In article mathematical formalization of concept of a lag effect of system as a whole, and in particular a lag effect of the social and economic system arising at studying of processes and the phenomena of a labor market is considered.This property allows to consider a problem of a temporary gap between operating impact and result of change of system of a labor market on this influence.

Keywords: Labor market, lap effect, optimizing tasks, economic-mathematical modeling,operating influence, social and economic system

Labour market is a complicated social and economic system, which requires the necessity to consider a number of characteristic properties (stochasticity,nonlinearity,inertance,nonstationarity) for investigation and modelling labor market processes and phenomena. In this article the problem of optimum control of a labour market is mathematically formalized. This allows for regional system of a labor market to reach desirable indicators, namely the set unemployment rate.

Keywords: Labor market, optimum control, optimizing tasks, principle of a maximum of Pontryagin, social and economic system