ПРО ПРОДУКТИВНІСТЬ МАТРИЦІ В МОДЕЛІ ЛЕОНТЬЄВА

Abstract

Leont’ev's static model (input-output model) is the main inter- sectoral balance model, which is used in government statistical divisions of many countries, including Ukraine. At the base of this model is the principle of balance, i.e. the principle of inter-sectoral balance of available material, labor, financial and other resources and the need for them. In Leont’ev's model, it is supposed that each industry domain produces only one kind of goods. The balance model is a system of equations, each of which expresses the balance between the output of the industry domain and the total need for it. In this approach, the economic system consists of economic agents, each of which produces a product, one part of which is consumed by other agents, and the other is taken out of the system as final consumption. If instead of the concept of product to introduce a more general concept of resource, in Leont’ev's model can be also included natural resources, such as land, forest, mineral, etc. The central role in Leont’ev's model is assigned to the matrix of technological coefficients or technological matrix (matrix of direct costs). If this matrix is productive, then the economic system will have only one stable equilibrium position, so the issue of productivity of the technological matrix is one of the main in this model. In this paper is proved the theorem on the necessary and sufficient conditions for the productivity of the technological matrix in Leont’ev's model. Some fragments of this theorem have already been published in the scientific and pedagogical literature, but in general, this theorem and the method of its proving can be considered as new. In further research, we can consider a dynamic or open Leont’ev's model, when we study not only the position of equilibrium, but also the path to it. With this model, you can reveal hidden production, hidden industrial demand and hidden final consumption.