Economic-mathematical Methods Research Articles

Problems of assessing the balance of economic systems

Subject. The article investigates a model of the balance of the national economic system. Objectives. The study aims at identifying the main characteristics of the balance of economic systems to create a methodology for assessing the balance of the national economic system, and factors affecting it. Methods. We employed general scientific methods of cognition. The systems approach and logical generalization enabled to develop priority areas of the proposed methodology. We also applied methods of statistical analysis of economic data, economic-mathematical methods. Results. We proposed our own methodology for distribution of economic activities by type of subsystems, based on the proposed by G.B. Kleiner model, in two versions, i.e. excluding and including exports and imports. We also offered recommendations and strategies for improving the balance of the economy, which contribute to increasing its competitiveness and sustainability in the face of modern challenges and changes in the world arena. Our model enables to assess the impact of external factors, like global economic trends, changes in the world trade and crisis situations, on the economic stability of a country and development of its industries. Conclusions. The analysis of changes in the balance index in the context of foreign trade and industries helps assess the dynamics of balance and identify factors, including the impact of the coronavirus pandemic, that may affect the economic stability and development of the country.

Financial Capacity of Insurance Companies as a Factor of Stable Development of the Ukrainian Insurance Market

Abstract The relevance of the article is based on an in-depth study of the financial potential of insurers and its impact on the insurance market, which provides valuable information for the stakeholders of the insurance industry. Therefore, this study aims to determine approaches to revealing the essence of the financial capacity of insurers, based on the scientific tools of financial science. The leading approach to the study of this problem is the analysis of the dynamics of liabilities (raised and borrowed funds) and equity capital of insurers and the relationship between them, which enables a comprehensive look at the impact of these indicators on the development of insurance market and internal and external factors that have both an objective and subjective impact on the financial capacity of insurers and the insurance market. The article defines the stages and methodology of assessing the financial condition of insurers. In particular, the normative method, the comparative method, the static method, the formallogical method, the economic-mathematical method, the method of analysis and synthesis became the leading research methods. These assessment methods are crucial for the timely determination of the current state of financial capacity and its potential. Using a multivariate correlation-regression model, the authors demonstrate the importance of various components of financial capacity. The presented results will be useful to various stakeholders in the insurance industry as they provide a deeper understanding of their financial strength, including the dynamics of liabilities, equity and leveraged funds. First of all, it was established that financial resources are the basis of financial capacity. Secondly, the definition of the insurance company’s financial resources as a source and component of the company’s functioning is formulated. Thirdly, it is shown that the insurer’s financial capacity is logically dependent on its investment capacity, which is determined by the amount of financial resources. It was also determined that financial capacity is a dynamic quantity and is manifested only in the process of its use and ideally should be accompanied by its growth. Among them, it was proved that the main components that significantly affect the formation of the financial potential of insurers and the growth of the insurance market of Ukraine are insurance reserves and authorized capital. These conclusions can easily become the basis for the formation of further state insurance policy, which will be followed through legislative reforms, increased competition in the insurance market and will result in an increase in the level of trust among the population.

