City with forward and backward linkages

This paper considers the spatial structure of a city subject to final demand
and vertical linkages. Individuals consume differentiated goods (or services) and firms
purchase differentiated inputs (or services) in product (or service) markets where forms
compete under monopolistic competition. Workers rent their residential lots in an urban
land market and contribute to the production of differentiated goods and inputs. We show
that firms and workers co-agglomerate and endogenously form a city. We characterize and
discuss the spatial distribution of firms and consumers in such cities on one- and twodimensional spaces (linear city and planar city). We show that final demand and vertical
linkages raise the urban density and reduce the city spread. We finally show that a city is
too much dispersed compared to the social optimum.