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Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance

Kulyk М.M., Academician of the National Academy of Sciences of Ukraine, Dr. Sci. (Eng.), Professor
Institute of General Energy of the National Academy of Sciences of Ukraine, 172 Antonovycha str., Kyiv, 03150, Ukraine
Language: Russian, English
Source: The Problems of General Energy, 2016, 4(47):5-22
Section: Scientific foundations of the development and optimization of fuel-and-energy balances
UDC: 622.324
Received: 26.10.2016
Published: 24.11.2016


Based on the performed analysis of numerous publications containing the models of equilibrium prices and outputs in the theory of intersectoral balance, we have proved that the use of transposed matrices of direct cost in such models is unreasonable and leads to serious mistakes. We have proposed correct systems of equations connecting equilibrium prices and outputs in the data structure “expenditure–output.” We have shown in the general form that such systems belong to the class of homogeneous systems of linear algebraic equations, and their matrices are singular and have ranks smaller by one than the matrix dimensions. It has been established that such systems give degenerate solutions. With the use of these properties, from the continual set of solutions of the refined models of equilibrium prices and outputs, we have isolated in the general form a class of their solutions that can be applied for determining practically acceptable values of these indices. We have proposed an algorithm of such determination that provides for the broadening of the structure of data “expenditure–output.” Our analytic investigations are illustrated by an example of the calculation of equilibrium prices and outputs based on the tables “expenditure–output” in Ukraine in 2012.

Keywords: equilibrium prices, expenditure, output, matrix, determinant, rank, sector.


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