Geodesic
Reduction of the mathematical model of some problems of mathematical economics to systems of differential equations that can be solved in quadratures
Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 187-200 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $t\in [0;+\infty)$ and both components increase and tend to the values we found.
Keywords: mathematical model, Ramsey — Kass — Koopmans problem, monotony of the function of saving and capital, competitive households, stationary savings rate. 
@article{CHEB_2024_25_3_a11,
     author = {A. I. Kozko and L. M. Luzhina and A. Yu. Popov and V. G. Chirskii},
     title = {Reduction of the mathematical model of some problems of mathematical economics to systems of differential equations that can be solved in quadratures},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {187--200},
     year = {2024},
     volume = {25},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_3_a11/}
}
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A. I. Kozko; L. M. Luzhina; A. Yu. Popov; V. G. Chirskii. Reduction of the mathematical model of some problems of mathematical economics to systems of differential equations that can be solved in quadratures. Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 187-200. http://geodesic.mathdoc.fr/item/CHEB_2024_25_3_a11/