Retraining in an interdependent system of labor markets: A network analysis

The study of a system of markets for labor of different categories (heterogeneous labor) must be based on the recognition that individual workers may move from one category to another through schooling and retraining. Here such transitions are viewed as a flow through a retraining network. The nodes of the network represent various stages of education and acquired abilities. The directed links represent avenues of possible schooling and retraining. If wages are rigid downwards, failing to fall in the face of a weakening demand for labor, there may be unemployment at one or several nodes of the retraining network. An optimizing principle, inspired by developments in the analysis of spatial networks, is presented which solves for the supply of labor of each category, the number of workers enrolled in the various retraining activities, and the possible unemployment at each node of the network. The Lagrange multiplier of each market balance is the market wage rate, whether the labor market is in equilibrium or not.