Bottleneck congestion and urban spatial structure with heterogeneous households: Equilibrium, capacity expansion and congestion tolling

We propose an analytical solvable model for household residential location choice in a linear monocentric city corridor with bottleneck congestion. Households are heterogeneous in terms of their income. The bottleneck is located between central downtown and adjacent suburb. The urban equilibrium is formulated as the solution of differential equations. We analytically explore the distributional effects of bottleneck capacity expansion on households and the bottleneck capacity investment issues under no toll and first-best and second-best tolls. The results show that the benefits of different-income households from bottleneck capacity expansion change with toll schemes. Specifically, under the no toll and first-best toll, those who gain most are the mid-income households residing at the bottleneck and in a suburban location (close to the bottleneck) respectively, whereas those who gain least are the poorest or richest households. Under the second-best toll, there are two possible cases: the poorest households gain most while the richest households gain least, or the mid-income households residing at the bottleneck gain most while the richest or poorest households gain least. With constant return to scale for capacity investment, self-financing principle still holds for the first-best and second-best tolling in the urban spatial context. Ignoring the changes in urban spatial structure due to household relocation may cause overinvestment or underinvestment in optimal bottleneck capacity under the no toll, but definitely underinvestment under the first-best and second-best tolls.