Space, Search and Efficiency

We investigate the role of spatial frictions in search equilibrium unemployment. For that, we develop a model of the labor market in which workers’ location in an agglomeration depends on commuting costs, the endogenous price of land and the value of job search and employment. We first show that there exists a unique and stable market equilibrium in which both land and labor markets are solved for simultaneously. We then compare this decentralized equilibrium to a social planner’s optimum and we find that distortions (subventions or imperfect competition in the transport market) modify the usual Hosios efficiency condition. Indeed, the social planner needs to adjust the transportation spending of the decentralized equilibrium. Given differences in commuting costs between the employed and the unemployed, this is realized by a change in the fraction of unemployed workers: the socially optimal number of unemployed workers depends both of matching externalities and on distortions in the transport market. In absence of these distortions and despite spatial terms in wages, the standard condition holds: a spatial efficient equilibrium may thus occur. We however show that space has still an important role on the interaction between land and labor markets, and decompose the equilibrium unemployment rate into two parts: a pure non-spatial one (which corresponds to the standard matching model) and a mixed of non-spatial and spatial elements, the first element amplifying the other one.