Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance
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 co...
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| Date: | 2016 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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General Energy Institute of the National Academy of Sciences of Ukraine
2016
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| Online Access: | https://systemre.org/index.php/journal/article/view/582 |
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| Journal Title: | System Research in Energy |
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System Research in Energy| _version_ | 1860506997628076032 |
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| author | Kulyk М.M. |
| author_facet | Kulyk М.M. |
| author_sort | Kulyk М.M. |
| baseUrl_str | https://systemre.org/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2023-10-17T08:35:32Z |
| description | 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. |
| doi_str_mv | 10.15407/pge2016.04.005 |
| first_indexed | 2026-03-24T02:02:19Z |
| format | Article |
| id | systemreorg-article-582 |
| institution | System Research in Energy |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:02:19Z |
| publishDate | 2016 |
| publisher | General Energy Institute of the National Academy of Sciences of Ukraine |
| record_format | ojs |
| spelling | systemreorg-article-5822023-10-17T08:35:32Z Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance Перегляд можливостей моделей рівноважних цін і випусків в теорії міжгалузевого балансу Kulyk М.M. equilibrium prices, expenditure, output, matrix, determinant, rank, sector. рівноважні ціни, витрати, випуск, матриця, детермінант, ранг, сектор. 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. На основі проведеного аналізу численних публікацій, що містять моделі рівноважних цін і випусків теорії міжгалузевого балансу, доведено, що використання в них транспонованих матриць прямих витрат є необґрунтованим та призводить до грубих помилок. Запропоновані коректні системи рівнянь, що зв’язують рівноважні ціни та випуски в структурі даних «витрати-випуск». Показано в загальному вигляді, що такі системи належать до класу однорідних систем лінійних алгебраїчних рівнянь, їх матриці є особливими і мають ранги, що на одиницю менші за розмірність матриць. Встановлено, що такі системи надають вироджені рішення. З використанням цих властивостей із континуальної множини рішень уточнених моделей рівноважних цін і випусків у загальному вигляді виділений клас їх рішень, які можна використовувати для визначення практично прийнятних значень цих показників. Запропоновано алгоритм такого визначення, що передбачає розширення структури даних «витрати-випуск». Аналітичні дослідження ілюстровані прикладом розрахунку рівноважних цін і випусків на базі таблиць «витрати-випуск» в Україні у 2012 році. General Energy Institute of the National Academy of Sciences of Ukraine 2016-11-24 Article Article application/pdf https://systemre.org/index.php/journal/article/view/582 10.15407/pge2016.04.005 System Research in Energy; No. 4 (47) (2016): The Problems of General Energy; 5-22 Системні дослідження в енергетиці; № 4 (47) (2016): Проблеми загальної енергетики; 5-22 2786-7102 2786-7633 en https://systemre.org/index.php/journal/article/view/582/509 |
| spellingShingle | equilibrium prices expenditure output matrix determinant rank sector. Kulyk М.M. Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| title | Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| title_alt | Перегляд можливостей моделей рівноважних цін і випусків в теорії міжгалузевого балансу |
| title_full | Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| title_fullStr | Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| title_full_unstemmed | Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| title_short | Revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| title_sort | revision of the possibilities of the models of equilibrium prices and outputs in the theory of intersectoral balance |
| topic | equilibrium prices expenditure output matrix determinant rank sector. |
| topic_facet | equilibrium prices expenditure output matrix determinant rank sector. рівноважні ціни витрати випуск матриця детермінант ранг сектор. |
| url | https://systemre.org/index.php/journal/article/view/582 |
| work_keys_str_mv | AT kulykmm revisionofthepossibilitiesofthemodelsofequilibriumpricesandoutputsinthetheoryofintersectoralbalance AT kulykmm pereglâdmožlivostejmodelejrívnovažnihcínívipuskívvteoríímížgaluzevogobalansu |