Goodwill measurement in consolidated financial statements

The largest business in terms of capitali­zation value, revenues and profits was formed as a result of a business combination. Consolidated financial statements are of undoubted value to users and stakeholders in assessing risks, prospects and analyzing the interaction of companies within the group. Special indicators of consolidated financial statements, such as goodwill, allow estimating the expected value of acquired companies in a business combination. However, the current methodology does not allow for the evaluation of all aspects of value that constitute goodwill. The aim of the article is to supplement the methods of goodwill valuation in business combinations for further substan­tiated disclosure in consolidated finan­cial statements, in accordance with the interests and needs of investors and managers. The research methodology is based on a systematic approach, critical analysis, synthesis, induction and deduc­tion, comparison, economic-mathematical methods of goodwill calculation, and genera­lization of principles of consolidated reporting. An analysis of key international standards allowed us to determine the peculiarities of applying the acquisition method for different types of business combinations. The share of ownership in an investee determines the nature of influence and the method of consolidation. Goodwill is the difference between the purchase price and the fair value of the net assets acquired in a business combination. When companies merge, goodwill reflects the intangible aspects of the business and the expected added value, which serves as the investment object. Therefore, methods for valuing goodwill during business combinations are identified to disclose in consolidated finan­cial statements in accordance with IFRS. Additionally, a group of complementary good­will valuation methods is systematized to determine and justify all aspects of forming the undisclosed added value of the investee compa­ny. The proposed methodology allows for considering the interests of various stakeholders in goodwill valuation. It is crucial to regard the goodwill disclosed in the financial statements as consent and willingness of the parent company to pay more, based on evidence and calculations obtained through a comprehensive goodwill valuation methodology. The proven hypothesis of the research suggests that for a justified valuation of goodwill during consolidation, it is necessary to supplement existing approaches and measure the value of brand, long-term stability, sustainable development, corporate so­ci­al responsibility, and utilize artificial intelli­gence. Goodwill reflects strategic value but may also be subject to impairment if its value is not sufficiently supported by expected profits.

The study of some issues of the application of cryptocurrency mining technology in Kazakhstan

Object: Analyze the use of cryptocurrency mining technology in Kazakhstan and develop recommendations for improving its effective operation.
 Methods: We have used scientific methodological and research approaches, such as comparison, grouping, analysis, classification, statistical data, induction, deduction, economic-mathematical methods, and modeling.
 Findings: The study's practical significance is that these principles and approaches can be used to form a mining farm development strategy. The proposals presented will improve the digital efficiency of the company and stabilize and improve its financial and economic situation by making appropriate management decisions. The study results make it possible to solve problems related to the ability of enterprises to provide a medium and long-term stable position in the market and flexibly adapt to the environment.
 Conclusions: Based on the study, the concept of “cryptocurrency”, “mining”, and “mining farm” was clarified as a particular form of a new information economy and society that combines its input stages of the technological chain or stages of its release in order to achieve significant competitive advantages compared to specialized types of digital money. The features of digital money, such as cryptocurrencies and their mining, which include various platforms, objects, and types but have common elements, technologies, development management, and risks, were identified. A methodology for analyzing the IT architecture of cryptocurrency and the volatility of the digital currency is proposed, which allows one to find out quantitative and qualitative indicators, assess the extensiveness, intensity, and efficiency of the use of cryptocurrency, and determine the reserves for its full use.

ASSESSING THE IMPACT OF ARCHITECTURE EFFICIENCY ON THE BUSINESS MODEL COMPETITIVENESS

The purpose of this research is to develop a methodological approach to assessing the impact of the architecture effectiveness of the enterprise business model on the level of its competitiveness. The study methodology suggests the author’s approach to assessing the architecture effectiveness and the level of enterprise competitiveness. The scenario approach was used in order to the evaluate the connection between competitiveness, business model potential and enterprise architecture based on the economic-mathematical method of solving the nonlinear optimization problem through the use of hierarchical synthesis. The study was conducted according to the materials from 15 private clinics in Ukraine. The analysis of the obtained indices of architecture efficiency, competitiveness and potential level of the business model of the private clinics under study was carried out. It is determined that the level and growth rates of the enterprise architecture efficiency of private clinics have significant distinctions, which affect the level of their competitiveness. A group of leading companies in terms of the level of business model potential is singled out based on the definition of the correlation between the level of business model potential and the enterprise architecture efficiency. It is established that the level of business model potential of private clinics is substantially dependent on the level of enterprise architecture efficiency. It is proved that the efficiency of enterprise architecture has a significant influence on the potential and competitiveness of the business model. The novelty of the study consists in the methodological approach to assessing the impact of business model architecture on the level of its competitiveness, taking into consideration the identification of functional rather than strictly parametric correlation between variables. This research can be useful for professionals, scientists and researchers involved in developing and implementing effective business models and designing the enterprise architecture in order to achieve the company’s strategic intentions and to create and maintain competitive market positions.

