DOI: https://doi.org/10.15587/1729-4061.2019.170516

Algorithmizing the methods of basis matrices in the study of balace intersectoral ecological and economic models

Volodymyr Kudin, Andriy Onyshchenko, Igor Onyshchenko

Abstract


Ecological-economic models (such as Leontiev-Ford) play a special role in solving the fundamental problems of long-term planning, taking into account the factor of environmental management. On their basis, the task of justifying the magnitude of the costs of environmental protection can be implemented, considering the socio-economic effect and their distribution in the territorial-industry context.

Based on the proposed balance model, typical generalizations («extensions») of the model are highlighted, which, in general, increase its dimension, but do not «fall out» of the linear class. In particular, the issues of analyzing the impact on changes in the volume of gross sectoral issues as a result of changes in structural industry proportions are studied, corresponding to changes in the technological structure of the functioning of the ecological-economic system in the sectoral context.

In order to solve the problem, it was developed to use the algorithms of basis matrix method, which are equipped with the technology for determining solutions of the system of matrix linear equations in accordance with the changes and generalize the model. At the same time, changes may be experienced by individual elements or a group of elements, one or a group of rows (columns), in blocks of matrix submatrices. The proposed algorithms are implemented for the case of changes in the matrix of constraints of the original system without recalculation (again).

We considered various variants of changes in the model and their influence on the new solution in case of «perturbation» in submatrices of the constraint matrix (group of elements forming a block) of the model. In particular, the variant with the «inclusion («exclusion») of new blocks of submatrices, that is an increase (or decrease) in the dimension of the original constraint matrix of mathematical model. Such models are provided by a linear system, in particular, a system of linear algebraic equations (SLAE).

Such an approach makes it possible to carry out directional changes in the model in order to achieve the desired proportions of the «useful» and «harmful» component in the production structure (as a solution to the problem).

Further development of the proposed theory makes it possible to proceed to the study of aggregation issues of the balance scheme «input-output», determining a specific corridor of permissible changes in order to achieve a target reference point for the volume of sectoral output.

Keywords


matrix systems; international environmental agreements; basis matrix method; matrix ecological-economic models

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References


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Onyshchenko, A. M., Onyshchenko, A. M. (2011). Metodolohiya matematychnoho modeliuvannia ekonomiko-ekolohichnoi vzaiemodiyi v umovakh realizatsiyi Kiotskoho protokolu. Ekonomichna kibernetyka, 4-6 (70-72), 17–26.

Capros P., Georgakopoulos P., Van Regemorter D., Proost S., Schmidt T. F. N., Koschel H. et. al. (1999). Climate Technology Strategies 2: The Macro-Economic Cost and Benefit of Reducing Greenhouse Gas Emissions in the European Union. Vol. 4. New York: Physica-Verlag Heidelberg, 224. doi: https://doi.org/10.1007/978-3-642-58690-3

Böhringer, C., Rutherford, T. F. (2010). The Costs of Compliance: A CGE Assessment of Canada’s Policy Options under the Kyoto Protocol. World Economy, 33 (2), 177–211. doi: https://doi.org/10.1111/j.1467-9701.2009.01229.x

Skhreyver, A. (1991). Teoriya lineynogo i tselochislennogo programmirovaniya. Vol. 1. Moscow: Mir, 360.

Yudin, D. B., Gol'shteyn, E. G. (1964). Zadachi i metody lineynogo programmirovaniya. Moscow: Sovetskoe radio, 491.

Kudin, V. I., Lyashko, S. I., Hritonenko, N. V., Yatsenko, Yu. P. (2007). Analiz svoystv lineynoy sistemy metodom psevdobazisnyh matrits. Kibernetika i sistemniy analiz, 4, 119–127.

Bogaenko, V. A., Skopetskiy, V. V., Kudin, V. I. (2012). Ob osobennostey organizatsii vychisleniya na osnove metoda bazisnyh matrits. Kibernetika i sistemniy analiz, 4. P. 146–154.

Bogaenko, V. A., Skopetskiy, V. V., Kudin, V. I. (2009). Analiz vychislitel'nyh skhem modelirovaniya protsessov geogidrodinamiki. Problemy upravleniya i informatiki, 4, 62–72.

Voloshin, О., Kudin, V., Onyshchenko, A., Khrushch, L. (2017). Formation of priorities of national mezoekonomical politics under the conditions of implementation on of the Paris agreements. International journal “Information Models and Analyses”, 6 (1), 68–83.

Voloshin, O., Kudin, V., Onyshchenko, A., Tverdokhlib, Y. (2018). Economic analysis of influence of implementation of international environmental. International Journal “Information Theories and Applications”, 25 (2), 17–32.


