Resumen
This article suggests a mathematical justification of the possibility of transition to progressive taxation on personal incomes, allowing socially redistribute the tax burden between different groups without losing the total amount of tax yield to the state budget from personal income tax. The methods of the transition from a flat to a progressive tax scale of income taxation developed. A generalized mathematical model of transition to progressive taxation, which allows evaluating all possible options for the proposed reform of flat rate transformation, is suggested. An algorithm of modeling progressive income taxation is proposed, which takes into account the likelihood of tax evasion. In the following parts of the article a probabilistic model of progressive income taxation and a mechanism to optimize the level of tax rates is formed. A linear progressive tax scale with and without tax evasion are developed based on actual statistics.Keywords: tax, innovation, probability, method, modelJEL Classifications: C10, H24