Optimal size of a residential area within a municipality

The purpose of this paper is to analyze the optimal size of a residential area within a municipality under different market structures. We find that under a private duopoly the optimal size of the residential area depends on the ratio between transportation costs and a negative externality due to congestion. The optimal size is the whole municipality when the ratio is low enough and a small area of the municipality when the ratio is high enough. The transition from a flat residential area to a more compact one is not continuous, so some large-enough residential areas are never optimal. Under a mixed duopoly the transition from a flat residential area to a more compact one is continuous as the ratio increases. By comparing the two cases we find that for intermediate values of this ratio a flat city is optimal for a private duopoly while compact cities emerge under a mixed duopoly.