GOST Style Citations


Ramochnaya konventsiya Organizatsii Obedinennyh Natsiy ob izmenenii klimata. URL: https://www.un.org/ru/documents/decl_conv/conventions/climate_framework_conv.shtml

Kiotskiy protokol k Konventsii ob izmenenii klimata. Bonn, 2000. 33 p.

Sustainable Innovation Forum. URL: http://www.cop21paris.org

Wirth D. The Paris Agreement as a New Component of the UN Climate Regime // International Organisations Research Journal. 2017. Vol. 12, Issue 4. P. 185–214. doi: https://doi.org/10.17323/1996-7845-2017-04-185 

Stavins R. Linkage of Regional, National, and Sub-National Policies in a Future International Climate Agreement // Towards a Workable and Effective Climate Regime. 2015. P. 283–296.

Kokorin A. New Factors and Stages of the Global and Russian Climate Policy // Economic Policy. 2016. Vol. 11, Issue 1. P. 157–176. doi: https://doi.org/10.18288/1994-5124-2016-1-10 

State and trends of carbon pricing. URL: http://www.climateaction.org/images/uploads/documents/9781464810015.pdf

Greenhouse gas mitigation scenarios for major emitting countries / Kuramochi T. et. al. // NewClimate. 2017.

Green F., Stern N. China's changing economy: implications for its carbon dioxide emissions // Climate Policy. 2017. Vol. 17, Issue 4. P. 423–442. doi: https://doi.org/10.1080/14693062.2016.1156515 

National post-2020 greenhouse gas targets and diversity-aware leadership / Meinshausen M., Jeffery L., Guetschow J., Robiou du Pont Y., Rogelj J., Schaeffer M. et. al. // Nature Climate Change. 2015. Vol. 5, Issue 12. P. 1098–1106. doi: https://doi.org/10.1038/nclimate2826 

Research on Output Growth Rates and Carbon Dioxide Emissions of the Industrial Sectors of EU-ETS: Final Report. Oxford Economic Forecasting. Oxford, 2006. 67 p.

Voloshin A. F., Goritsyna I. A. Mekhanizmy raspredeleniya kvot na vybrosy po Kiotskomu protokolu. URL: http://foibg.com/ibs_isc/ibs-10/ibs-10-p23.pdf

Onyshchenko A. M., Onyshchenko A. M. Metodolohiya matematychnoho modeliuvannia ekonomiko-ekolohichnoi vzaiemodiyi v umovakh realizatsiyi Kiotskoho protokolu // Ekonomichna kibernetyka. 2011. Issue 4-6 (70-72). P. 17–26.

Climate Technology Strategies 2: The Macro-Economic Cost and Benefit of Reducing Greenhouse Gas Emissions in the European Union / Capros P., Georgakopoulos P., Van Regemorter D., Proost S., Schmidt T. F. N., Koschel H. et. al. Vol. 4. New York: Physica-Verlag Heidelberg, 1999. 224 p. doi: https://doi.org/10.1007/978-3-642-58690-3 

Böhringer C., Rutherford T. F. The Costs of Compliance: A CGE Assessment of Canada’s Policy Options under the Kyoto Protocol // World Economy. 2010. Vol. 33, Issue 2. P. 177–211. doi: https://doi.org/10.1111/j.1467-9701.2009.01229.x 

Skhreyver A. Teoriya lineynogo i tselochislennogo programmirovaniya. Vol. 1. Moscow: Mir, 1991. 360 p.

Yudin D. B., Gol'shteyn E. G. Zadachi i metody lineynogo programmirovaniya. Moscow: Sovetskoe radio, 1964. 491 p.

Analiz svoystv lineynoy sistemy metodom psevdobazisnyh matrits / Kudin V. I., Lyashko S. I., Hritonenko N. V., Yatsenko Yu. P. // Kibernetika i sistemniy analiz. 2007. Issue 4. P. 119–127.

Bogaenko V. A., Skopetskiy V. V., Kudin V. I. Ob osobennostey organizatsii vychisleniya na osnove metoda bazisnyh matrits // Kibernetika i sistemniy analiz. 2012. Issue 4. P. 146–154.

Bogaenko V. A., Skopetskiy V. V., Kudin V. I. Analiz vychislitel'nyh skhem modelirovaniya protsessov geogidrodinamiki // Problemy upravleniya i informatiki. 2009. Issue 4. P. 62–72.

Formation of priorities of national mezoekonomical politics under the conditions of implementation on of the Paris agreements / Voloshin О., Kudin V., Onyshchenko A., Khrushch L. // International journal “Information Models and Analyses”. 2017. Vol. 6, Issue 1. P. 68–83.

Economic analysis of influence of implementation of international environmental / Voloshin O., Kudin V., Onyshchenko A., Tverdokhlib Y. // International Journal “Information Theories and Applications”. 2018. Vol. 25, Issue 2. P. 17–32.







Copyright (c) 2019 Volodymyr Kudin, Andriy Onyshchenko, Igor Onyshchenko

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061