana, Mexico City 01219, Mexico)

  • Dominique Brun-Battistini

    (Departamento de Física y Matemáticas, Universidad Iberoamericana, Mexico City 01219, Mexico)

  • Benjamín Nuñez-Zavala

    (Departamento de Física y Matemáticas, Universidad Iberoamericana, Mexico City 01219, Mexico)

  • Jorge E. Macías-Díaz

    (Department of Mathematics and Didactics of Mathematics, Tallinn University, 10120 Tallinn, Estonia
    Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico)

Abstract

This article proposes two conformal Solow models (with and without migration), accompanied by simulations for six Organisation for Economic Co-operation and Development economies. The models are proposed by employing suitable Inada conditions on the Cobb–Douglas function and making use of the truncated M -derivative for the Mittag–Leffler function. In the exact solutions derived in this manuscript, two new parameters play an important role in the convergence towards, or the divergence from, the steady state of capital and per capita product. The economical dynamics of these nations are influenced by the intensity of the capital and labor factors, as well as the level of depreciation, the labor force rate and the level of saving.

Suggested Citation

  • Luis A. Quezada-Téllez & Guillermo Fernández-Anaya & Dominique Brun-Battistini & Benjamín Nuñez-Zavala & Jorge E. Macías-Díaz, 2021. "An Economic Model for OECD Economies with Truncated M -Derivatives: Exact Solutions and Simulations," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1780-:d:602932
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    References listed on IDEAS

    as
    1. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    2. Barossi-Filho, Milton & Goncalves Silva, Ricardo & Diniz, Eliezer Martins, 2005. "The empirics of the Solow Growth Model: Long-term evidence," Journal of Applied Economics, Universidad del CEMA, vol. 8(01), pages 1-21, May.
    3. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    4. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    5. Milton Barossi-Filho & Ricardo Gonçalves Silva & Eliezer Martins Diniz, 2005. "The Empirics of the Solow Growth Model: Long-Term Evidence," Journal of Applied Economics, Taylor & Francis Journals, vol. 8(1), pages 31-51, May.
    6. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    7. Elvio Accinelli & Juan Gabriel Brida, 2005. "Re-formulation of the Solow economic growth model whit the Richards population growth law," GE, Growth, Math methods 0508006, University Library of Munich, Germany.
    8. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Nicolò Cangiotti & Mattia Sensi, 2023. "Exact solutions for a Solow-Swan model with non-constant returns to scale," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(4), pages 1278-1285, December.

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