Reduction of the mathematical model of some problems of mathematical economics to systems of differential equations that can be solved in quadratures
https://doi.org/10.22405/2226-8383-2024-25-3-187-200
Abstract
The article discusses the problems associated with the Ramsey — Kass — Koopmans mathematical model of economic growth. An auxiliary system of differential equations is being constructed, for which it is possible to obtain a solution in quadratures. Based on the obtained solution, the upper estimates of the consumption function are found. Using the upper estimates of the consumption function, we find the maximum value of the time interval in which there are solutions to the auxiliary system of differential equations for the considered parameter values.
Under a special initial condition, we show that there is a solution to the Cauchy problem (𝐾(𝑡), 𝐶(𝑡)) on the entire ray 𝑡 ∈ [0;+∞) and both components increase and tend to the values we found.
About the Authors
Artem Ivanovich Kozko
Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics
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 Presidential Academy of National Economy and Public Administration
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
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Review
For citations:
Kozko A.I., Luzhina L.M., Popov A.Yu., Chirskii V.G. Reduction of the mathematical model of some problems of mathematical economics to systems of differential equations that can be solved in quadratures. Chebyshevskii Sbornik. 2024;25(3):187-200. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-3-187-200
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