Процедура визначення оптимальної фондоозброєності на основі виробничих функцій

Oleksandr Yankovyi; Volodymyr Yankovyi

doi:10.33987/vsed.4(68).2018.77-87

Authors

Oleksandr Yankovyi Odessa National Economic University, Ukraine https://orcid.org/0000-0003-2413-855X
Volodymyr Yankovyi Odessa National Economic University, Ukraine https://orcid.org/0000-0001-7005-5291

DOI:

https://doi.org/10.33987/vsed.4(68).2018.77-87

Keywords:

optimal capital-labor ratio, production function, equimarginal principle, marginal rate of factors substitution

Abstract

The article discusses the theoretical and applied aspects of the procedure for enterprises optimal capital- labor ratio determining with using a two-factor production functions. The constant neglect of the capital-labor ratio managing issues, determining its optimal value at the production, steadily leads to the irrational use of basic production assets and labor. And this inevitably manifests itself in the competitiveness reducing of separate domestic enterprises and industries, in the deterioration of their financial condition, and ultimately leads to bankruptcy. As a result of the conducted mathematical analysis, the extremes were searched for the most popular in economic researches a two-factor production functions ‒ Cobb-Douglas, CES-functions, linear functions, Allen functions by the value of the capital-labor ratio. On the basis of microeconomic theory, in particular, the equimarginal principle, the hypothesis of a single marginal rate of resources substitution in conditions of optimal capital-labor ratio was tested. The procedure for the optimal capital-labor ratio determining in the framework of any two-factor production functions with using the marginal rate of substitution is substantiated. The proposed procedure consists in determining the marginal rate of substitution as the ratio of the marginal products of production factors and equating it to a unit, or to the ratio of average prices for resources. The obtained interrelation allows us to simply derive the formula of optimal capital-labor ratio, provided that the variation indicators of sold products, fixed assets and wages at the enterprise are adequately described by the corresponding production function with a non-zero substitution. The trajectory of production growth at the enterprise in the long-term period, which is an isocline, passing through the points of optimal capital-labor ratio for the growing costs of production resources, is determined.

Author Biographies

Oleksandr Yankovyi, Odessa National Economic University

Doctor of Economics, Professor, Head of Enterprise Economics and Business Organization Department

Volodymyr Yankovyi, Odessa National Economic University

PhD in Economics, Assistant Professor of Department of Economics, Law and Business Management

References

Vitlinskyi, V. V. (2003). Economy modeling [Modeliuvannia ekonomiky], KNEU, Kyiv, 408 s. [in Ukrainian]

Grabovetskyi, B. Ye. (2006). Production functions: theory, construction, using in production management: monograph [Vyrobnychi funktsii: teoriia, pobudova, vykorystannia v upravlinni vyrobnytstvom: monohrafiia], UNIVERSUM, Vinnytsia, 137 s. [in Ukrainian]

Kulyk, A. B. (2010). Modeling of production functions [Modeliuvannia vyrobnychykh funktsii], Vcheni zapysky, No. 12, s. 283–288 [in Ukrainian]

Moroz, O. V., Grabovetskyi, B. Ye., & Mironova, Yu. V. (2010). Production functions in economic research at the microlevel [Vyrobnychi funktsii v ekonomichnykh doslidzhenniakh na mikrorivni], Ekonomichnyi prostir, No. 35, s. 112–119 [in Ukrainian]

Pavelescu, F. (2011). Some aspects of the translog production function estimation, Romanian Journal of Economics, Vol. 32, Issue 1 (41), pp. 131–150.

Turner, K., Lange, I., Lecca, P., Jung, Ha S. (2012). Econometric estimation of nested production functions and testing in a computable general equilibrium analysis of economy-wide rebound effects, Stirling Economics Discussion Paper 2012-08, Stirling Management School, University of Stirling.

Daniels, Gerald and Kakar, Venoo (2017). Economic growth and the CES production function with human capital economics, Bulletin, Vol. 37, Issue 2, pp. 930–951, available at: https://ssrn.com/abstract=2878578 or DOI: 10.2139/ssrn.2878578.

Alvarez-Cuadrado, F., Van Long, N., & Poschke, M. (2017). Capital-labor substitution, structural change, and growth, Theoretical Economics, Vol. 12, Issue 3, pp. 1229–1266. DOI: 10.3982/te2106.

Miller, E. (2008). An assessment of CES and Cobb-Douglas production functions, D.C: Congressional Budget Office, Washington.

Goonatilake, R. (2014). Impacts of labor and capital on manufacturing production function. British Journal of Economics, Management & Trade, Vol. 4, Issue 2, pp. 158–172. DOI: 10.9734/bjemt/2014/5619.

Xianbai, Li. (2008). The Cobb-Douglas production function, costs, factor quantity employed and parametric estimation: a firm level perspective, Journal of Beijing Institute of Technology, Vol. 10. Issue 6, pp. 70–76.

Henningsen, A., & Henningsen, G. (2012). On estimation of the CES production function – revisited, Economics Letters, Vol. 115, pp.67–69. DOI: 10.1016/j.econlet.2011.12.007.

Econometrics (2003). Ed. by A. F. Kabak, O. V. Protsenko [Ekonometriia; za red. A. F. Kabaka, O. V. Protsenko], NMTSO-ODEU, Odesa, 562 s. [in Ukrainian]

Yankovyi, V. O. (2006). Forecasting the break-even area of investment in the baking industry through the production function [Prohnozuvannia zony bezzbytkovosti investytsii u khlibopekarsku promyslovist za dopomohoiu vyrobnychoi funktsii], Vìsnik social’no-ekonomìčnih doslìdžen’, No. 22, s. 410–414 [in Ukrainian]

Cherevko, Ye. V. (2007). The optimal capital-labor ratio and initial capital [Optymalna fondoozbroienist ta pochatkovyi kapital], Vìsnik social’no-ekonomìčnih doslìdžen’, No. 26, s. 359–365 [in Ukrainian]

Yankovyi, V. O. (2016). Mathematical analysis of neoclassical production functions [Matematicheskiy analiz neoklassicheskikh proizvodstvennykh funktsiy], Ekonomіka: realіi chasu, No. 2 (24), s. 78–83, available at: http://economics.opu.ua/files/archive/2016/No2/78.pdf [in Russian]

Yankovyi, V. O. (2018). Capital-labor ratio in machine building of Ukraine: reality and optimality [Fondoozbroienist u mashynobuduvanni Ukrainy: realnist і оptimalnist], Екоnomіkа Ukrainy, No. 8, s. 16–29 [in Ukrainian]

Koval, V., Slobodianiuk, O., Yankovyi, V. (2018). Production forecasting and evaluation of investments using Allen two-factor production function, Baltic Journal of Economic Studies, Vol. 4, No. 1, pp. 219–226. DOI: 10.30525/2256-0742/2018-4-1-219-226.

Galperin, V. M. (2004). Microeconomics [Mikroekonomika], Institut «Ekonomicheskaya shkola», Sankt-Peterburg, 482 s. [in Russian]

Perloff, J. M. (2014). Microeconomics. Chapter 7: Costs, available at: http://wps.aw.com/bp_perloff_microecon_7/242/61990/15869495.cw/content/index.html.