Game Analysis of Strategies for Providing Material Support to the Population

The article focuses on the possibilities of game analysis of options for providing material support to the population, implemented in the form of a game with nature – a generalized player, whose inclusion in the game analysis allows us to consider the diverse interaction of economic agents with the socio-economic environment. This set of methods has a number of advantages among the complex of mathematical methods in economics and management in conditions when regression models become irrelevant due to increasing uncertainty or lack of sufficient initial data. The purpose of the study is to overcome the insufficient use of the potential of game models in the practice of modeling social situations, taking into account the real information conditions that have developed to date. The research methods are the methods of game theory (construction of a set of active strategies for providing material support to the population; identification of possible variants of states of nature reflecting the possibilities of the number of people who really need material support; determination of the optimal strategy for providing material support, taking into account the selected optimality criterion). Their use contributes to improving the quality of decisions made in the field of providing material assistance to the population. Among the results of the study, we will indicate the implementation of all the necessary stages of the game analysis of strategies for providing material support to the population. The proposed mechanism for assessing the usefulness of funds, used for material support of the population, takes into account various contributions to the assessment of the final utility of the distribution of funds, arising both in cases of receiving funds by those in need and in cases of non-receipt of funds by those in need, as well as in cases of receiving funds by citizens who do not really need financial assistance. The authors have made calculations and assessed the consequences of strategies, the implementation of which involves reducing the number of citizens who receive financial assistance (with simultaneous dynamics of the amount of financial assistance). The game analysis of strategies for providing material support to the population became possible due to the construction of a game model of a basic level of complexity that takes into account the main scenarios of the development of the social situation under consideration. In the process of studying the constructed game model, a high degree of sensitivity of strategies for providing material assistance to the population to the choice of the optimality criterion, as well as its parameter, was established. This feature requires clarification of the information situation in which the strategy of providing financial assistance is chosen. In conclusion, we note that the material of the article may be useful for consideration with subsequent pilot testing at various levels of state and municipal administration, when developing and adopting legislative initiatives on social support measures aimed at strengthening the targeting of financial assistance to the population. Also, the material and tools of this study can serve in the course of improving existing and developing new academic disciplines, the content of which is related to the quantitative analysis of socio-economic problems and situations.

Возможности цифровой трансформации малых и средних сельскохозяйственных предприятий в современных условиях

Abstract. The author presented the results of scientific developments of data transformation when performing certain tasks (inventory, sale of grain to the population) by a visiting employee using a mobile application. The purpose of the study is to develop theoretical provisions and practical recommendations to ensure the solution of economic problems of the functioning of small and medium-sized businesses of the agro-industrial complex using a mobile application. Methods. In the course of the study, general scientific methods of theoretical and empirical knowledge were used: analysis and synthesis, monographic, basic array, design-constructive, deduction and induction, economic-statistical and economic-mathematical methods (comparison, summary and grouping, tabular, graphic). Experimental method, practical modeling, including conducting a statement experiment, analysis and generalization of the obtained data. Results. The development of small and medium-sized agricultural enterprises as a socio-economic phenomenon affects many objects and generates certain connections between them, which allows us to consider small and medium-sized businesses from the point of view of systematic analysis. The conceptual interest and capabilities of agricultural producers in a system approach to human resources management with optimization of the main technological process management system will allow achieving an effective result of activities in the innovative environment of the organization. The results of research work can serve as a theoretical and practical basis for the activities of owners, leaders of small and medium-sized businesses in order to improve the process of digitalization of agricultural production; for the activities of state authorities – support for the development of small and medium-sized businesses with the aim of economic growth of the country; for investors – assessment of investment opportunities in the agro-industrial complex. Scientific novelty. A mechanism has been developed to optimize and improve the efficiency of production processes; attracting domestic and foreign investments in the development of industries of the agro-industrial complex. Feeding the country is a great mission, fulfilling it one of the main components of national security and preserving the integrity of the country. The undisputed priority will be interest in an effective, balanced production process, innovative and technical development and digitalization of agriculture.

