Review of mathematical models in economics based on differential equations.

Abstract

Mathematical models in the form of differential equations used in economics are considered, taking into account such important economic factors as business cycle analysis, economic growth through savings, production, capital growth, labor growth, demand, supply, savings and profits. Examples of the application of differential equations in economics are presented in the form of the following mathematical models: Harrod-Domar, Solow economic growth, models of overlapping generations (Samuelson-Diamond model), Ramsey-Cass-Kupmans, economic growth of Romer, Kaldor, Phillips. According to the results of the analytical review of mathematical models, it was found that the Harrod-Domar model is used to analyze business cycles, as well as a tool to explain the growth rate of the economy through savings and productivity of capital. The Solow model takes into account the influence of factors such as capital stock, population growth and technological progress, the action of more factors, more fully reflects the picture of economic growth compared to the Domar-Harrod model. The Friedman-Phelps model addresses the issue of consumption, which is related to units of work in equilibrium in which the marginal volume of production per worker should be equal to the growth rate of labor at maximum consumption per individual. The Ramsey-Cass-Kupmans model takes into account consumption at a given point in time and explains long-term economic growth rather than fluctuations in the business cycle, and does not include market imperfections, household heterogeneity or exogenous critical situations. The analysis of Romer's model shows that long-term capital growth depends on exogenous parameters, including population growth. The study of the feedback between inflation and unemployment to achieve economic stability is taken into account in the Phillips model.