In this chapter, we extend the different models proposed in Chapter 1 by introducingworkers' heterogeneity, high mobility costs and wage posting. In Section 2, workers are ex-ante heterogenous in terms of some idiosyncratic characteristics, which implies that, once they find a new job, they must bear a training cost that is match-specific and stochastically determined. Thus, there is a training decision rule because workers are not ready to accept a job if it implies extremely high training costs. In this model, the training cost is a sunk cost because it is of no use for the next job and it is thus forfeited. Moreover, after training, all workers are assumed to provide the same productivity and thus, are ex-post identical. Compared to the models in Chapter 1, the urban-land-use equilibrium is not affected while, in the labor market, there is a new equation: the training decision rule. This leads to a new source of inefficiency due to training costs. Indeed, in the market solution, workers tend to refuse socially beneficial jobs due to the fact that while workers bear all training costs, the revenues from production are divided between firms and workers through bargaining.
In Section 3, workers are ex-ante identical, but they are ex-post heterogenous in terms of match productivities. Contrary to Chapter 1, job destructions are now endogenous, which is consistent with the evidence of Davis, Haltiwanger, and Schuh (1996). More precisely, it is assumed that each job is characterized by a fixed irreversible technology, so that each time there is a technological shock, the quality of the match and the productivity deteriorate.