Abstract
The paper presents studies of linear models of economic dynamics of the Neumann-Gale type, taking into account their possible stationarity, presents an analysis of existing classification approaches to the concept of optimality, presents their advantages and comparative characteristics, it is noted that the first type model open connects the concept of optimality with discounted maximization total utility. The first considers a closed system, the technological description of which includes the reproduction of all the resources necessary for development, including labor. Such a system has no external goals; its natural end in itself is development at the maximum pace. This is the most abstract and idealized scheme, but on the other hand it was it that made it possible to develop such fundamental concepts as equilibrium, a ray of (Neumann) balanced growth. Later, the apparatus of the closed model was replenished with the concepts of “direct and inverse Bellman operators”, “effective functional” (“potential”) of the model, etc. The second approach involves explicit accounting for consumption. Here the description becomes open, consumption is derived from the "technology" and described using the utility function. A new approach to the concept of “optimal development strategy” is proposed, a detailed analysis of the corresponding model is given. The article consists of three sections. 1 - staging part; 2 - analysis of the model with illustrative examples; 3 - conjugate (dual) model. The last section contains the main result on the connection of the optimal trajectories of the direct and dual problems. The paper provides an overview of literary sources in the subject area, as well as an economic interpretation of the results.
Highlights
Любое оптимальное решение означает согласование степени достижения цели с располагаемыми ресурсами
The paper presents studies of linear models of economic dynamics of the Neumann-Gale type, taking into account their possible stationarity, presents an analysis of existing classification approaches to the concept of optimality, presents their advantages and comparative characteristics, it is noted that the first type model open connects the concept of optimality with discounted maximization total utility
The first considers a closed system, the technological description of which includes the reproduction of all the resources necessary for development, including labor
Summary
В этом смысле использование методов математического программирования можно рассматривать как инструмент согласования решений, в котором значимость всех ресурсов одинакова: нехватка любого из них ограничивает рост функции цели независимо от ценности ресурсов, суммы затрат по его дополнительному привлечению и т. В [1] ставилась задача согласования отраслевых планов размещения производства, для решения которой строилась так называемая функция отказа, показывающая изменение (приращение) отраслевых издержек при отказе от лучшего, с точки зрения отрасли, варианта размещения предприятия в данном пункте. Тогда задача сводилась к нахождению минимума суммы этих функций для всех отраслей и промузлов с учетом общесистемных ограничений. В [5,6] функции отклика вводятся как элемент имитационных систем, необходимый для формирования задачи согласования. Затем в координирующем блоке модели отдельных блоков заменяются на их функции отклика и рассчитывается оптимальное решение системы
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Voronezh State University of Engineering Technologies
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
