Probability model of poverty calculation subject to different forms of income taxation

The article highlights a probabilistic model constructed for calculating the number of poor and the total income tax levied on all taxpayers under different income tax systems. There is considered the proportional income tax system adopted in the Russian Federation, as well as single-stage systems with both fixed and variable tax rates, in which individuals with low incomes are exempted from income tax. For these tax systems there have been found the dependences of the expected value of the number of the poor and the total income tax on the tax rate, tax-free minimum, and also on the laws of probabilities distribution of total income and the living wage of an individual. A numerical simulation of the found dependences was carried out. The conditions under which the abolition of income tax for individuals with low incomes reduces the number of poor were determined. Mathematical criteria are formulated with the help of which it is possible to assess the feasibility of moving from a proportional system to single-stage income tax systems.