About the ideal economic situation - the growth of capital and the function of consumption in some models of economic growth
https://doi.org/10.22405/2226-8383-2023-24-2-256-265
Abstract
The article is devoted to the Ramsey — Kass — Koopmans economic growth model. We investigated the monotonicity of the functions 𝐶(𝑡) and 𝐾(𝑡) under a special initial condition.
Our results are obtained using an auxiliary system of differential equations, which is similar to the original system of differential equations arising in the case of constancy of the stationary rate of savings.
About the Authors
Artem Ivanovich Kozko
Lomonosov Moscow State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Lyubov Mikhailovna Luzhina
Lomonosov Moscow State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Anton Yurievich Popov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Vladimir Grigorievich Chirskii
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
References
1. Acemoglu, Daron. 2009, “The Neoclassical Growth Model. Introduction to Modern Economic Growth”, Princeton: Princeton University Press. pp. 287–326. ISBN 978-0-691-13292-1.
2. B´enassy, Jean-Pascal. 2011, “The Ramsey Model. Macroeconomic Theory”, New York: Oxford University Press. pp. 145–160. ISBN 978-0-19-538771-1.
3. Kozko A.I., Luzhina L.M., Popov A.Yu., Chirskii V.G. 2022, “The method of approximate solution of a system of differential equations from the Ramsey–Kass–Koopmans model, based on the solution in quadratures of one subclass of similar systems”, Chebyshevskii Sbornik. vol.23(4), September. pp. 115-125. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-115-125.
4. Kozko A.I., Luzhina L.M., Popov A.Yu., Chirskii V.G. 2019, “Optimal exponent in the Ramsey —Kass —Koopmans problem with logarithmic utility function”, Chebyshevskii Sbornik. vol. 20(4), September. pp. 197-207. (In Russ.) https://doi.org/10.22405/2226-8383-2018-20-4-197-207.
5. Kozko, A. I., Luzhina, L. M., Popov, A. Yu., Chirskii, V. G. 2020, “On the Ramsey — Kass —Koopmans problem for consumer choice”, Results of science and technology. Modern mathematics and its applications. Thematic review. vol. 182, September, pp. 39-44. (In Russ.) DOI: 10.36535/0233-6723-2020-182-39-44.
6. Kozko, A. I., Luzhina, L. M., Popov, A. Yu., Chirskii, V. G. 2019, The model of the problem Ramsey —Kass —Koopmans // Moscow state pedagogical University (Moscow). Classical and modern geometry, materials of the international conference dedicated to the 100th anniversary of V. T. Bazylev. under the editorship of A. V. Tsarev. Moscow. pp. 87-88.
7. Kozko A.I., Luzhina L.M., Popov A.Yu., Chirskii V.G. 2019, “Assessment of the necessary initial economic resource in the Ramsey —Kass —Koopmans problem”, Chebyshevskii Sbornik. vol. 20(4), September, pp. 188-196. (In Russ.) https://doi.org/10.22405/2226-8383-2018-20-4-188-196.
8. Kozko A.I., Luzhina L.M., Popov A.Yu., Chirskii V.G. 2022, “The consumption function in the Ramsey—-Kass—-Koopmans economic growth model in the case of a stationary saving function”, Chebyshevskii Sbornik. vol. 23(1), September, pp. 118-129. (In Russ.) https://doi.org/10.22405/2226-8383-2018-20-4-188-196.
9. Rahul, Giri. “Growth Model with Endogenous Savings: Ramsey —Cass —Koopmans Model”, 2018, https://gente.itam.mx/rahul.giri/uploads/1/1/3/6/113608/ramsey-cass-koopmans_model.pdf.
10. Barro, Robert J., Sala-i-Martin, Xavier. 2003, “Economic growth (2nd ed.)”, Massachusetts: MIT Press, ISBN 9780262025539.
11. Groth, Christian and Koch, Karl-Josef and Steger, Thomas Michael. 2006, “Rethinking the Concept of Long-Run Economic Growth (April 2006)”, CESifo Working Paper Series, no. 1701. Available at SSRN: https://ssrn.com/abstract=899250.
12. Groth, Christian and Koch, Karl-Josef and Steger, Thomas Michael. 2010, “When Economic Growth is Less than Exponential”, Economic Theory, vol. 44, no. 2, pp. 213-242.
13. Groth, C. 2010, “Chapter 10: The Ramsey Model”, Available at: http://web.econ.ku.dk/okocg/VV/VV-2010/Lecture%20notes/Ch7-2010-1.pdf.
14. Romer, D. 2006, “Advanced Macroeconomics. 3rd ed”, New York: McGraw-Hill/Irwin, pp. 651.
15. Robert J. Barro. 1999, “Ramsey Meets Laibson in the Neoclassical Growth Model”, The Quarterly Journal of Economics, Oxford University Press, vol. 114, no. 4, pp. 1125-1152.
16. King Robert, G., and Sergio Rebelo. 1993, “Transitional Dynamics and Economic Growth in the Neoclassical Model”, American Economic Review. vol. 83, September, pp. 908-931.
17. Pierre-Olivier, Gourinchas. 2014, “Notes for Econ202A: The Ramsey —Cass —Koopmans Model”, UC Berkeley Fall, https://eml.berkeley.edu/ webfac/gourinchas/e202a_f14/Notes_Ramsey_Cass_Koopmans_pog.pdf.
18. Eglit Y., Eglite K., Dudin V., Yurchenko E. 2022, “Consumption function and estimation of its parameters from experimental data”, Transport business in Russia. vol. 2, pp. 7-9.
Review
For citations:
Kozko A.I., Luzhina L.M., Popov A.Yu., Chirskii V.G. About the ideal economic situation - the growth of capital and the function of consumption in some models of economic growth. Chebyshevskii Sbornik. 2023;24(2):256-265. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-2-256-265
Views:
478
Email this article 