A Simplified Approach to Analyzing Multi-regional Core-Periphery Models

This paper shows that the evolutionary process of spatial agglomeration in multi-regional core-periphery models can be explained analytically by a much simpler method than the continuous space approach of Krugman (1996). The proposed method overcomes the limitations of Turing's approach which has been applied to continuous space models. In particular, it allows us not only to examine whether or not agglomeration of mobile factors emerges from a uniform distribution, but also to trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as from a uniform pattern) with decreases in transportation cost.agglomeration; core-periphery model; multi-regional; stability; bifurcation

Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?

This study develops a model in which heterogeneous commuters choose their residential locations and departure times from home in a closed monocentric city with a bottleneck located at the entrance to the central business district (CBD). We show that commuters sort themselves both temporally and spatially according to their income, value of time, and flexibility at the equilibria with and without an optimal congestion pricing. These two equilibria exhibit fundamentally different properties, indicating that congestion pricing alters the urban spatial structure. We then consider two cases wherein rich commuters are either flexible or inflexible and demonstrate that (a) rich commuters reside farther from the CBD in the former case and closer to the CBD in the latter case; (b) congestion pricing makes cities denser and more compact in the former, whereas it causes cities to become less dense and to expand spatially in the latter; and (c) in both cases, pricing helps rich commuters but hurts poor commuters. We further reveal 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, while those residing farther from the CBD lose. This suggests that expanding capacity financed by the revenue from congestion pricing could be regressive in a city where rich commuters are inflexible

Who gains and who loses from congestion pricing in a monocentric city with a bottleneck?

This study develops a model in which heterogeneous commuters choose their residential locations and departure times from home in a closed monocentric city with a bottleneck located at the entrance to the central business district (CBD). We show that commuters sort themselves both temporally and spatially according to their income, value of time, and flexibility at the equilibria with and without an optimal congestion pricing. These two equilibria exhibit fundamentally different properties, indicating that congestion pricing alters the urban spatial structure. We then consider two cases wherein rich commuters are either flexible or inflexible and demonstrate that (a) rich commuters reside farther from the CBD in the former case and closer to the CBD in the latter case; (b) congestion pricing makes cities denser and more compact in the former, whereas it causes cities to become less dense and to expand spatially in the latter; and (c) in both cases, pricing helps rich commuters but hurts poor commuters. We further reveal 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, while those residing farther from the CBD lose. This suggests that expanding capacity financed by the revenue from congestion pricing could be regressive in a city where rich commuters are inflexible

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

Bottleneck congestion and distribution of work start times: The economics of staggered work hours revisited

Since the seminal work of Henderson (1981), a number of studies examined the effect of staggered work hours by analyzing models of work start time choice that consider the trade-off between negative congestion externalities and positive production externalities. However, these studies described traffic congestion using flow congestion models. This study develops a model of work start time choice with bottleneck congestion and discloses the intrinsic properties of the model. To this end, this study extends Henderson’s model to incorporate bottleneck congestion. By utilizing the properties of a potential game, we characterize equilibrium and optimal distributions of work start times. We also show that Pigouvian tax/subsidy policies generally yield multiple equilibria and that the first-best optimum must be a stable equilibrium under Pigouvian policies, whereas the second-best optimum in which policymakers cannot eliminate queuing congestion can be unstable

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

Origin of power laws and their spatial fractal structure for city-size distributions

City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States indicates that the scaling law stems from a spatial fractal structure owing to the coordination of industrial locations. While the locations of individual industries change considerably over time, there is a persistent pattern in that the localized industries at a given time are found only in larger cities. The spatial organization of cities exhibits a stable hierarchical structure in which larger cities are spaced apart to serve as centers for surrounding smaller cities, generating a recursive pattern across different spatial scales. In our theoretical replication of the observed regularities, diversity in scale economy among industries induces diversity in their location pattern, which translates into diversity in city size via spatial coordination of industries and population. The city-size power law is a generic feature of Monte-Carlo samples of stationary states resulting from the spontaneous spatial fractal structure in the hypothetical economy. The identified regularities reveal constraints on feasible urban planning at each regional scale. The success or failure of place-based policies designed to take advantage of individual cities' characteristics should depend on their spatial relationships with other cities, subject to the nationwide spatial fractal structure

A Simplified Approach to Analyzing Multi-regional Core-Periphery Models

This paper shows that the evolutionary process of spatial agglomeration in multi-regional core-periphery models can be explained analytically by a much simpler method than the continuous space approach of Krugman (1996). The proposed method overcomes the limitations of Turing's approach which has been applied to continuous space models. In particular, it allows us not only to examine whether or not agglomeration of mobile factors emerges from a uniform distribution, but also to trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as from a uniform pattern) with decreases in transportation cost

Bottleneck congestion and residential location of heterogeneous commuters

This study examines the effects of bottleneck congestion and an optimal time-varying congestion toll on the spatial structure of cities. We develop a model in which heterogeneous commuters choose departure times from home and residential locations in a monocentric city with a bottleneck located between a central downtown and an adjacent suburb. We then demonstrate that commuters sort themselves temporally and spatially on the basis of their value of travel time and their flexibility. Furthermore, we reveal that introducing an optimal congestion toll alters the urban spatial structure, which contrasts with the previous literature. We further demonstrate through an example that congestion tolling can cause the city to physically expand outward, which helps rich commuters but hurts poor commuters