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Conditions of Balanced Growth for Model of Economy with Search Friction and Variable Number of Economically Active Population

E.M. Ilyin
N.G. Kosolapenko
leading researcher, Institute for Regional Economic Studies of Russian Academy of Science, PhD in Physics and Mathematics
researcher, Institute for Regional Economic Studies of Russian Academy of Science
St. Petersburg
St. Petersburg


  • mathematical modeling
  • aggregated models of economic growth
  • search and matching models
  • natural unemployment rate
  • balanced growth trajectories
  • time lag
  • asymptotic stability of solutions
  • employment rate
  • capital available
  • dynamics of fixed capital
  • We examine the model of the economy with search friction in the labor market and a variable number of economically active population. The main demographic assumption is that the population is believed to be stable, that is, having a constant age structure and a constant population growth rate. Unlike the standard versions of similar models, where vacancies can be created by firms freely and free of charge, the number of vacancies is determined by a given share of fixed capital. The capital is converted into vacancies gradually, according to the stationary Poisson process. The change in the value of capital is described by a standard equation with a neoclassical production function. The conditions for the existence and stability of the equilibrium trajectories of the model are analyzed. It turns out that the equilibrium trajectories of the model are effective in the sense that the average equilibrium wage level established during the negotiation process exceeds the amount of unemployment benefit. We show that, in the framework of the model in question, an increase in the rate of growth of stable population on equilibrium trajectories, other things being equal, leads to an increase in the level of equilibrium unemployment, a decrease in wages and a decrease in the number of vacancies.