Intangible resources as the basis of intelligent support in effective decision-making at all life-cycle stages of an investment and construction project

Improving approaches to the management of an investment and construction project at all stages of its life cycle, including justification of investments, engineering surveys, architectural construction and organisational-technological design, construction, operation, decommissioning, demolition and disposal of the facility, including in conditions of uncertainty and risks, represents a key strategic direction for the development of enterprises. The problem of improving the efficiency of managing the company intangible assets appears relevant, since the efficiency of decisions, in particular, and the efficiency of the enterprise as a whole, largely depends on its solution. The study used methods of a system analysis, statistical-comparative and economic-mathematical methods, as well as the methods of economic and statistical analysis of indicators, characterising intangible assets, including the ranking method. The authors studied the life cycle features of an investment and construction project for enterprises of the mining and processing complex. The stage phases of the investment and construction project, linked to the specifics of the Far Eastern mining industry, are considered. The need for a detailed structuring of life cycle phases and stages for an investment and construction project for a digital intelligent support of effective decision-making, as well as for a use of the potential of intangible resources of performers, is substantiated. In this paper, the developing Soyuznoye graphite deposit (Dalgrafit LLC) is used to design a sequence of processes and procedures for the implementation of the considered project. Based on the existing potential of enterprise intangible resources, management measures are proposed aimed at improving project management processes with the possibility of digitalising individual business processes of the enterprise.

ЕКОНОМІКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ДИНАМІКИ ЕНЕРГОСПОЖИВАННЯ ЗБАГАЧУВАЛЬНОЇ ФАБРИКИ

The purpose of the work is to establish the dependence of electricity costs on the dynamics of energy consumption from the dynamics of ore supply to the beneficiation plant bunker, namely from the loading period and its duration, and to develop, on the basis of the identified patterns of organizational, technical and economic measures to reduce the energy component of the cost of production of iron ore concentrate at the mining enrichment enterprises. Economic-mathematical methods were used to develop models of the formation of electricity costs on the dynamics of energy consumption, namely: the theory of impulse processes for the development of a model of ore supply to the bunker of the beneficiation factory; operational calculation methods, ore beneficiation theory and power supply theory for the development of a dynamic beneficiation process line model and power consumption model; methods of spectral analysis to identify the dynamic component of active power and electrical energy consumed by the ore beneficiation process; Cost analysis methods were used to calculate electricity costs; economic-mathematical modeling of energy consumption dynamics was performed by computer modeling using the Mathcad software package. An economic-mathematical model of the energy consumption dynamics of the enrichment factory was developed. The regularities of influence of ore loading parameters of beneficiation factory bunkers on the dynamics of the formation of electricity costs during the production of iron ore concentrate have been revealed. Mathematical dependencies of costs for the dynamic component of electrical energy on the time parameters of the process of loading ore into the hopper of the beneficiation factory, namely on the period and time of loading, were obtained. Organizational and economic measures have been developed to load the bunkers of the beneficiation factory, which ensure the saving of electricity. The regularities of influence of ore loading parameters of beneficiation factory bunkers on the dynamics of the formation of electricity costs during the production of iron ore concentrate have been revealed. The principles of building a system of financial incentives for operational and dispatching personnel for saving electricity based on the results of economic and mathematical modeling have been developed. For the first time, it wa s established that the energy component of the production cost of iron ore concentrate depends not only on the quantity and quality of ore, but also on the dynamic parameters of the process of loading ore into the bunkers of the beneficiation factory, while this established dependence has a non-linear nature on the period and time of loading. The proposed measures to save electricity due to the implementation of rational modes of loading bunkers of the beneficia-tion factory with ore can be used in the development of energy saving plans and programs and the development of job instructions for the dispatching staff of the ore beneficiation factory, which will allow to reduce the energy component of the production cost of iron ore concentrate. A system of financial incentives for operational dispatching staff of the beneficiation factory has been developed, which takes into account the saving of electrical energy due to the management of the ore loading of the bunkers of the beneficiation factory and the intensity of the staff’s work.

