2022, issue 3, p. 56-66
Received 16.09.2022; Revised 07.10.2022; Accepted 15.11.2022
Published 29.11.2022; First Online 10.12.2022
https://doi.org/10.34229/2707-451X.22.3.6
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Mathematical Models of M.V. Mykhalevych for Forecasting Structural and Technological Changes
Petro Stetsyuk *
, Maria Grygorak , Oleg Berezovskyi , Oleksii Lykhovyd
V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
* Correspondence: This email address is being protected from spambots. You need JavaScript enabled to view it.
Introduction. The identification of structural and technological disproportions that affect crisis phenomena in the economy and the analysis of ways to eliminate them require a wide application of quantitative research methods, in particular, mathematical modeling. “Input-Output” tables of Leontief turned out to be quite a convenient tool for analyzing these economic issues. In Leontief-type models, the matrix of technical coefficients (matrix of direct costs) is assumed to be known and calculated on the basis of statistical information from the “input-output” tables. M.V. Mykhalevych formulated the “inverse” problem: how to determine those structural and technological changes that would reduce the cost of production and thereby increase the incomes of end consumers and make the economy more dynamic. Or, in other words, how to choose or adjust technical coefficients to improve the properties of the economic process. This work is devoted to two optimization problems built on the basis of models of this type.
The purpose of the article is to optimize the interdisciplinary planning of structural and technological changes.
Results. Inverse models of the Leontief type for optimization of structural and technological transformations in economic systems are considered. These models are formulated in terms of nonlinear programming problems and include two objective functions for maximization: total consumer incomes and the “income growth–production growth” multiplier. Algorithms and software for solving these problems are presented. Numerical optimization procedures are based on Shor's r-algorithm.
Conclusions. The use of inverse models of the Leontief type will allow choosing promising directions of structural and technological transformations in both the macro- and microeconomy. The proposed mathematical apparatus based on non-smooth optimization algorithms proved to be a sufficiently effective tool for solving appropriate optimization problems in practice.
Keywords: structural and technological changes, inter-industry balance, Leontief model, “input-output” matrix, inverse Leontief-type models, non-smooth optimization algorithms, software.
Cite as: Stetsyuk P., Grygorak M., Berezovskyi O., Lykhovyd O. Mathematical Models of M.V. Mykhalevych for Forecasting Structural and Technological Changes. Cybernetics and Computer Technologies. 2022. 3. P. 56–66. (in Ukrainian) https://doi.org/10.34229/2707-451X.22.3.6
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ISSN 2707-451X (Online)
ISSN 2707-4501 (Print)
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