MODELING THE DYNAMICS OF OUTPUT OF PRODUCTION USING PRODUCTION FUNCTIONS IN POLAR AND SPHERICAL COORDINATES

Koroed DI Fartushny ID Candidate. Sci. Science, Associate Professor
National Technical University of Ukraine "KPI"

MODELING THE DYNAMICS OF OUTPUT OF PRODUCTION USING PRODUCTION FUNCTIONS IN POLAR AND SPHERICAL COORDINATES
In this article was analyzed the economic-mathematical dependence of factors of
production and physical output of production process of enterprise of any form of activity
using the apparatus of production functions in polar coordinates. A feature of this
approach is that unlike the production functions in the Cartesian coordinate system in an
apparatus, developed during the process of this research, the emphasis is not on the
definition of a quantitative measure of the factors of production, but on their relationship
to each other. This approach can be used as a practical tool for solving a number of
planning and practical analytical problems of the company. Mathematical model that was
used in this research study is based on a production function Cobb-Douglas form and the
budget constraint. Were calculated the main numerical characteristics of the production
function in polar coordinates, namely: average return ( average product ) of factor of
production, the marginal return ( marginal product ) of factor of production, the elasticity
of output to production resources. Found that the marginal products of capital and labor
are quantitatively less than the average products of these inputs. Has also been developed
and proposed a general algorithm for solving this problem, which includes obtaining input
of various kinds, solving of this mathematical problem, obtaining decisions, their
interpretation and bringing it to leadership.
Keywords: economic-mathematical model, production function, polar coordinates. 

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