An analytical model for residential location choices of heterogeneous households in a monocentric city with stochastic bottleneck congestion

We propose an analytically solvable model for the residential location choices of heterogeneous households in a linear monocentric city corridor with bottleneck congestion. Residents have heterogeneous income, and make a joint choice of residential location and departure time. There is a bottleneck with a fixed or with a stochastic location between central downtown and adjacent suburb of the city. The urban system equilibrium and the effects of bottleneck capacity expansion on the city system are analytically investigated, together with the design of the bottleneck capacity. We show that the residents spatially sort themselves along the city corridor from CBD outward in a descending order of their values of time. Expanding bottleneck capacity leads to an increase in the commuting costs of the downtown residents but a decrease in the commuting costs of the suburban residents. All residents of the city benefit from the bottleneck capacity expansion, with the highest benefit for the relatively mid-income residents, and the lowest benefit for the lowest-income or the highest-income residents, depending on the status quo of the bottleneck capacity. Expanding the bottleneck capacity leads to urban sprawl, and a decrease in total net land rent. Ignoring the effects of the bottleneck capacity expansion on the urban spatial structure overestimates the social surplus. The bottleneck location's stochasticity smoothes the residential distribution, increases the system's transportation cost, and decreases household utility and social surplus.