constructing the average income tax rate schedule does not assume the existence of a non-taxable minimum income, which is more consistent with the real-world practice of using income tax in recent decades. At the same time, the presented proofs of the main statements related to this model are more elementary, in particular, they do not rely on Pontryagin's maximum principle. For its part, in the new approximation model for constructing progressive income tax schedules of marginal rates, which has undergone the most radical modernization, excessively rigid nonlinear restrictions on the class of acceptable approximations are excluded, due to which, under weak assumptions about the input parameters of both models, it was possible to guarantee the non-emptiness of this class. © 2020 Saint Petersburg State University. All rights reserved.