CASPIAN JOURNAL

MANAGEMENT AND HIGH TECHNOLOGIES

THE FORECASTING OF STATE MULTI-DIMENSIONAL DYNAMIC SYSTEM BY COBB - DOUGLAS FUNCTION

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Masaev Sergey N. THE FORECASTING OF STATE MULTI-DIMENSIONAL DYNAMIC SYSTEM BY COBB - DOUGLAS FUNCTION // Caspian journal : management and high technologies. — 2021. — №1. — pp. 54-62.

Masaev Sergey N. - Siberian Federal University, 79, Svobodnyy Ave., Krasnoyarsk, 660041, Russian Federation

The high speed of predicting the state of the research object by two factor mathematical models makes them in demand today. In the article, the forecasting accuracy is achieved by performing the task of identifying the research object. A two - factor Cobb - Douglas model for predicting the state of the production system is considered. A review of researches on the application of the two factorial Cobb - Douglas model showed that it is well known and widespread. In modern conditions, the change in the nature of the interaction of production factors under the influence of new factors reduces the accuracy of the forecast. The growth in the number of factors of production and the influence of the external environment make it difficult to use the Cobb - Douglas function. Changes in the relationship of factors of production form new local functions. It was found that in complex dynamic objects the importance of local functions changes. A change in the interaction of production factors depends on the influence of the external environment and determines the dynamics of the development of the system. An algorithm COBBA for calculating a two factor model of a production system is proposed. In the author's method and program, an algorithm is implemented and the values of the Cobb - Douglas production function are obtained. To assess the interaction of production factors in the research, a dynamic system is considered, which consists of eight enterprises. The classical calculation of the two factor model as a dynamic system through the regression equation is performed. Also we calculated three local functions that can be used in the Cobb - Douglas function for forecasting. The regression equation is used for operational (fast) forecasting by a dynamic system, taking into account changes in its dimension and the influence of environmental parameters. The specified forecast accuracy has been achieved.

Key words: control theory, dynamical system, Cobb - Douglas function, two factor model, production system, factors of production, local function, identification