Multiplier of consumer expenditures in the model of economic management of water resources of the Kyrgyz Republic

The expenses of the population are one of the main factors determining aggregate demand, which creates the basis for the reproductive process and economic development of the state. The volume of aggregate demand in the Kyrgyz Republic is largely determined by the development of trade and economic cooperation with China. This justifies the relevance of assessing their impact on economic growth against the background of new challenges of various kinds in the conditions of unstable social and economic development of Kyrgyzstan. The relations of trade indicators with China and GDP, the value of final consumption of Kyrgyz households as part of GDP in comparison with other countries are shown. The calculated indicators of marginal propensities to consumption and saving are analyzed; the multiplier of expenditures for Kyrgyzstan. A noticeable dependence of the indicator of economic development and foreign trade activity with the use of statistical and economic-mathematical methods with an acceptable coefficient of elasticity has been revealed. Conclusions are drawn about the impact of consumer spending on aggregate demand and changes in GDP, about the correspondence of real processes to the Keynesian theory of the investment multiplier and individual deviations from it in a developing economy.

E-COMMERCE IN UKRAINE: TAXATION CHALLENGES AND GLOBAL TRENDS

The economic sector of Ukraine has experienced transformative shifts toward e-commerce. This prosperous sphere of the digital economy attracts much prominence among legislative bodies since its growth rates increase annually, making the issue of taxation urgent. The article is aimed at monitoring the status of e-commerce through the prism of the development and spread of e-commerce in the domestic segment of the Internet, the impact of e-commerce on the national economy, and also at developing proposals for improving certain aspects of the taxation of business entities in Ukraine with due regard for the positive international experience and minimising the risks of fraud in the sale of goods (services) on the Internet. The study employs a combination of general theoretical and economic-mathematical methods, which are fundamental to scientific inquiry. This article presents research findings related to several key aspects. First, it examines the development and proliferation of e-commerce within Ukraine. Second, it elucidates the impact of e-commerce on the national economy. Additionally, the article addresses pertinent issues regarding the taxation of entities engaged in e-commerce within contemporary contexts. Moreover, it delves into the complex problem of protecting e-commerce participants from online fraud. Finally, the article suggests measures that can positively affect the taxation framework governing e-commerce and minimize the associated risks of fraudulent activities within the online marketplace. The author provided general conclusions on legislative changes against the background of the development of online commerce, analysed the peculiarities of the development and functioning of e-commerce under martial law, and, based on data from other countries, formed a unified vision of further changes in this area. The materials presented in this article hold practical value for a diverse audience, including scholars and practitioners in the field of e-commerce, educators at higher education institutions, and stakeholders concerned with the continued development and regulation of e-commerce

Capability of Higher Education in Overcoming Digital Inequality in the Conditions of the Crisis in Ukraine

Abstract The purpose of the article is to assess the gap between people’s readiness for effective activity in the digital economy and to identify the functional capabilities of universities to reduce this gap. The research used methods of generalizations, logical, systematic, and comparative analysis, and statistical-economic, sociological, and economic-mathematical methods and techniques. The results of the study showed that the digitalization of the economy, the state, and society, which is taking place in Ukraine, requires a significant increase in the level of society’s readiness for digital changes. For effective integration into the digital environment, in particular in the field of education, it is necessary to create a digital infrastructure that meets EU standards. The authors conducted a study of the development of the digital inclusive component of the regions of Ukraine.Proposed ways of digital development of society. In particular, it has been proven that promoting the development of the provision of educational services improves the digital literacy of the population for daily tasks and for employers to minimize the gaps between the digital environment and people’s skills. It is substantiated that the acquisition of new digital skills and competencies of employees requires the development of training networks and the improvement of foreign language knowledge, both for young people and for other generations.

