Economic and mathematical modeling of long-term development of national industry in the conditions of digitalization with the use of a production function

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The article substantiates the expediency of modeling the development of national industry taking into account how the main interconnected key sectors of Ukrainian economy (not only processing and extractive industries, but also agriculture) are developing, as well as taking into account the factors that cause changes in this development over time. Based on previous researches, multiplicative production function has been chosen as the base for building the model, which was modified by taking into account the peculiarities of the Fourth Industrial Revolution and the specifics of individual industries in Ukraine. The economic-mathematical model of long-term development of specified branches of economy of Ukraine in the conditions of digitalization was proposed, in which the value added in the branch is the dependent variable, and the classic components of production functions (labor and the capital) are the independent variables, as well as the new factor – digitalization, and factors, specific to individual industries (world food price index for agriculture and world raw material price index for the extractive industry). A specific feature of the model is also the use of correction factors that reflect the change in the return of factors over time and increase the accuracy of calculations. In addition, separate models have been developed to calculate each of the main factors, based on the dynamics of investments, taking into account the recursive influence of value added, propensity to invest, the condition of the world economy and other specific factors. The calculation of value added in agriculture, extractive and processing industries of Ukraine in 2010-2019 was performed using the model. The adequacy of the model was validated based on the results of its parameterization, which showed sufficient accuracy for the implementation on practice, as the average absolute error of approximation ranges from 2.94% to 4.14% depending on the industry, with abnormal 2014-2015 excluded from the calculations. The value of GDP in the country as a whole was calculated on the basis of the results of value added calculations by key industries. Taking into account the fact that the proposed set of models does not include all industries, a regression model was used to calculate GDP, to which value added for the identified key industries was used as factor. It is established that the proposed model is quite accurate and can be used to calculate the GDP of Ukraine on the basis of value added calculations in agriculture, extractive and processing industries. Given the prospects of practical use of the model for management decisions, the elasticity of the main driving factor (investments) of the development of individual industries was assessed for the main variables, which, in particular, showed that the exchange rate of hryvnia to the US dollar has a negative impact on investments, and the most pronounced – on investments in fixed assets of the processing industry. This questions the widespread idea that the devaluation of the hryvnia stimulates domestic production.