Equilibrium land use in a linear city with a central shopping district

We investigate the equilibrium pattern of residential, business and integrated areas in a city where households and firms have employment and trade relationships. The employment relationship requires commuting, and thus generates an attraction between firm-household pairs. The trade relationship requires firms to transport output to the central shopping district and requires households to travel to the central shopping district for consumption. As a result, it attracts households and firms to the centre. The equilibrium pattern that emerges depends on the relative magnitude of three different urban transport costs (commuting cost, output transport cost, shopping cost), and on the relative convexity of households’ and firms’ benefits from locating near the centre. As the distance from the centre increases, if households’ marginal benefit from locating near the centre diminishes more rapidly (or increases less rapidly) than firms’ marginal benefit, business areas can only emerge at the centre or at the city limits. In the opposite case, residential areas can only emerge at the centre or at the city limits. With linear commuting costs and inelastic use of land and labour, there are 11 possible symmetric equilibrium land use patterns. Additional patterns arise if these assumptions are relaxed.