The Study of the Mathematical Model of Optimal Economic Growth
A model of optimal economic growth has been constructed and studied in this scientific paper. It was found three points of equilibrium. Their stability is investigated, and an economic interpretation of the results is presented. It is shown that the movement of the trajectory to a stable fixed point means that the development of the economy in the field of stability will occur in the direction of reducing the average consumption of the population to zero. In this paper, the prerequisites are obtained that allow the process to intercept on a stable trajectory: initial value of capital-labor ratio k0 and initial value of average consumption per head of population c0. With the right choice of these parameters, the economic system will fall on a stable trajectory, which leads to the assigned task - optimal economic growth. It is shown that non-compliance with these conditions will lead either to ‘hungry’ consumption, or to ‘eating away’ of all capital. At the equilibrium point, the level of consumption (per head of population) is constant and cannot increase over time. This is due to the static production function, in which there is no technological progress.
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