Optimal Control of the Profit Tax Rate Based on the Nonlinear Dynamic Input-Output Model

Development of nonlinear dynamic controlled input-output models and their analysis are of interest both to mathematicians and economists. This paper discusses one of such models. The focus is on relations between phase variables (outputs) and macroeconomic parameters, and also on the consumption sphere modeling. The main objective of this work is to show how to effectively manage the profit tax rate to maximize the budget revenue while maintaining a given economy growth. This economic task is reduced to a nonlinear problem of optimal control. To solve this problem, we use the adaptive method of optimal control (Gabasov's method). The main idea is to reduce an optimal control problem to an interval problem of linear programming. We test the approach on the example of German economy. The model is determined based on the information obtained from the WIOD tables and World Bank data (Germany, period: 2013-2014). Our approach is implemented as a software package in MATLAB environment.