An urban labor market with frictional housing markets: theory and an application to the Paris urban area

We build a tractable model of frictional labor markets and segmented housing markets to study welfare effects of regulations, including spatial misallocation and deviation from competitive pricing of rents. The model is summarized by a labor demand curve depending on rents and wages, a wage curve reflecting labor market tightness and rents, and finally a rent curve reflecting employment. In this economy, the rent gradient in the flexible rent sector is higher than in a purely competitive housing market. This leads to spatial misallocation due to some employees commuting too much and some non-employed living inefficiently close to jobs. In turn, reducing generalized commuting costs reduces the rent gradient in the flexible rent sector and the cost of spatial misallocation of workers. The reduction in market rents is maximal when labor markets are less frictional and housing markets are more frictional, and welfare gains are larger when both are more efficient.