New analytical capabilities of neoclassical production functions

Volodymyr Yankovyi
PhD in Economics, Associate Professor, Department of Economics and Business Planning, Odessa National Economic University, E-mail:vladimir_ya@ukr.net

Cite this article:

Yankovyi, V. (2016), New analytical capabilities of neoclassical production functions. Ed.: M. Zveryakov (ed.-in-ch.) and others [Vyrobnycha funktsiia z postiinoiu elastychnistiu zamishchennia resursiv; za red. M. I. Zveriakova (gol. red.) ta in.], Socio-economic research bulletin; Vìsnik socìal’no-ekonomìčnih doslìdžen’ (ISSN 2313-4569), Odessa National Economic University, Odessa, No. 2 (61), pp. 136–145.

Abstract

Theoretical questions of microeconomics, in particular, use of neoclassical production functions in the simulation of output based on the most important factors presented in terms of value are discussed. The optimal capital-labor ratio, that maximizes output for a given overall cost of capital (minimizes the total cost for a fixed output) for two-factor Cobb-Douglas function and CES-function is examined. The values of marginal rate of substitution of resources and equilibrium equation of manufacturer are also considered. Minimum overall costs of capital in the case of an optimal capital-labor ratio for the Cobb-Douglas function are defined. The marginal rate of substitution of resources is equal to one and marginal products of capital and working are the same (equilibrium equation of manufacturer) demonstrated in this case. The formula of the optimal capital-labor ratio is derived for CES-function. It is shown that the minimum total capital expenditures are defined similarly with the Cobb-Douglas, and the marginal rate of substitution of resources is also equal to one. It means that both neoclassical production functions under consideration behave themselves in extreme situations identically. Basic inequality is derived. It provides break-even investment in existing production, adequately described by a CES-function, on condition of investing in additional funds in the proportion of optimal capital-labor ratio. Three cases of break-even zones depending on the degree of homogeneity of the CES-function are considered. A new interpretation of marginal rate of substitution of resources as an indicator of disparities in investing funds in aggregate factors «capital» and «labor» is proposed. Practical advice on management actions of the manufacturer in violation of a single norm of substitution of resources is provided. The causes of violations of inequalities that define the zones of break-even investment are also analyzed. The main factor concluding such violations in the econometric study is a low value of coefficients scale of two-factor neoclassical functions. This is the result of imperfections in the external environment of the manufacturer. Mainly fiscal nature of the current tax policy in relation to small and medium business functions appears in the calculation of the Cobb-Douglas function and CES-function at the low values of coefficient scale.

Keywords

microeconomics; production functions; replacement resources; zones of breakeven investment.

JEL classification: C620; C670; D240;  DOI: https://doi.org/10.33987/vsed.2(61).2016.136-145

UD classification: 519.862:330.356.7

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