Anatolij Pitelin

Sergei Graborov

The article deals with the optimization of nonlinear multidimensional tax structure under the majority rule. The optimization under the majority rule means determining the composition of the citizens’ majority and tax structure providing the minimum of tax payments for each team member. The vector optimization of the tax structure serves as a source model. Fixed rates of income and assets, as well as by their demand functions characterize all the citizens-taxpayers. Income and property taxes are paid under a nonlinear scale, and the consumption tax is based on a linear scale, with tax rates and tax bases thresholds being the optimizable values. In addition to the tax functions and individual criteria, the composition of the source model includes some limitations on the aggregate amount of tax payments, as well as on the valid values of tax rates. The original model is converted into the task of majority optimization. In order to accomplish this task, the group of simple common citizens, whose individual criteria will be taken into account, is determined. The values of threshold levels for the tax bases and corresponding tax rates to them, which are the best at the same time for all the members of the majority, are considered to be a decision of this task. It is shown that a steady majority group of citizens, in which nobody would benefit, if he goes out of it, may be formed of the taxpayers, whose income or property does not exceed the median sizes. And the best way for all members of this group is the progressive income and assets taxation. The need of introducing some additional conditions forming a coalition, which ensure taking a single decision on optimal tax rates by all members of the majority group is established. The conditions (under which the criteria of all members of this group are the same) are found and proven, and that guarantees taking a single decision on tax rates. The paper presents a majority of the optimal variant of common using progressive direct and differential indirect taxes for citizens. The order and the formulas for calculating the respective tax rates are presented.