The paper considers a microeconomic model of the construction business economy, assuming that it is a stable object in a crisis. The paper presents the distinctive features of the microeconomic formulation of the problem of finding a method for optimal separation of construction materials into consumed and accumulated parts. This area is constantly paid attention to and described in the media, sometimes with much unexpected outcome for investors. It is quite natural that consumption is optimized, just as in macroeconomics, but not in its pure form. The integral discounted utility of consumption is maximized. The communication equation in this paper differs from the similar macroeconomic equation, as the construction business exists and survives even in crisis conditions not in the same way as it does in social environments.
One of the important and urgent tasks of microeconomics is the problems of research of the economic system, in which there are restrictions associated with the planned volume of output or the size of the enterprise production capacity. These constraints are set by the requirement that the analyzed trajectories do not leave some given region of the control existence space. Most often, such restrictions for all time points are set in the form of inequalities, and certain requirements are imposed on the function of the phase coordinates of the object, their value at a given time. This problem is classified as an optimal control problem with mixed and phase constraints. In general, this area is of scientific interest and requires consideration. In this case, we study the microeconomic model of the household economy as the most stable object in the conditions of crises. The accumulated savings are subject to a natural phase constraint of non-negativity. This led to the study of the features of the microeconomic formulation of the problem of finding a method for the optimal division of material resources into consumed and accumulated parts, since the imposition of a natural phase restriction on the non-negativity of accumulated savings makes everything much more complicated. Just as in macroeconomics, consumption is optimized, but not in its pure form, but the integral discounted utility of consumption is maximized. The relation equation in this paper differs from a similar macroeconomic equation, since the household exists and survives in crisis conditions in a different way than do social organisms and large enterprises. That is why the article formulates and proves sufficient conditions for solving the problem with a phase constraint.
The paper studies variational formulation of the optimal control problem of consumption by classical macroeconomic Harrod-Domar model capital-output ratio of income gain is not constant and depends on time as a function of arbitrary nature.
Московский физико-технический институт (национальный исследовательский университет), Долгопрудный, Россия В статье макроэкономическая теория экономического роста Солоу рассматривается в усложненном случае, когда технический прогресс является воплощенным в капитале. При этом производственная функция зависит от эффективного капитала и трудового ресурса. Авторами детально исследуется эффективность капитала. Обыкновенное дифференциальное уравнение баланса для капитала выводится на основе главного экономического тождества: доход, т. е. выпуск промышленной продукции, равен сумме потребления и инвестиций. На основании обыкновенного дифференциального уравнения баланса для капитала получено обыкновенное дифференциальное уравнение для капиталовооруженности. Темпы роста эффективности капитала, трудового ресурса, нормы накопления и темпы амортизации капитала задаются экзогенно. В ходе исследования установлено, что это уравнение имеет существенные отличия от аналогичного обыкновенного дифференциального уравнения для капиталовооруженности в случае, когда технический прогресс является воплощенным в труде. Ключевые слова: производственная функция, эффективность капитала, капиталовооруженность, уравнение для капиталовооруженности.
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