Рассмотрена математическая модель экономического роста, представляющая собой модификацию модели Харрода-Домара. В результате анализа поведенческих свойств предложенного экономического механизма выявлена гиперболическая динамика накопления капитала с конечным временем жизни макроэкономической системы.
Розглянуто математичну модель економічного зростання, яка є модифікацією моделі Харрода–Домара. В результаті аналізу поведінкових властивостей запропонованого економічного механізму виявлено гіперболічну динаміку накопичення капіталу з кінцевим часом життя макроекономічної системи.
The given work is devoted to analysis of traditional procedure of forming up the differential equations, which are used for modeling macroeconomic processes. There is a number of contradictions which were not evaluated properly in due time. In the process of investigations related to the search of the overcoming, alternative concepts of mathematical modeling for economic dynamics are set up. The incorrectness of the Harrod’s model, widely presented in corresponding literature, is determined. According to this model, there is the possibility of macroeconomic growth on the unlimited time period. The incorrectness is explained by the application of standard mechanism of continuous analysis for balance correlations, which, in fact, are discrete. The correct model of economic growth is set up; this model indicates the inevitability of economic crisis appearance. This model is based on the integral dependence of capital on income. This model gives a constructive opportunity for crisis prevention. The time estimation for crisis is given. It is shown that economic activity activation accelerates the crisis events. In order to weaken possible crisis consequences, the model of economic dynamics is proposed. It is done taking into account the capital depreciation that leads to showing down the economic growth. In conclusion it is drawn that the depreciation limits the process of growth, but it doesn’t eliminate the time of upper turning point. All the modifications of classical models for economic growth examined in this work are linear and homogeneous in time. The circumstance mentioned in this work gives the possibility for application of the methodology of econometric analysis of the time series for solving the tasks of the real economic processes identification.
