Abstract
The problem of finding the borders of the critical value of the economic number and obtaining relationships that allow a qualitative analysis of the state of economics of various macroeconomic objects is considered. To solve this problem, the apparatus of vector analysis and the theory of dimensions are used. As a result of the research the order of change modulus of rate of unstable development of economy during creation of gross product of the given volume is found. It is proved that the growth of the main factors of production is proportional to the scale of the economy. The boundary of the emergence of resistance to the development of the economy, which appears due to external and internal factors, is found. An equality is obtained that allows us to evaluate the effectiveness of the development of investments at any time intervals. The basic properties of the economic number are studied and its application for the study of the economies of various objects is found. An additional tool has been obtained for dynamic comparative analysis of various economies, regardless of their volumes and economic indicators.