Ramsey’s growth model
DOI:
https://doi.org/10.5564/jimdt.v5i1.3315Keywords:
Hamiltonian function, utility function, steady-state values, production function, Jacobian matrixAbstract
The objective of this study is to utilize the Ramsey-Cass-Koopmans (RCK) model within a closed economy framework. We utilize a fundamental RCK model and incorporate the steady state condition of the dynamic model by employing matrix eigenvalues. The dynamic model analyzes the utilization of data from the period of 1995-2021, taking into account the production function and population growth. To maximize well-being, it is necessary for capital to be 3 times its current level, while the production amount should be increased by 1.6 times.
Рамсейн өсөлтийн загвар
Энэхүү судалгааны ажлаар хаалттай эдийн засаг дахь Ramsey-Cass-Koopmans (RCK) нарын загварыг ашиглахыг зорилоо. Бид RCK нарын үндсэн загварыг ашигласан ба нэмэлтээр матрицын хувийн утгуудыг ашиглан тогтвортой төлөвийн динамик загвар нь асимптот тогтвортой эсэхийг шалгах нөхцөлийг тусгасан. Тодорхойлсон динамик загварууд нь асимптот тогтвортой эсэхийг 1995-2021 оны статистикийн тоон мэдээлэл, үйлдвэрийн функц болон хүн амын өсөлтийн үнэлгээг ашиглан шалгасан. Шинжилгээний үр дүнд Монголын эдийн засгийн хувьд нийгмийн сайн сайхан байдалд хүргэх максимум хэрэглээг хангахын тулд капиталын хэмжээг 3 дахин, үйлдвэрлэлийн хэмжээг 1.6 дахин нэмэгдүүлэх шаардлагатай байна.
Түлхүүр үгс: Ханамжийг максимумчлах, Гамильтоны функц, тогтвортой төлөв, үйлдвэрлэлийн функцийн үнэлгээ, Жаковын матриц
57
References
F. P. Ramsey, “A Mathematical Theory of Saving,” The Economic Journal, Vol. 38, no. 152, Dec., pp. 543-559, 2002, doi: https://doi.org/10.2307/2224098.
R. M. Solow, “A Contribution to the Theory of Economic Growth,” The Quarterly Journal of Economics, Vol. 70, no. 1, Feb., pp. 65-64, 1956, doi: https://doi.org/10.2307/1884513.
D. Cass, “Optimum Growth in an Aggregative Model of Capital Accumulation,” The Review of Economic Studies, Vol. 32, no. 3, July., pp. 233-240, 1965, doi: https://doi.org/10.2307/2295827.
T. C. Koopmans, “On the concept of optimal economic growth,” The Econometric Approach to Development Planning. North-Holland, Amsterdam, 1965.
T. Smith, Models in Ecology, Cambridge University Press: Cambridge, 1974.
J. G. Brida and E. Accinelli, “Тhe Ramsey model with logistic population growth,” Economics Bulletin, Vol.3, no.15, pp.1-8, 2007.
O. Bundau and M. Neamtu, “Optimal conditions for the control problem associated to a Ramsey model with endogenous population,” Recent Advances in Mathematics and Computers in Business, Economics, Biology and Chemistry, pp.175-180, 2010.
C. Budnyam and Ts. Batsukh, Theory and application of production function, Ulaanbaatar, 1997.
J. W. Pratt, “Risk aversion in the small and in the large,” Econometric, Vol.32, pp.122-136, 1964, doi: https://doi.org/10.2307/1913738.
K. C. Cheng, “Growth and recovery in Mongolia during transition,” IMF Working Paper, pp.1-26, 2003, doi: https://doi.org/10.5089/9781451875133.001.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Ankhbayar Chuluunbaatar
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The authors grant the Journal of Institute of Mathemathics and Digital Technology a license to publish the article and identify itself as the original publisher.
Articles in the Journal of Institute of Mathemathics and Digital Technology are Open Access articles published under a Creative Commons Attribution-NonCommercial 4.0 International License - CC BY NC.
This license permits NonComericial use, distribution and reproduction in any medium, provided the original work is properly cited.
