A Study of the Efficiency of Functioning of the National Economy Using the Tools of the «Input – Output» Model

The aim of the article is to determine the indicators of efficiency of functioning of the national economy by the methods based on the economic-mathematical model of «input – output», and to conduct their comparative analysis. The publication allocates two main approaches to assessing and analyzing the efficiency of functioning of economic systems that use the above mentioned model. According to the first of them, the Frobenius number of the technological matrix of V. Leontiev’s model is considered as an indicator of efficiency (productivity, cost). Another approach uses the relevant elements of the matrices of the coefficients of direct and total material costs to build performance indicators. By demonstrating numerical examples, it is shown that performance indicators using Frobenius numbers can give incorrect results for some changes in the values of the elements of the technological matrix. This circumstance casts doubt on the possibility of using such indicators in the economic and mathematical analysis of macrosystems of production and distribution of products under the description of their functioning by V. Leontiev’s models. The carried out analysis of the dynamics of efficiency indicators, which are based on the elements of the main matrices of the «input – output» model, and the GDP growth rate indicator, calculated for the national economy in 2012–2020, shows that the processes of change in the size of the Ukrainian economy in this period are not directly related to the efficiency of its functioning and are determined mainly by simple scaling. Further research can be developed in the direction of using the economic and mathematical apparatus of the «input – output» models to form recommendations for improving the efficiency of the functioning of the relevant economic systems, as well as a more detailed analysis of the features of the dynamics of the Ukrainian economy.