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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 278–298 (Mi tm3234)  

This article is cited in 21 scientific papers (total in 21 papers)

Construction of a regulator for the Hamiltonian system in a two-sector economic growth model

A. M. Tarasyev, A. A. Usova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
References:
Abstract: We consider an optimal control problem of investment in the capital stock of a country and in the labor efficiency. We start from a model constructed within the classical approaches of economic growth theory and based on three production factors: capital stock, human capital, and useful work. It is assumed that the levels of investment in the capital stock and human capital are endogenous control parameters of the model, while the useful work is an exogenous parameter subject to logistic-type dynamics. The gross domestic product (GDP) of a country is described by a Cobb–Douglas production function. As a utility function, we take the integral consumption index discounted on an infinite time interval. To solve the resulting optimal control problem, we apply dynamic programming methods. We study optimal control regimes and examine the existence of an equilibrium state in each regime. On the boundaries between domains of different control regimes, we check the smoothness and strict concavity of the maximized Hamiltonian. Special focus is placed on a regime of variable control actions. The novelty of the solution proposed consists in constructing a nonlinear stabilizer based on the feedback principle. The properties of the stabilizer allow one to find an approximate solution to the original problem in the neighborhood of an equilibrium state. Solving numerically the stabilized Hamiltonian system, we find the trajectories of the capital of a country and labor efficiency. The solutions obtained allow one to assess the growth rates of the GDP of the country and the level of consumption in the neighborhood of an equilibrium position.
Received in July 2010
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 271, Pages 265–285
DOI: https://doi.org/10.1134/S008154381004019X
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
Language: Russian
Citation: A. M. Tarasyev, A. A. Usova, “Construction of a regulator for the Hamiltonian system in a two-sector economic growth model”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 278–298; Proc. Steklov Inst. Math., 271 (2010), 265–285
Citation in format AMSBIB
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\by A.~M.~Tarasyev, A.~A.~Usova
\paper Construction of a~regulator for the Hamiltonian system in a~two-sector economic growth model
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 278--298
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 271
\pages 265--285
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  • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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