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 Trudy MIAN, 2010, Volume 271, Pages 278–298 (Mi tm3234)

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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 265–285

Bibliographic databases:

UDC: 517.977.52

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 MIAN, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 278–298; Proc. Steklov Inst. Math., 271 (2010), 265–285

Citation in format AMSBIB
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This publication is cited in the following articles:
1. A. M. Tarasyev, A. A. Usova, “Stabilizing the Hamiltonian system for constructing optimal trajectories”, Proc. Steklov Inst. Math., 277 (2012), 248–265
2. A. M. Tarasev, A. A. Usova, W. Wang, O. V. Russkikh, “Postroenie optimalnykh traektorii integrirovaniem gamiltonovoi dinamiki v modelyakh ekonomicheskogo rosta pri resursnykh ogranicheniyakh”, Tr. IMM UrO RAN, 20, no. 4, 2014, 258–276
3. Aleksandr M. Tarasev, Anastasiya A. Usova, Yuliya V. Shmotina, “Raschet prognoznykh traektorii razvitiya ekonomiki pri nalichii strukturnykh izmenenii”, MTIP, 8:3 (2016), 34–66
4. Tarasyev A.M. Usova A.A. Turygina V.F., “Structural Changes in Economic Growth Models”, IFAC PAPERSONLINE, 50:1 (2017), 4875–4880
5. Xue H., Zhang Sh.J., “Relationships Between Engineering Construction Standards and Economic Growth in the Construction Industry: the Case of China'S Construction Industry”, KSCE J. Civ. Eng., 22:5 (2018), 1606–1613
6. Tarasyev A. Usova A., “Robust Methods For Stabilization of Hamiltonian Systems in Economic Growth Models”, IFAC PAPERSONLINE, 51:32 (2018), 7–12
7. Aleksandr M. Tarasev, Anastasiya A. Usova, “Otsenka gladkoi approksimatsii proizvodstvennoi funktsii dlya integrirovaniya gamiltonovykh sistem”, MTIP, 12:1 (2020), 91–115
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