• Vasyl Hryhorkiv
  • Mariia Hryhorkiv



modeling, two-sector economy, dynamics, utilization.


Today the economy as an object of research cannot be considered separately without ecology, since anthropogenic impact on the environment is getting more and more powerful not only in certain regions, but also on a planetary scale. Greening the economy is becoming especially urgent and is associated with the development of new resource-saving and environmental technologies, preserving natural potential and reducing the level of environmental pollution, raising the level of environmental education and culture in society, ensuring the environmental quality and safety of human life, etc.
The purpose of this research is to develop a conceptual approach to modeling ecologically and socially balanced economy, in which the production of the main aggregate products, utilization of pollution products of industrial and non-industrial pollution nature, and pollution control are exercised.
The task of the work is to build models of ecological and economic dynamics, the trajectories of which have the corresponding socio-economic characteristics of a clustered, in the economic sense, society and are acceptable for the ecological economy.
The methodology research includes principles, conceptual approaches and methods for constructing and analyzing differential models of economic and ecological-economic dynamics.
The results of the work related to the developed dynamic model of a two-sector ecological economy, in which one sector produces the main aggregate product and the second sector utilizes pollution products, are created by the producers of the first sector and the societal life. The model admits a number of modifications, allows to classify them as a separate class of models of ecological and economic dynamics. Models of this class are formalized in the space of socio-economic and environmental variables, which include liquid savings of production owners (producers) and workers employed in both sectors of the economy, prices for basic products, tariffs for utilization of pollution, volumes of environmental pollution.

How to quote:

Grigorkiv VS, Grigorkiv MV Dynamic models of two-sector ecological economy in the case of linear behavioral functions of its subjects. Scientific notes of the National University "Ostroh Academy". Series "Economics": a scientific journal. Ostrog: NaUOA Publishing House, March 2021. № 20 (48). Pp. 141–146.

Formulas: 16; fig .: 0; tab .: 0; bibl .:.


1. Forrester J. World dynamics. Moscow: Nauka, 1978. 168 p.
Forrester, Dzh. (1978). World dynamics. M, Science, 168 p. [in Russian].
2. Meadows D. H., Meadows D. L., Randers J. Beyond growth: uch. pos. Moscow: Progress, Pangea, 1994.
304 s.
Meadows D.H., Meadows D.L., Randers J. (1994). Beyond growth. Uch. pos. M.: Progress,
Pangea, 1994. 304 p. [in Russian].
3. Leontiev VV, Ford D. Cross-sectoral analysis of the impact of economic structure on the environment.
Economics and mathematical methods. Moscow. 1972. T. 8. № 3. S. 370–400.
Leont'ev, VV, Ford, D. (1972). Interdisciplinary analysis of the influence of economic structure on the environment
Mezhotraslevoj analiz vlijanija struktury jekonomiki na okruzhajushhuju sredu [Economics and Mathematical
Methods], vol. 3, pp. 370-400. [in Russian].
4. Moiseev NN Modern anthropogenesis and civilizational faults. Ecological and political analysis. Moscow: MNEPU, 1994. 47 p.
Moiseev NN (1994). Modern anthropogenesis and civilizational faults. Jekologopolitologicheskij analiz.
[Modern anthropogenesis and civilizational faults. Ecological and political analysis] M.: MNJePU, 47 s. [in Russian].
5. The concept of mathematical support of new information technologies for the assessment of environmental solutions / Lotov AV, Petrov AA, Pospelov IG, Shananin AA Moscow: Pereslavl-Zalessky, 1990. 61 p.
Lotov AV, Petrov AA, Pospelov IG, Shananin AA (1990). Koncepcija matematicheskogo obespechenija novyh
informacionnyh tehnologij ocenki jekologicheskih reshenij [The concept of mathematical support for new information
technologies for assessing environmental solutions]. Moscow-Pereslav'-Zalessky, 61 p. [in Russian].
6. Lyashenko IN, Mikhalevich MV, Uteuliev NU Methods of ecological and economic modeling. Nukus: Bilim, 1994. 236 p.
Lyashenko, IN, Mihalevich, MV, Uteuliev, NU (1994). Metody jekologo-jekonomicheskogo modelirovanija
[Methods of the eco-economic modeling]. Nukus,: Bilim, 236 p. [in Russian].
7. Lyashenko IM Economic and mathematical methods and models of sustainable development. Kyiv: Higher School, 1999. 236 p.
Lyashenko IM (1999). Ekonomiko-matematychni metody ta modeli stalogo rozvytku [Economic and mathematical
methods and models of sustainable development]. K.: Vyshha shkola, 236 s. [in Ukrainian].
8. Onishchenko AM Modeling of ecological and economic interaction in the process of implementing the decisions of Kyoto
protocol: monograph. Poltava: Poltava writer, 2011. 398 p.
Onyschenko, А.М. (2011). Modeliuvannia ekoloho-ekonomichnoi vzaiemodii v protsesi vykonannia rishen '
Kiots'koho protokolu: [monohrafiia] [Modeling of ecologic-economic interaction in the process of implementation
decisions of Kyoto Protocol]. Poltava writer, Poltava, 398 p. [in Ukrainian].
9. Kuzubov MV, Edinak OM, Ovander NL Modeling of economic and ecological-economic processes.
Kyiv: KSU, 2010. 170 p.
Kuzubov MV, Yedynak OM, Ovander NL (2010). Modeling of economic and ecological-economic
protsesiv [Modeling of economic and ecological-economic processes]. K.: KSU, 170 s. [in Ukrainian].
10. Buyak LM Mathematical models of general economic dynamics taking into account socio-economic
clustering: a monograph. Chernivtsi: Chernivtsi National University University, 2016. 392 p.
Buiak L.M. (2016). Matematychni modeli zahal'noi ekonomichnoi dynamiky z urakhuvanniam sotsial'noekonomichnoi klasteryzatsii: monohrafiia [Mathematical models of general economic dynamics taking into account
socio-economic clustering: monograph]. Chernivtsi: Chernivets'kyj nats. un-t, 392 p. [in Ukrainian].

Ліцензія Creative Commons

This magazine is licensed under a Creative Commons Attribution-Noncommercial 4.0 International License.

The texts of the journal's articles are checked with the help of an anti-plagiarist





Mathematical modeling and information technologies in economics