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MODELING UNEMPLOYMENT RATE IN ECONOMY WITH SEARCH FRICTIONS AND CONSTANT SIZE OF ECONOMICALLY ACTIVE POPULATION



E.M. Ilyin
N.G. Kosolapenko
emil@emi.nw.ru
nina_k@emi.nw.ru
leading researcher, St. Petersburg Institute of Economics and Mathematics of the Russian Academy of Science, PhD in Physics and Mathematics
researcher, St. Petersburg Institute of Economics and Mathematics of the Russian Academy of Science
Saint-Petersburg
Saint-Petersburg

Keywords:

  • mathematical modeling
  • aggregated models of economic growth
  • search and matching models
  • natural rate of unemployment
  • time lag
  • asymptotic stability of solutions
  • employment rate
  • capital available
  • dynamics of fixed capital
  • We examine the problem of the natural unemployment rate within the model of the labor market with search frictions. We assume that the number of vacancies is determined endogenously as a given share of fixed capital that is converted into vacancies according to the stationary Poisson process. The dynamics of capital is described by an equation with a neoclassical production function. The conditions of the existence and asymptotic stability of equilibrium states of the model are analyzed. We show that the stability of the equilibrium depends on the unemployment rate. We find out how much the average negotiated salary exceeds the unemployment benefit. We also discuss the problem when the equilibrium employment level will reach its optimum from the point of view of social well-being.