Statistical mechanics of labor markets

On the basis of statistical mechanics, we introduce a probabilistic model of labor markets for university graduates in Japan. In order to make a model of the market efficiently, we shall take into account the following assumptions. Namely, each company fixes the number of opening positions for newcomers and the number itself is independent of business year. The ability of gathering newcomers depends on the result of matching process in past business years. This fact means that the ability of the company is weaken if the company did not make their quota or the company gathered applicants too much over the quota. All labors, in particular, university graduates who are looking for their jobs can access the public information about the ranking of companies. By assuming the above essential key points, we construct the energy function of each company and describe the probability that an arbitrary company gets students at each business year by a Boltzmann-Gibbs distribution. We evaluate the relevant physical quantities such as the employment rate. We find that the system undergoes a phase transition from the `good employment phase´ to `poor employment phase´ with spontaneous symmetry breaking when one controls the degree of importance for the ranking. With the assistance of a chaotic map for the inflation rate given by Neugart (2004), we also attempt to draw the so-called Philips curve. The condition on which the long-time average of inflation rate becomes negative with high unemployment rate, which might be regard as an indicator for a sort of `crisis´ is discussed.