Search, wage posting, and urban spatial structure

We develop an urban-search model in which firms post wages. When all workers are identical, the Diamond paradox holds, i.e. there is a unique wage in equilibrium even in the presence of search and spatial frictions. This wage is affected by spatial and labor costs. When workers differ according to the value imputed to leisure, we show that, under some conditions, two wages emerge in equilibrium. The commuting cost affects the land market but also the labor market through wages. Workers' productivity also affects housing prices and this impact can be positive or negative depending on the location in the city. One important aspect of our model is that, even with positive search costs, wage dispersion prevails in equilibrium, a feature not possible in the non-spatial model.