Dynamic optimization of investments in the economic growth models

Consideration was given to the optimal control of investments in the economic growth model. The basic construction of the model is the production function relating the growth of production with the dynamics of production factors, and the investments in the production factors are the control parameters. The integral indicator of the discounted consumption index is the optimization functional. The Pontryagin principle of maximum for problems on infinite horizon was used to construct the optimal investment control. For the corresponding Hamiltonian system, considered were its qualitative properties such as existence and uniqueness of the steady state, properties of the eigenvalues and eigenvectors of the linearized system, and characteristics of the saddle point. This analysis allows one to obtain an algorithm to construct the optimal growth trajectories. The model was calibrated for the USA macroeconomic indicators.