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DOI: http://dx.doi.org/10.20534/EJEMS-17-1-82-86
Korkuna Natalia Mikhaylovna, Postgraduate student of the Department of Mathematical Modeling of Social and Economic Processes (KMMSEP) of Ivan Franko National University of Lviv E-mail: nkorkuna@gmail.com
Justification of the concept of mathematical methods and models in making decisions on taxation
Abstract: The paper presents the concept of the application of mathematical methods and models in making decisions on taxation in Ukraine as a phased process. Its performance result is the selection of an effective decision based on regression and optimization models.
Keywords: tax system, taxation, optimization models, tax burden, tax rate, concept of taxation, shadow economy.
The tax system in Ukraine is a combination oftaxes and duties (mandatory payments) established on the basis ofthe legal rules that regulate the amount, form and timing ofcol-lection oftaxes and payments into the government budgets.
According to the practice, the result of tax burden increase and, in its turn, increase of budget revenue, is always the acceleration of inflation processes. This happens because the tax rate increase results in the increase in prices for goods and services leading to the worsening of the financial standing of economic entities and ordinary individuals. For the process of tax system reformation in the country it is required to use the most effective methods of taxation of economic entities, and to determine the optimal tax rates for their activities. However, much too low tax rates will result in low tax revenues,
and much too high tax rates will force business into a shadow economy. In this regard, the scientific studies related to determining the optimal tax burden in the country take on particular importance. The practice of making macroeconomic decisions requires the creation of tools that would enable a sufficient degree of reliability to evaluate the effectiveness of the state fiscal policy in terms of its impact on the level of business activity in the country. The urgent task for Ukraine is to search its.own concept of taxation that would meet the peculiarities of the real situation in the economy because-the overapply-
ing of forms and methods of tax policy employed in the world's practice not only failed to provide the desired results but also aggravated the controversy and misunderstanding between the state and entrepreneurship.
The problems ofthe tax system reformation in the conditions of the Ukrainian economy market transformation, theoretical and practical aspects of the income taxes impact on the budget, the tax system optimization from the point of fiscal adequacy and economic efficiency were highlighted in the researches of such well-known national economists, such as V L. Andrushchenko [1], L. O. Bili-aievska-Plotnyk [2], O. D. Vasylyk [3], V. V. Korolenko [4], Y. I. Liashenko [5], T. F. Mykhailova [6], and A. M. Soko-lovska [7]. The economic and mathematical model of tax burden control, scientific and practical recommendations for effective use of tax potential ofUkraine's economy were developed in the research papers of I.Ya. Chugunov [8], S. L. Londar [9], G. S. Yastrebova [10], and O. Grin [11].
However, the task of the research of support for making decisions in taxation and building the economic and mathematical models that, in the best way, allows illustrating the process of the state budget replenishment and determining the optimal tax burden, is vital for the contemporary economic science and requires a detailed and comprehensive analysis and the searching for the effective methods of solution.
Figure 1. The concept of the application of mathematical methods and models in making decisions on taxation
One of the options of solving this task may be the concept that we offered — to use mathematical methods and models for making decisions on taxation and effective growth of the budget revenue by means of the methods of economic and mathematical modeling (Fig. 1). In our opinion, the study of the process of provision the support for making decisions in Ukraine's taxation should include three main stages as following:
1. The Study of taxation development trends;
2. The Determining of the factors that influence the budget replenishment with the cognitive modeling applied;
3. The Development of the effective methods of tax revenue optimization.
During the first stage of the concept, the collection of statistical data that describe the current conditions
of the government and local budgets and the trends of their replenishment process development is performed; and their economic analysis is carried out. Also, during this stage there is the selection of the indicators that will be used for the-building of economic and mathematical models further on.
It is possible to get the information about tax and non-tax revenues to be based on the statistical data that describe the current conditions of the government and local budgets replenishment. The State Statistics Service of Ukraine provides a lot of such data. Its Department of Structural Statistics and Corporate Finance Statistics gives forth the statistical publications, such as "Business Entities Activities", "Small Business Entities Activities". The comprehensive publications are "Annual Abstract of Statistics of Ukraine", "The Regions of Ukraine", "Ukraine by the Numbers", and "Statistical Bulletin".
Based on the statistical data sets, it is appropriate and convenient to build various economic and mathematical models and implement them by using corresponding software. The practical value of the economic and mathematical modeling is the potential possibility to formalize processes characterized by high level of uncertainty and randomness (in particular, the processes of the government budget replenishment and determining of the tax burden also meet these requirements).
The applying of the economic and mathematical modeling makes possible the analyzing of the trends of all levels budgets replenishment at different times, to study and compute the impact of various factors on the value of budget revenues and to determine an optimal tax burden.
The trend analysis [12, 13] was used to study the trends of the tax system of Ukraine following up the period of the years 2001 to 2015. The Building of time trends through time series modeling is the method, which is recommended at the-starting of the analysis in order to have the first impression of the process development trends and the-determining, which models should be applied in future to approximate the process.
We have selected some equations, which are frequently used for the building of time trends, in particular linear, logarithmic, quadratic, with a power, exponential, the unknown parameters of which are calculated by least square method.
