макроэкономика,
математические методы в экономике,
модель Гудвина,
метод Пуанкаре
Abstract
The relevance of the topic. There are a considerable number of macroeconomics models that try to explain and predict long-term trends and dynamics of important economic indicators. One of these is the Richard Goodwin model, which was proposed in the early 1970s. It is based on the idea of the relationship between wages, unemployment and inflation. From a mathematical point of view, the Goodwin macroeconomic model is a system containing a small parameter. It is worth noting that such systems are very difficult to study. Here are a few more models for comparison. Exactly. The AS-AD model combines the movement of aggregated supply and demand for goods and services. It describes the relationship between the price level and real GDP and pays great attention to the welfare of consumers and companies, preferences and technology changes. The IS-LM model analyzes the relationship between the level of interest rates, investments and income in the economy. Unlike the Goodwin model, the IS-LM model focuses mainly on the financial and monetary aspects of the economy. The Solow growth model describes the process of economic growth in the long term and focuses on capital formation and technological progress. Classical economic theory assumes the cyclical nature of ongoing processes. This article presents their mathematical interpretation and shows how mathematical methods can be used to analyze and forecast the dynamics of economic indicators. In this context, the relevance of the task under consideration is obvious today. Goal. Determining the level of GDP that will ensure stability in the country's economy and in the lives of its citizens for a long time. Methodology. Application of the Poincare method to solve the formulated problem. Results and conclusions. The quantitative size of the limit cycle is determined, which reflects the periodic processes occurring in the Goodwin economic system, according to the input parameters. The stability of these processes has been proven. The sustainable cyclical nature of the economic process, which ensures the effective development of the state, is not always achieved. To do this, a number of rather stringent requirements must be met. In addition, it is also quite difficult to draw conclusions about the scope of this cycle from a practical point of view. But if it succeeds, then it is possible to make long-term forecasts regarding the development and the level of the main economic indicators that this development will ensure. The scope of application. Economic forecasting.
