Optimal Investment Level into Science in Terms of Proportional Economic Growth

摘要

In this article we highlight the problem of determining the optimal level of investments directed into the science and education field at the ratio required to ensure the sustainable development of regional economic systems. The main attention is paid to the analysis of financial flows in the Russian economy, aimed at the research and development (R&D). In our work we identified and explained the dynamics of investment flows in R&D and highlighted the main causes of the financial flows variable dynamics directed to the high-tech industry. Over the past decade, Russia has been reduced the number of personnel engaged in scientific fields. At the same time an increase of investment flows in the high-tech industry occurred. To adjust and increase the impact of investment flows science-based projections are required. To solve this problem we developed an proportional growth model in which the dynamics of capital and labor meets the proportionality conditions. Proportionality conditions of economic growth in this model are obtained by solving the output maximization problem under fixed costs at each time period. Investments directed into labor resources serve as control parameters and are intended to maintain the balanced development of economic systems. In this paper, we define the proportion between capital and labor resources and combine them through the price formation mechanism. The price formation mechanism is described by a combination of Cournot duopoly model and the Cobb-Douglas production function. Solutions of the first level of optimization are aggregated in proportion to the overall cost of labor and then transferred to the upper level of optimization. The model is resulted in the system of nonlinear differential equations whose stationary points generate the steady state of the economics.