Optimal proportions in growth trends of resource productivity

In the paper, a dynamic optimization model of investment in improvement of the resource productivity index is analyzed for obtaining balanced economic growth trends including both the consumption index and natural resources use. The research is closely connected with the problem of shortages of natural resources stocks, the security of supply of energy and materials, and the environmental effectiveness of their consumption. The main idea of the model is to introduce an integrated environment for elaboration of a control policy for management of the investment process in development of basic production factors such as capital, energy and material consumption. An essential feature of the model is the possibility to invest in economy's dematerialization. Another important construction is connected with the price formation mechanism which presumes the rapid growth of prices on exhausting materials. The balance is formed in the consumption index which negatively depends on growing prices on materials. The optimal control problem for the investment process is posed and solved within the Pontryagin maximum principle. Specifically, the growth and decline trends of the Hamiltonian trajectories are examined for the optimal solution. It is proved that for specific range of the model parameters there exists the unique steady state of the Hamiltonian system. The steady state can be interpreted as the optimal steady trajectory along which investments in improving resource productivity provide raising resource efficiency and balancing this trend with growth of the consumption index. The fact of existence of the steady state demonstrates the possibility of the growth path in an economy with exhausting resources. Sensitivity analysis of steady state solutions is implemented to demonstrate adequate trends of the model trajectories. As a result of analysis, one can elaborate investment strategies in economy's dematerialization, resource and environmental management for improving the resource productivity index and, consequently, for shifting the economic system from non-optimal paths to the trajectory of sustainable development