Time-varying congestion tolling and urban spatial structure

This study develops a model in which heterogeneous commuters choose their residential locations and departure times from home in a monocentric city with a bottleneck located at the entrance to the central business district (CBD). We systematically analyze the model by utilizing the properties of complementarity problems. This analysis shows that, although expanding the capacity of the bottleneck generates a Pareto improvement when commuters do not relocate, it can lead to an unbalanced distribution of benefits among commuters: commuters residing closer to the CBD gain and commuters residing farther from the CBD lose. Furthermore, we reveal that an optimal time-varying congestion toll alters the urban spatial structure. We then demonstrate through examples that (a) if rich commuters are flexible, congestion tolling makes cities denser and more compact; (b) if rich commuters are highly inflexible, tolling causes cities to become less dense and to spatially expand; and (c) in both cases, imposing a toll helps rich commuters but hurts poor commuters.