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Optimization of the capital-labor ratio on the basis of production functions in the economic model of production

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Category: Economy and Management

Last Updated on 01 September 2019

Published on 19 August 2019

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Authors:

O.Yankovyi, Dr. Sc. (Econ.), Prof., orcid.org/0000-0003-2413-855X, Odessa National Economic University, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Yu.Goncharov, Dr. Sc. (Econ.), Prof., orcid.org/0000-0002-3800-8038, International University of Economics and Humanities Academician Stepan Demianchuk, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V.Koval, Dr. Sc. (Econ.), Prof., orcid.org/0000-0003-2562-4373, Odessa Institute of Trade and Economics of Kyiv National University of Trade and Economics, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

T.Lositska, Cand. Sc. (Econ.), orcid.org/0000-0003-3117-3281, Kyiv National University of Trade and Economics, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract:

Purpose. Development of a procedure for determining the optimal capital-labor ratio within the framework of two-factor production functions, as well as an analysis of the conditions for its implementation in practice.

Methodology. In the process of the conducted mathematical analysis, the search for the extrema of the most popular in economic studies, of two-factor production functions, namely the Cobb-Douglas production function, CES-function, linear function, Allen’s function in terms of capital assets, was performed. The limit rate of the technological substitution of factors in conditions of optimal capital-labor ratio was found, which proved to be unique in all investigated production functions. The indicated relationship was verified on the basis of microeconomic theory, in particular, using the equilibrium principle.

Findings. The hypothesis of the single marginal rate of technological substitution in conditions of optimal capital-labor ratio is verified. On the basis of the microeconomic theory, the procedure for determining the optimal capital-labor ratio in the framework of any two-factor production functions is substantiated due to the marginal rate of technological substitution. The proposed procedure consists in determining the marginal rate of technological substitution as the ratio of the marginal products of the production factors and equating it to one unit. The obtained ratio makes it possible to deduce the formula of optimal capital-labor ratio, provided that the indicators of the dynamics of realized products, main assets and labor remuneration in the enterprise are adequately described by the corresponding production function with non-zero substitution.

Originality. Development of a procedure for optimization of capital-labor ratio within the framework of substitutional two-factor production functions based on the formulas of their marginal rate of technological substitution.

Practical value. Theoretical conclusions and proposals were tested on the example of a Ukrainian enterprise in the field of mechanical engineering. The results of the research can be used to manage capital-labor ratio by determining its optimal volume in production, which opens the possibility of rational use of basic productive assets and labor at domestic enterprises which are characterized by relative over-equipment with high moral and physical equipment decay.

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