The article supplies assessment and analysis of sustainability of the socio-economic development of amalgamated territorial communities in Lviv region of Ukraine basing on the methodological approach, proposed by the authors and founded on the principal functions, performed by the territorial communities, and on the estimates of the degree of their fulfilment. Those methods suggest use of a set of indices, which express sustainable or unsustainable development of the economic indices and consider their different intention. Referring to the indices of execution of the local budgets of 22 communities in Lviv region, the authors of the research assess the socio-economic situation of amalgamated territorial communities. Results of the calculations confirm the sufficient sustainability of the socio-economic development of amalgamated territorial communities in Lviv region. However, in 2018, the communities had trouble in executing their socio-economic budgets. The best results of development of the socio-economic indices were demonstrated by Babyna ATC, Davydiv ATC and Zabolottsi ATC, the worse ones – by Biskovychi ATC, Hrabovets ATC and Novyi Kalyniv ATC. To raise the level of the socio-economic standards of living of the “low-performing” amalgamated territorial communities and to support their sustainable development, the government should supply its assistance. Keywords: sustainability, socio-economic development, amalgamated territorial communities, Lviv region, Ukraine

The article supplies assessment of the efficiency of resource potential employment by some communities in Lviv region. The work studies the main sources of the resources of amalgamated territorial communities and makes grouping of them according to the criteria of their essence and importance in the strategy of development of the community’s resource potential. The research analyzes financial capability of the communities, considers the recent results, obtained by Ukrainian scientists concerning the resource potential of amalgamated territorial communities. The authors of the work applied the methods of standard coefficients to transfer the indices of quantity into quality analogues. The indices were used to make rating of amalgamated territorial communities, to depict different factorial and resultant aspects of the resource potential of amalgamated territorial communities and assess them. Applyng the method of standard coefficients and matrix of the Boston Consulting Group, the work determines position of each community referring to density of population and resource of the capacity for work of amalgamated territorial communities. It also calculates rating indices for comparison of public formations in social sphere, and estimates expenditures for administrative personnel of each community. The proposed methods enable keeping track with not only dynamics of the rating assessment of communities, but also priority of the factorial indices concerning improvement and development of the communities. Those methods can be used not just referring to rural, but also to urban formations, based on a uniform measuring for all peculiarities. It helps to move from subjectivism and inconvenient use of expert assessments and weighting coefficients while completing the uniform integrated indices.  Keywords: territorial community; social development; resource support; administrative and territorial reform; method of standard coefficients; matrix of the Boston Consulting Group.

The paper presents the results of evaluation of the efficiency of employment of the communities’ resource potential using different approaches on the example of Lviv region in Ukraine. The proposed methodology secures creation of a rational system of monitoring of the results of activities of amalgamated territorial communities (ATC) and determines what factorial indices should be improved and concerned by the communities’ managers to conduct more efficient managerial work in the community. For example, in the communities with the budget that is sufficient to secure the increasing development of the community (Davydiv, Dubliany, Zabolottsi ATC), the primary focus can be done on the social development and growth of the infrastructural base, whereas in the ATCs with the low level of economic development (Volia-Baranetska, Lukiv, Mizhenets ATC), the most important task is to secure the sufficient extended growth of the population’s income.

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.