Comparative analysis of production function models of the machine building and metalworking industry in the Samara region

The published article is devoted to the development and identification of mathematical models of the functioning of the mechanical engineering and metalworking industry in the Samara region. The initial data of official statistics on the results of the functioning of the mechanical engineering and metalworking industry of the Samara region in the period from 1965 to 2021 have been collected and systematized. The parameters of Cobb-Douglas production functions have been identified at various study intervals in versions of the original and smoothed actual statistical data. Both the entire time period of the study and individual local intervals of stable and crisis functioning of the analyzed production system were considered as parameter identification intervals. The values of the parameters of production functions were calculated for different periods of the study and the qualitative characteristics of the obtained model solutions were calculated. A comparative analysis of the parameters and characteristics of the resulting models was carried out. Identification of unknown parameters considered in the work of production functions was carried out using the least squares method. The study used official statistical data from the Samara Regional Committee of State Statistics as empirical material.