Issue: № 11, 2022
Doi: https://doi.org/10.37634/efp.2022.11.1
The development of Ukraine's economy is taking place in the conditions of contradictory trends of getting rid of the consequences of the totalitarian past with a rigid planned economy that did not take into account rapid changes in demand and production, and efforts to become a country with a real market economy. Therefore, the ability to forecast prospects for Ukraine's economic progress is very important. To solve the problems, Leontiev's dynamic model with three types of production activity was used: the production of work tools (industry 1), the production of labor items (industry 2), the production of consumer goods (industry 3), which, according to the authors, best corresponds to the modern realities of the Ukrainian economy. Data for calculating the coefficients of the model were taken from the website of the State Statistics Office for the years 2010-2020 on a quarterly basis. The grouping of data was carried out according to the requirements of the model, by compiling the indicators of the branches of production that are included in the corresponding type of production activity. The model of production of consumer goods is described by an exponential dependence with the addition of sinusoidal effects. The derivatives of the first order were replaced by the differences of the next and previous values of the indicators. The data of each indicator for the previous period were taken as the basis of the arguments. The frequency and amplitude of the two sinusoids were determined through spectral analysis. The calculation of coefficients of models for the production of work tools and the production of work items was carried out by the method of regression analysis. The coefficient of determination of the models exceeded 0.9. Cauchy's problem regarding the production of labor tools has been solved. Based on the coefficients of the tool production model a, g1, b1, b2, coefficients r0 (r zero) and lambda are determined, which allow to assess the state of the country's economy. A system of three equations was used to calculate the forecast for 2021-2022. A comparison of the forecast with DerzhStat data for 2021 showed acceptable forecasting accuracy.
Keywords : Leontiev model, Cauchy problem, nonlinear model, forecast, economy of Ukraine
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