The article deals with topical issues of the application of production functions for the study of macroeconomic indicators of the regional economic system on the example of the agro-industrial complex of the Rostov region. In the conditions of sanctions, the justification of the state agrarian policy may be significant, which is possible with the use of production functions. The use of functions of this type for this purpose has a rich history. Production functions for the analysis of macroeconomic indicators began to be used at the beginning of the XX century. The value of the application of production functions is determined by the following. They allow us to study the indicators of the regional economic system using the "black box" method. Based on the results of the analysis of this function, it is possible to form the agrarian policy of the region. A representative sample of the factors of production of the agricultural and industrial complex of the Rostov region has been formed. The macroeconomic indicators of the considered economic system are calculated. As a result of the research, a mathematical model of the agricultural and industrial complex of the Rostov region was obtained in the form of a production function, an equation for calculating capital return, labor productivity and other indicators.