Modeling the production function with the account for the change of factors’ output over time on the example of manufacturing industry in Germany

The article analyzes production functions, investigates the features of the Cobb-Douglas function in its multiple variations. On the basis of the analysis carried out, as well as the practical needs of modeling the production systems, the necessity of modeling the production function with the account for the change in the output of production factors over time, is substantiated. As well as with the account for the factor of the modern industrial revolution, characterized by the digitalization of manufacturing.An approach to the development of a function is proposed, which takes into account the change in the output of production factors over time in the context of digitalization. The corresponding production function was modeled based on the example of the manufacturing industry over 2000-2019 in Germany, which is a country that is among the first to introduce modern technologies, including digital ones. The results of modeling the value added using the production function with and without the account for the change in the weight coefficients of the factors over time are presented.It was found that adding the correction factors that define the change in weight coefficients for the factors of the production function over time increased the accuracy of the calculations. Also, a decrease in the resulting (after taking into account the coefficient change over time) exponent coefficient was revealed in the digitalization factor and its increase in the factor of fixed assets involved in the production process (the cost of machinery and equipment) - the output on fixed assets increases annually, and the output of the digitalization factor decreases by about the same extent.It was found that since the relative output of digitalization decreases over time, if there is a need to achieve growth in output through digitalization, it has to be carried out at a growing pace, that is, investments should increase over time. In addition, the earlier investments are introduced, the greater the effect they will give. When modeling the sectors of the Ukrainian economy, it’s advisable to use correction coefficients calculated based on the German data, rather than calculate them based on past periods on the basis of Ukrainian data. From the point of view of practical calculations, this is justified not only by the belated repetition of the technological development processes of developed countries by developing ones (that is, Ukrainian enterprises are introducing the same technologies, but with a delay of 5-10 years or more), but also by the greater relevance of German statistics to the needs of modeling.