Estimation of Economic System's Proportional Development Using Economic Growth Model

Sustainable development of socio-economic systems at various levels is now a major research topic. The relevance of this topic lies in the scale and importance of the tasks, included in the process of ensuring the sustainability of the economic systems development. One of the most important components of socio-economic systems the sustainable development is to ensure its economic security. The process of ensuring the economic security of the region is in maintaining a stable functioning of the territory, with the constant improvement of the socio-economic situation. The main parameters of the development of the socio-economic system affect the process of achieving economic security in the region. These parameters must be determined and predicted to adjust the functioning of the socio-economic system of the region. To simulate the level and dynamics of GRP indicators, capital per employee, as well as the optimal investment plan, we used the model of economic growth of R. Solow. The considered model combines classical constructions of the theory of economic growth and modern methods for analyzing the theory of optimal control, in particular, generalizing the Pontryagin maximum principle for problems with an infinite planning horizon. Investments in fixed capital are the control parameter in the model, which allows ensuring the growth of output through the production function. Thus, the use of modification of the Solow model will allow to predict the dynamics of the main macroeconomic indicators for the subjects in the short and long term, as well as to assess the potential of the regions to ensure sustainable proportional development.