Weighing logistics: on the issue of accuracy of determining the weight of the transported goods

Methods. The results are obtained with the following methods: the method of abstractions in determining the essence of the category of «social justice»; general to specific method in establishing the unity of the existing concepts of social justice; standard methods of sociological research in determining the value system of the Ukrainians towards social justice. Results. As a result of the conducted research, the possible value of financial losses during the sale of such goods as sand, wheat, fodder corn, food corn, iron ore pellets, titanium ore, and rolled ferrous metals was determined. These losses can range from hundreds to tens of thousands of hryvnias. The list of available offers of electronic scales for weighing goods on land was analyzed, the value of error when weighing with automobile and wagon scales was determined. The possibility of describing the error using a logarithmic equation has been demonstrated, which proves that the relative weighing error decreases as the mass increases. The equation formula was found by the analytical economic-mathematical method using Microsoft Excel spreadsheets. Based on the use of the properties of the dispersion of weighing, a logistical and organizational method of increasing the accuracy of weighing has been developed, which consists in several repeated weighings and determining the resulting weight as the arithmetic mean of all attempts. A formula was developed to determine the optimal number of repeated weighings to increase accuracy, taking into account the cost of one weighing and losses during a single weighing. The method of weighing cargo on water was analyzed, its limitations were revealed and the need for its improvement was indicated in terms of taking into account such factors as water salinity, through which the draft of the vessel is measured. An analytical dependence has been developed to determine the weight of the goods loaded onto the vessel by its draft depending on the salinity of the water in which the vehicle is located. Novelty. In the process of analyzing exporters’ losses during product weighing, logistical and organizational measures have been developed that are guaranteed to reduce losses. Practical value. Techniques are proposed that will reduce the exporter’s losses when weighing goods both on land and at sea, which will allow adjusting the size of the weighing error with available devices.

EVALUATION OF INNOVATIVE TRANSPORT TECHNOLOGIES FOR SEPARATE COLLECTION OF SOLID MUNICIPAL WASTE

The article discusses the assessment of innovative transport technologies for the separate collection of municipal solid waste (MSW). It was revealed that the processes associated with the separate collection and removal of municipal solid waste need to be implemented innovative solutions that will optimize these processes and significantly reduce costs. Therefore, a scheme was proposed with the introduction of a garbage truck with the possibility of separate collection of waste and the installation of sensors that monitor the filling of containers for collecting municipal solid waste.
 Purpose. Development of an effective scheme for organizing the movement of garbage vehicles and optimization of transport processes for the separate collection of MSW through the introduction of innovative transport technologies.
 Methodology in article economic-mathematical methods, and also statistical methods were used.
 Results. The most informative parameters have been obtained, showing some features for identifying solutions that allow increasing the volume of the solid food waste collection process.
 Practical implications it is expedient to apply the received results the economic subjects which are carrying out foreign economic activity, one of which elements are export operations.

Modeling and Forecasting of Production an Agricultural Product

Purpose: The purpose of the research is to analyze the dynamics of agricultural production, to determine the effect of different parameters on the result of production with the help of an econometric model, and to enforce production forecasting. Methods: The data of the Statistical Committee of the Azerbaijan Republic for the last 15 years were used in the research. According to the obtained data, using the EXSEL software package, the dependence between the production of agricultural products and affecting factors was determined with the help of economic-mathematical methods, and the expected change tendency of production was defined with the help of programming methods. Results: Increasing the production of agricultural products is currently maintaining its relevance both in terms of meeting the necessary raw material needs of the country, as well as solving the food problem and eliminating dependence on imports. Possible prospects for solving these problems require the application of innovative agricultural technologies to production, effective use of fertilizers, land, human resources and investments, taking into account the factors affecting production. Optimizing the mentioned factors leads to the achievement of high productivity, which is the basis of production growth, ensuring the most complete use of resource potential in agriculture. From this point of view, the modeling of production through economic-mathematical methods is possible to determine the quantitative relationship between product production and the factors affecting it, to optimize and predict the use of resources based on the obtained production function. Conclusion: It gives an opportunity to evaluate the effect of those factors on the dynamics of production in quantitative terms by comprehensively investigating the factors affecting production in agriculture, which is considered quite a risky field. At the same time, the methodology utilized provides a foundation for figuring out more effective methods of using production resources, allowing for the prediction of future changes that might take place in production.

