L. F. Chernogor - Dr.Sc. (Phys.-Math.), Professor of the Space Radiophysics Department, V.N. Karazin Kharkiv National University. E-mail: Leonid.F.Chernogor@univer.ua

The model for the population on the planet Earth advanced by S. P. Kapitsa has been generalized. The exhaustion of the nonrenewable natural resources is taken into account. A simple analytical model for changes in the population N(t) is presented. The changes N(t) have mathematically been modeled in response to changes in the rate of resource consumption. The misallocation of resources has been shown to result in an abrupt drop in N already in the middle of the XXI century, which results in an absolute degradation of our civilization in XXIII - XXIV centuries. A reasonable management of the planet-s resources can result in the population stabilization at a level significantly lower than the S. P. Kapitsa model predicts. However, the stabilization is preceded by an increase of 7-9 billion people in the middle of the XXI century. The optimal volume of the world's population leading to the life with dignity is equal to approximately 6 billion.