Optimal Two Sector Growth Models with Three Factors

The paper is devoted to construction of optimal trajectories in the model, which balances growth trends of investments in capital and labor efficiency. The model is constructed within the framework of classical approaches of the growth theory. It is based on three production factors: capital, educated labor and useful work. GDP level is described by a production function of the Cobb–Douglas type. The utility function of the growth process is given by an integral consumption index discounted on the infinite horizon. The optimal control problem is posed to balance investments in capital and labor efficiency. The problem is solved on the basis of dynamic programming principles. A novelty of the solution consists in constructing nonlinear stabilizers constructed on the feedback principle, which leads the system from any current position to a steady state. Growth and decline trends of the simulated trajectories are studied for all components included in the model.