Comparative Analysis of the Effectiveness of the Budget Funds Use at the Regional Level

The purpose of the study. The purpose of the paper is to assess the effectiveness of the use of regional budget expenditures on the example of the budgets of the Nizhny Novgorod and Mur-mansk regions. Materials and methods. General scientific methods are involved: analysis, synthesis, gener-alization, classification; and specifically scientific methods: dynamics analysis, correlation and re-gression analysis, neural network modeling. The information base of the study includes indexes of the execution of the federal budget of the Russian Federation (information from the Federal Treas-ury of the Russian Federation) and regional budgets published in the relevant laws of the regions; statistical data published by Rosstat. The novelty of the research approach lies in the combination of traditional and economic-mathematical methods with the use of the Cobb-Douglas production func-tion. This fact provided an opportunity to assess the impact of budget expenditures on individual factors of production that determine the volume of public product produced. The paper presents a comparative assessment of the effectiveness of budget planning based on normative and program-target methods.Results. It was found that the use of budget funds in the Murmansk region is more effective than in the Nizhny Novgorod region. In this region, starting from 2019, the priority of the task of developing a program-targeted method of budget planning has been reduced, but the region has achieved high efficiency in the use of budget funds due to rational management of budget debt. The budget of the Murmansk Region is characterized by a significant reduction in the debt burden, which reduces the share of public debt servicing costs, and the ratio of the amount of public debt to the expenditures of the regional budget by the end of 2021 approached zero. The study showed that budget expenditures have a significant positive impact on the growth of the capital factor. At the same time, the growth of budget expenditures has a more negative impact on the development of the labor factor. It was found that when using the program-target method, a number of program ex-penditures have a positive impact on the growth of the labor force in the regions, but the degree of such influence is insignificant.Conclusion. In the course of the study, the authors concluded that the efficiency of using budget funds in the Murmansk region is higher than in the Nizhny Novgorod region. This circum-stance indicates a greater influence on the efficiency of the use of budget funds of the quality factor of public debt management in comparison with the influence of the factor of the application of the program-target method of budget planning. The results of the conducted research may be useful to government agencies responsible for planning and budgeting.

The modern mathematical models in economics and finance

With this article, we open a new section in this journal: the application of mathematical methods in economics and finance. A few topics we would like to discuss to get started are corporate finance, investments, business valuation, taxation, and ratings. We describe shortly mathematical models in these areas. In the field of corporate finance, we discuss the foundations of two main theories of capital structure, the Modigliani-Miller and the modern theory of Brusov-Filatova-Orekhova (BFO theory). We compare them and describe the differences between them and their results. In the field of investments, we describe two modern investment models: (1) with debt repayment at the end of the project and (2) with uniform debt repayment and discuss their properties and applications. In business valuation, we discuss the problems that exist in this area and ways to solve them. In rating methodology, a new approach is devoted to the rating of non–financial issuers, as well as to long–term and arbitrary duration project rating. The key factors of a new approach are the adequate use of discounting of financial flows virtually not used in existing rating methodologies, and the incorporation of rating parameters (financial "ratios") into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory). This article is devoted to the analysis of the theoretical mathematical methods and models based on first principles. The novelty of this consideration is due to the fact that we are considering and discussing recently developed mathematical models in economics and finance.

FORECASTING INVESTMENT ACTIVITIES OF RAIL TRANSPORT ENTERPRISES USING TREND MODELS

The object of the study is the investment activity of railway transport enterprises. The purpose of the work is to forecast the investment activity of railway transport enterprises by using economic-mathematical methods and models, namely trend models. The information base of the study is the data of the State Statistics Service and the Ministry of Finance. It has been proven that the transport industry is one of the important branches of the national economy, which provides a logistic connection from the transportation of passengers to the transportation of goods. On the basis of economic-mathematical models (one-dimensional trend forecasting methods), a conceptual scheme for building forecast values of investment activities of railway transport enterprises has been suggested, with the help of which it is possible not only to forecast capital investments but also to propose measures for their increase. The results of investment forecasting by funding sources are given (at the expense of state budget funds, local budget funds, own funds of enterprises and organizations, bank loans and other loans, funds of foreign investors, funds of domestic investment companies, funds, etc., public funds for housing construction, other funding sources). Investments are distinguished by types of economic activity: "Transport, warehousing, postal and courier activities". The received forecast values of investment activity have been interpreted. Measures to increase the investment activity of railway transport enterprises are proposed. The results of the study can form the basis of the formation of the state strategy for the regional development of the country and, separately, in the development of plans and recommendations for the development of railway transport enterprises at different levels of management.

