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Tr. Mat. Inst. Steklova, 2015, Volume 291, Pages 138–156 (Mi tm3666)  

Proportional economic growth under conditions of limited natural resources

A. V. Kryazhimskiyab, A. M. Tarasyevcd, A. A. Usovac, W. Wange

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b International Institute for Applied Systems Analysis, Laxenburg, Austria
c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
d Institute of Economics, The Ural Branch of Russian Academy of Sciences
e Center for Industrial Ecology, Department of Chemical Engineering, Tsinghua University, China

Abstract: The paper is devoted to economic growth models in which the dynamics of production factors satisfy proportionality conditions. One of the main production factors in the problem of optimizing the productivity of natural resources is the current level of resource consumption, which is characterized by a sharp increase in the prices of resources compared with the price of capital. Investments in production factors play the role of control parameters in the model and are used to maintain proportional economic development. To solve the problem, we propose a two-level optimization structure. At the lower level, proportions are adapted to the changing economic environment according to the optimization mechanism of the production level under fixed cost constraints. At the upper level, the problem of optimal control of investments for an aggregate economic growth model is solved by means of the Pontryagin maximum principle. The application of optimal proportional constructions leads to a system of nonlinear differential equations, whose steady states can be considered as equilibrium states of the economy. We prove that the steady state is not stable, and the system tends to collapse (the production level declines to zero) if the initial point does not coincide with the steady state. We study qualitative properties of the trajectories generated by the proportional development dynamics and indicate the regions of production growth and decay. The parameters of the model are identified by econometric methods on the basis of China's economic data.

Funding Agency Grant Number
Russian Science Foundation 14-18-00574
This work is supported by the Russian Science Foundation under grant 14-18-00574.


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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 291, 127–145

Bibliographic databases:

UDC: 517.977.52
Received: December 15, 2014

Citation: A. V. Kryazhimskiy, A. M. Tarasyev, A. A. Usova, W. Wang, “Proportional economic growth under conditions of limited natural resources”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 138–156; Proc. Steklov Inst. Math., 291 (2015), 127–145

Citation in format AMSBIB
\by A.~V.~Kryazhimskiy, A.~M.~Tarasyev, A.~A.~Usova, W.~Wang
\paper Proportional economic growth under conditions of limited natural resources
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 138--156
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 291
\pages 127--145

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