Тестування методу побудови виробничих функцій зі змінними коефіцієнтами (ВФЗКЕ)

• Дата: 2018
• Автори: Литвин, Олег Миколайович, Артюх, Марина Володимирівна
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Kamianets-Podilskyi National Ivan Ohiienko University 2018
• Онлайн доступ: http://mcm-tech.kpnu.edu.ua/article/view/140045
• Назва журналу: Mathematical and computer modelling. Series: Technical sciences

In the article we consider the classical Cobb-Douglas production function, which is a production function with constant coefficients and is used for the study of economical systems of any scale. The formula for the classical production function of Cobb-Douglas is given and it is explained that its parameters α, β are partial elasticity coefficients. But with a more detailed study it turned out that it is possible to construct a production function with variable elasticity factors. Such a production function with variable coefficients allows for better approximation of data. Examples are given of construction of a production function with variable coefficients and a production function with constant coefficients in which the quality of the approximation of the Cobb-Douglas production function and the production function with variable coefficients are compared. An example of a production function with variable coefficients for the study of the economy of agriculture in Ukraine is considered. In the course of the research, the authors found that the following is evident: the mean square deviation σ found for the approximation of experimental data by means of functions with variable elasticity coefficients can not be greater than the mean square deviation obtained for approximating functions with stable elasticity coefficients.Since the effectiveness of using the production function with variable coefficients in the study of economic problems is monitored, it is necessary to test the method of constructing production functions with variable coefficients. A theorem on the testing of the method for constructing production functions with variable coefficients (PFVCE) is formulated and proved. The result of a computational experiment using a production function with variable coefficients for illustrating the proved theorem is given. In the future, it is planned to continue research on the use of production functions with variable coefficients in other economic systems.