On Optimality of the Flat Proportional Tax Rate in a Two-Level Economic System

We study the functioning of an hierarchical system: the state–an investor (enterprise head)–manufacturing. For the system with various manufacturing functions we simultaneously solve the following two problems. For the investor we solve the consumption-investment problem, and for the state, the problem of increasing the tax collection. We prove a turnpike theorem on the optimal value of the investment part for the lower level of control in the two-level problem with flat proportional taxation. We give examples showing that there exists a situation for which the two-level problem of tax rate optimization has a nontrivial optimal solution.