  We introduce a probabilistic model of labor markets for university graduates,
in particular, in Japan. To make a model of the market efficiently, we take
into account several hypotheses. Namely, each company fixes the (business year
independent) number of opening positions for newcomers. The ability of
gathering newcomers depends on the result of job 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 university graduates who are looking for their jobs
can access the public information about the ranking of companies. Assuming the
above essential key points, we construct the local 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 sort of `phase transition' from the `good employment phase' to
`poor employment phase' when one controls the degree of importance for the
ranking.