FORECASTING THE CONSUMPTION OF FUEL AND ENERGY RESOURCES FOR MILITARY UNITS IN THE ARCTIC ZONE OF THE RUSSIAN FEDERATION

The Russian Arctic is one of the promising economic zones with a rich supply of natural resources. In a world in which territorial divisions, ideological rivalries, ethnic intolerance, and even nuclear proliferation can theoretically be normalized without the use of military force, it is the wealth of energy resources that remains the last casus belli that can lead to catastrophic consequences. That is why the Armed Forces of the Russian Federation are faced with the task of protecting state sovereignty and maintaining security in the Arctic zone. To maintain the combat capability and readiness of a military facility, it is necessary to maintain stocks of fuel and energy resources at the required level. Forecasting the consumption of fuel and energy resources is the most important task. This methodology takes into account factors of various types: periodic (cyclical) and random, including those inherent in military production. All factors affect energy consumption to varying degrees.
 Cyclical factors are the most predictable and have a greater impact on the consumption of fuel and energy resources. Although random factors occupy a small share in the process of energy consumption, the amplitude of deviations can be quite significant.
 The methodology makes it possible to determine the consumption of fuel and energy resources in the context of the increasing complexity of the relationship between the economy and energy and the growing uncertainty of the future development of military units and military bases in the Arctic zone of the Russian Federation based on the applied stochastic differential equation.
 Purpose. Develop a methodology for forecasting the consumption of fuel and energy resources for military units in the Arctic zone of the Russian Federation.
 Methodology in article economic-mathematical methods, and also statistical methods.
 Results: the most informative parameters were obtained, showing some aspects of the process of forecasting the consumption of fuel and energy resources.
 Scope of the results: it is advisable to apply the results obtained in the apartment-operational subdivisions of the logistics management bodies of the military districts to obtain predicted values of the consumption of fuel and energy resources (TER)at military infrastructure facilities (military camps).
 Practical implications it is expedient to apply the received results the economic subjects which are carrying out foreign economic activity, one of which elements are export operations.

Technical and economic assessment of maintenance and repair systems of agricultural machinery

Relevance. The efficiency of agricultural production largely depends on the technical condition of the agricultural machinery fleet. The technical condition, in turn, depends on many factors that determine the level of operation of the equipment. One of the most important factors determining the reliability of agricultural machinery, the cost of restoring and maintaining the working condition of agricultural machinery is the frequency of maintenance. As a result of studies conducted in the agricultural organizations of the region, it was revealed that engineering and technical services, when organizing maintenance and repair (TO and R), use canceled GOST, referring to the fact that domestic equipment, its reliability and performance are not able to recover when frequency of 125 hours. Therefore, the purpose of this study is to determine the effect of the frequency of maintenance and repair on the preservation of the resource and the indicator of the rate of change of the resource, on the performance of the machine-tractor unit (MTA), on fuel consumption, on the costs of restoring and maintaining the working condition of agricultural tractors.Methods. The following methods were used in the study: normative, statistical, expert assessments, experimental, calculation-constructive, economic-mathematical methods. For the economic justification of the periodicity of technical impacts of agricultural machinery, statistical data from agricultural organizations were used, GOST regulating the maintenance and repair of agricultural machinery were used.Results. The maintenance and repair system, regulated by GOST 20793-2009, meets the requirements of technical and production operation of tractors. Traction properties of tractors are higher by 0.7%, specific fuel consumption during agricultural technological operations is lower by 0.5%, labor costs for maintaining and restoring technical readiness are lower by 13.8%.