Modeling of a closed mono-branch labor market conditions

Abstract

Market modeling issues are currently acute as they are responsible for efficient operation of a labor market to achieve full employment and a high rate of economic growth. The aim of the study is to construct a theoretically reasonable closed mono-branch mathematical model that describes the behavior of economic agents at a labor market using a system of differential equations. The model is constructed on the following hypotheses: 1) a market is a closed system with a constant number of the unemployed (applicants) and employees; 2) employees and applicants can be divided into three conventional categories: low-skilled workers the demand for whom is low or absent, the number of these people is equal to the number of vacant positions at an enterprise; average-skilled workers, who may later join to a category of low-skilled or highly qualified workers; highly qualified workers and employers are mostly interested in them. To analyze the dynamic of average-skilled workers the staff training coefficient is implemented to select these employees. Shares of the each category representatives have been chosen as modeling variables. The staff training coefficient, as well as the number of employees and the unemployed and the amount of subjects of each category have been accepted to be constant according to the initial hypotheses. The dynamic of the variables is described by the system of three nonlinear differential equations. Consideration of the system peculiarities makes it possible to find the exact solution of the system in quadratures i.e. to determine the quantitative structure of each of the subjects of the labor market at any moment of time. Particular attention is paid to the asymptotic properties of solutions: the equilibrium points of the system have been found and their stability has been investigated. The research results have revealed that a proactive employer hires highly qualified workers and pays particular attention to human resource policy and it proves the model adequacy. The economic interpretation of the obtained mathematic results in the terms of the initial task has classified possible situations at a labor market and has made a conclusion about the dynamics of each category of the economic agents depending on the initial conditions. Further studies will be devoted to the system complication by including new parameters, e.g. salary impact factor, training costs spent on average-skilled employees, lag, etc. The model may be interesting for both the scholars studying labor market conditions and human resource managers. Keywords labor market conditions, dynamic model of a labor market, a closed system, employees, the unemployed, staff, staff turn-over, skills of employees, system of differential equations, asymptotic features.