For the study of the process of tax revenue into the budget, the regression analysis [14] was used as one of the most powerful and easiest tool for the practical implementation to measure the density of connection between the factors. By using regression models it is possible not
only to follow the current trends and specific features of the studied process but also to do forecast for the future periods and to develop the strategies of impact on specific factors aimed to change the resulting indicator.
The resulting linear equations of the regression, as well as the multifactor model [15] (for its building there selected the factors related to the dependent variable as close as possible) are used to assess the impact of each selected factor on the studied process and to forecast the scope of revenues into the government budget.
The result of the concept's first stage is the set of models that (determined on the basis of correlation and determination coefficients) most correctly describe the development of tax systems of Ukraine during the period from 2001 to 2015.
During the second stage of the concept it is proposed to analyze the factors that influence the budget revenues by means of applying the cognitive modeling. In particular, we will examine the factors that influence the replenishment of the government and local budgets in real-time mode.
The cognitive model (or cognitive map) of the system represents an oriented signed (weighted) graph, the nodes of which correspond to the elements (subsystems factors) of the system under investigation, and the arcs of which correspond to the relations between them. In terms of the issue under investigation, the important factors (the graph nodes) are the following:
• private enterprises;
• state institutions;
• natural individuals;
• the tax burden;
• shadow economy.
Thus, the first and the second stages of the concept include the consideration of the government budget replenishment process from the point of macroeconomics, i. e. it is possible to use the results of these stages implementation for the development of the recommendations for more effective management (the stimulation of the factors that positively influence the process, and the reduction of the detrimental effect of other factors) of the process of the development of the tax system of Ukraine.
The use of economic and mathematical modeling makes possible the time-wise analyzing of the trends of the replenishment of all levels budgets, to study and compute the impact of various factors on the amount of budget revenues and the area of taxation.
During the third stage of the concept, the development of the effective methods of the determining of the tax burden and budget allocation is carried out. The opti-
mization models were used for the development of these methods.
We proposed a task model for determining the optimal tax rate with the use of modified Laffer curve [16], which shows the relation between the value of a statutory aggregate tax rate and tax revenues. For example, if the current tax rates are too high, then their optimal decrease will make possible to increase the production providing that tax revenues are not changed or even increased.
For Ukraine, as for many other countries, the problem of shadow economy is particularly important. This is due to the fact that in the course of economic reforms and the introduction of market mechanisms of economic management, which were first carried out in the conditions of the most profound crisis, the extent of shadow economic activity and its role in the reconstructive process had increased dramatically. In view of the issues stated above, during this stage it was proposed an optimization task model for determining the optimal tax rate taking into account the shadow economy coefficient.
The two-factor optimization model for solving the issue of production planning that ensures the maximum tax payments to the budget [17], is also proposed to solve the issue of increasing tax revenues without increasing the tax burden on manufacturers. The model is applicable to enterprises that while using available resources are able to produce the products of various types. The use of models makes possible to plan the production when available resources are used to maximum, and at the same time the maximum profit and tax amount (excise duty) from sales is ensured.
For the efficient functioning of the state_budget system, it is required, on the one hand, to replenish the government and local budgets as maximum as possible, and on the other hand, to reallocate the budget funds in the optimal way. It stands to reason that the execution of budget expenditures is related to the use of budget funds, which is determined as budget financing [18] in the economic literature. The local budget expenditures are formed by means of assigning the expenditure functions to the bodies of state and local governments. The financing of local expenditures and the use of local fi-
nancial resources is closely related to the state budget expenditures. As it is the state that, while using financial resources, provides the opportunity for the performance of tasks and functions that it faces at one or another stage of social development.
The so-called chronic deficits of the budget, state specialized funds and the powerful state-owned companies lead to systemic macroeconomic problems. Thus, the current model of a budgetary system creates a space for the specific reorientation of financial flows, as the result of which the budgetary resources are often used for other than the purpose specified, ineffectively, and imbalances are formed at some levels of the budget system.
We have analyzed the effectiveness of the budget system of Ukraine, in particular the local expenditures financing, there was created the time trend dynamics of local expenditures, and there was developed the mathematical task model for the determining of the optimal allocation of funds among the regions and the task model for the-determining of the optimal allocation of the budget funds on the expenditure side [19].
The result of the third stage of the concept is a number of optimization models that can be used to increase revenues to budgets of all levels, to reduce the tax burden, effective budget allocation and optimization of taxation.
Conclusions. The implementation of the proposed concept of the use of mathematical methods and models of making decisions on taxation in Ukraine makes it possible to provide favorable conditions for the development of entrepreneurial activity of economic entities. The positive changes in the conditions of entrepreneur-ship may provide a prompt improvement of the living standards for particular persons (entrepreneurs, employees, and their families) and the development of the Ukrainian population well-being on the whole. The obtained results will be useful for the government authorities during the development of tax policy that would, on the one hand, facilitate the increase of tax revenues of the state, and on the other, would not be a disabling burden for business entities and would not force them into a shadow economy.
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