IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1712.09605.html
   My bibliography  Save this paper

Accelerators in macroeconomics: Comparison of discrete and continuous approaches

Author

Listed:
  • Valentina V. Tarasova
  • Vasily E. Tarasov

Abstract

We prove that the standard discrete-time accelerator equation cannot be considered as an exact discrete analog of the continuous-time accelerator equation. This leads to fact that the standard discrete-time macroeconomic models cannot be considered as exact discretization of the corresponding continuous-time models. As a result, the equations of the continuous and standard discrete models have different solutions and can predict the different behavior of the economy. In this paper, we propose a self-consistent discrete-time description of the economic accelerators that is based on the exact finite differences. For discrete-time approach, the model equations with exact differences have the same solutions as the corresponding continuous-time models and these discrete and continuous models describe the same behavior of the economy. Using the Harrod-Domar growth model as an example, we show that equations of the continuous-time model and the suggested exact discrete model have the same solutions and these models predict the same behavior of the economy.

Suggested Citation

  • Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Accelerators in macroeconomics: Comparison of discrete and continuous approaches," Papers 1712.09605, arXiv.org.
    • Handle: RePEc:arx:papers:1712.09605
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1712.09605
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tarasov, Vasily E., 2015. "Lattice fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 12-33.
    2. Vasily E. Tarasov & Valentina V. Tarasova, 2016. "Long and Short Memory in Economics: Fractional-Order Difference and Differentiation," Papers 1612.07903, arXiv.org, revised Aug 2017.
    3. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    2. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
    3. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vasily E. Tarasov & Valentina V. Tarasova, 2017. "Accelerators in Macroeconomics: Comparison of Discrete and Continuous Approaches," American Journal of Economics and Business Administration, Science Publications, vol. 9(3), pages 47-55, November.
    2. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    3. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Economic Growth Model with Constant Pace and Dynamic Memory," Papers 1701.06299, arXiv.org, revised Apr 2019.
    4. Valentina V. Tarasova & Vasily E. Tarasov, 2016. "Fractional Dynamics of Natural Growth and Memory Effect in Economics," Papers 1612.09060, arXiv.org, revised Jan 2017.
    5. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
    6. Vasily E. Tarasov, 2020. "Exact Solutions of Bernoulli and Logistic Fractional Differential Equations with Power Law Coefficients," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    7. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Dynamic intersectoral models with power-law memory," Papers 1712.09087, arXiv.org.
    8. Nosrati, Komeil & Shafiee, Masoud, 2018. "Fractional-order singular logistic map: Stability, bifurcation and chaos analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 224-238.
    9. Ahmed Alsaedi & Ravi P. Agarwal & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "Fractional-Order Integro-Differential Multivalued Problems with Fixed and Nonlocal Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    10. Michelitsch, T.M. & Collet, B.A. & Riascos, A.P. & Nowakowski, A.F. & Nicolleau, F.C.G.A., 2016. "A fractional generalization of the classical lattice dynamics approach," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 43-50.
    11. Tarasov, V.E., 2021. "Nonlinear fractional dynamics with Kicks," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    12. Vasily E. Tarasov, 2024. "Exact Finite-Difference Calculus: Beyond Set of Entire Functions," Mathematics, MDPI, vol. 12(7), pages 1-37, March.
    13. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    14. Vasily E. Tarasov, 2021. "Integral Equations of Non-Integer Orders and Discrete Maps with Memory," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    15. Vasily E. Tarasov, 2021. "General Fractional Dynamics," Mathematics, MDPI, vol. 9(13), pages 1-26, June.
    16. Vasily E. Tarasov, 2016. "Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations," Mathematics, MDPI, vol. 4(3), pages 1-13, June.
    17. Vasily E. Tarasov, 2015. "Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series," Journal of Mathematics, Hindawi, vol. 2015, pages 1-8, November.
    18. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    19. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    20. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1712.09605. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.