Optimal behavior of agents in a piecewise linear taxation environment

We study analytical properties of the optimal income taxation model. In this model we consider the maximization of utility of an agent of the given type. The real meaning of the utility is the net profit of the legal entity. The mathematical consideration of the taxation optimization uses methods of probability theory, functional analysis and optimal control. The totality of all agents in the economy is represented by the probability space of their types. Optimal income taxation differs from commodity taxation, another branch of the optimal tax theory. Actual taxes are commonly linear or segmented, which naturally suggests us to consider such cases in this research. To be more precise, we describe the general piecewise linear taxation model with increasing linear coefficients. The latter is necessary for the tax function to be convex. An explicit description of optimal functioning of agents depending on their types is obtained. In particular, we consider optimal labour effort and optimal utility.