The vital needs of man are a system that functions in a stationary mode and is sufficiently stable. At the same time, the cultural forms of satisfaction are dynamic, improving and changing in accordance with economic opportunities, ethnic culture and the cultural era. To a large extent, the energy saturation of these cultural forms (means, conditions, methods), meeting the vital needs of individuals that make up society, depends on social differentiation and the specifics of demographic dynamics. On the other hand, the historical stages of economic growth and state of the economy have an impact on socio-demographic processes and the natural movement of the population. All together is in a dense correlation and functional connection, the modeling of which is an important scientific task of practical importance. The examples given in the article illustrate the performance of this model, showing the congruence of the calculated and actual values of the demographic indices. The result of theoretical constructions, which are the basis for the formation of a unified economic and demographic theory, is the established connection between the growth of gross domestic product and the natural movement of the population with an increase in the totality of consumed values and their distribution in the direction of population growth or energy saturation of cultural forms of satisfy the vital needs of social individuals.