Procedure for determining the optimal capital-labor ratio on the basis of production functions

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.