Keywords: capital productivity, capital-labor ratio, productivity of labor, reference point, parabolic cone, elasticity, coefficient of technology


Traditionally, the analysis of the enterprise activity is carried out with a separate consideration of fixed assets and employees efficiency. But the complex modeling and research of these indicators and these processes are not executed. Therefore, there is a need to implement the transition to of  complex modelling and integrated research in the activity of the enterprise that can be implemented using the methodology of production functions. This is due to the fact that the methodology of production functions is the only classical model that makes it possible to comprehensively review and investigate the production activities of enterprises and industries. The main advantage of this model is that it analyzes the three most important factors of any production process - the value of fixed assets, the number of employees or the costs of labor in man-hours and the output in monetary or physical terms.

The purpose of the study is to substantiate theoretical methods for estimation production functions and to establish the causes of disagreements arising between them and statistical models.

In the study performed, the following tasks were solved:

  • the necessity of the transition from a separate analysis of the enterprise, when fixed assets and employees are considered separately, to their integrated consideration, that can be implemented using the methodology of production functions are justified;
  • the main shortcomings inherent in statistical models and in particular production functions are established;
  • theoretical methods of substantiation of indicators of the analytical (theoretical) production functions of Cobb-Douglas are applied.

A technique is proposed for the theoretical indication of the constituent elements of a production function - elasticity indicators α, β and coefficient A. Next, the Cobb-Douglas analytical production function is determined and investigated. The next and final stage is the analysis of discrepancies that are observed in the analytical and statistical functions.

The proposed methodology of modeling and planning for the development of an enterprise, which uses analytical production functions, significantly improves the reliability of decisions made, since it largely eliminates the shortcomings inherent in statistical functions.



Vyrobnycha funktsiia, Izokvanta, Izokosta (Production function, Isoquants, Isocost). Wikipedia. (in Ukrainian)

Skvortsov I. B., Tymchyshyn I. Ye., Yemelianov O. Yu. (1993) Analitychnyi metod vyznachennia parametriv multyplikatyvnykh vyrobnychykh funktsii (An analytical method for determining the parameters of multiplicative production functions). Lviv: NU “LP”. (in Ukrainian)

Bilyi L. A., Dutka H. Ya. (2011) Modeliuvannia ekonomichnykh protsesiv statystychnymy vyrobnychymy funktsiiamy (Modeling of economic processes by statistical production functions). Lviv: Technical news. (in Ukrainian)

Barro R. Dzh., Sala-i-Martin H. (2010) Jekonomicheskij rost (Economic growth). Moscow: BINOM. Knowledge Lab. (in Russian)

Hrabovetskyi B. Ye., Shvarts I. V. (2013) Vyrobnychi funktsii v ekonomichnykh doslidzhenniakh (Production functions in economic research). Sumy: Herald Sumdu. Economy Series. (in Ukrainian)

Kulyk A. B. (2010) Modeliuvannia vyrobnychykh funktsii (Modeling of production functions). Kyiv: Vcheni zapysky. (in Ukrainian)

Kurzenev V., Matveenko V. (2018) Jekonomycheskij rost (Economic growth). St. Petersburg: PITER. (in Russian)

Moroz O. V., Hrabovetskyi B. Ye., Mironova Yu. V. (2010) Vyrobnychi funktsii v ekonomichnykh doslidzhenniakh na mikrorivni (Production functions in economic research at the micro level). Dnieper: ECONOMIC SCOPE. (in Ukrainian)

Nureev R. M. (2008) Jekonomika razvitija: modeli stanovlenija rynochnoj jekonomiki (Development economics: models of market economy formation). Moscow: Norma. (in Russian)

Romer D. (2014) Vysshaja makrojekonomika (Higher macroeconomics). Moscow: Id Vshe. (in Russian)

Renshaw, Geoff. (2005) Maths for Economics. New York: Oxford University Press.

Solow R. M. (1956) A Contribution to the Theory of Economic Growth. Cambridge: The Quarterly Journal of Economics.

How to Cite
Skvortsov, I. B., & Kulyk, M. A. (2019). FEATURES OF THEORETICAL AND STATISTICAL MODELING OF COBB–DOUGLAS PRODUCTION FUNCTIONS. Scientific Bulletin of Ivano-Frankivsk National Technical University of Oil and Gas (Series: Economics and Management in the Oil and Gas Industry), (1(19), 53-67. https://doi.org/10.31471/2409-0948-2019-1(19)-53-67