Assessment and Forecast of the Efficiency of Use of the Financial Resources of Amalgamated Territorial Communities in the Context of European Integration - Khirivskyi, Roman; Petryshyn, Liudmyla; Pasichnyk, Tymofii; Brukh, Oksana; Bernatska, Iryna; Kucher, Lesia (European Journal of Sustainable Development, 2020)
The task of forecasting in economics is fulfilled by developing a variety of econometric models. The complexity of actual relations between the economic indices requires improvement of the existing and creation of new methods of modeling. That diversity is limited by the current set of elementary mathematical functions, whereas some of them cannot be applied in economics. At the beginning of the 21st century, it was proposed to use the functions of complex variable in economics. Due to their properties, which differ from the functions of real variables, they describe relations between the economic indices in a different way. Particularly, exponential presentation of a complex variable provides easy assessment of the relations between the economic index, presenting the real part of the complex number and the index, which describes its imaginary part. The trigonometric representation of the complex variable provides a more precise assessment of the studied econometric indices. Basing on the theory of the functions of complex variable, the authors of the article make assessment of the efficiency of funds use by the communities in Lviv region. In particular, the relation of the dynamics of income per one resident and the costs for maintenance of the managerial apparatus in terms of one resident in each of the amalgamated territorial community is considered as a function of complex variable. Using the statistical data, the authors have developed modules of complex variables and their arguments, which demonstrate the dynamics of relations between those components. The work also presents developed exponential functions of complex variable with the real coefficients, which have high approximation properties and can be used to make forecast of the efficient use of funds of each ATC in the future. The methodology can be used not only for assessment of the efficiency of funds use by amalgamated territorial communities, but also for evaluation of the general activity of communities, as well as for the analysis and forecast of production processes and planning on different enterprises. Keywords: complex numbers, economic and mathematical modeling, nonlinear models, territorial communities, Lviv region, social development, efficiency of the use of funds.