Endogenous job destruction and job matching in cities

We propose a spatial search-matching model where both job creation and job destruction are endogenous. Workers are ex ante identical but not ex post since their jobs can be hit by a technological shock which decreases their productivity. They reside in a city, and commuting to the job center involves both pecuniary and time costs. As a result, workers with high wages are willing to live closer to jobs to save on time commuting costs. We show that, in equilibrium, there is a one-to-one correspondence between the productivity space and the urban location space. Workers with high productivities and wages reside close to jobs, have low per distance commuting costs and pay high land rents. We also show that higher per distance commuting costs and higher unemployment benefits lead to more job destruction.