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

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.