Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities

The orientation and progress of spatial agglomeration for Krugman's core--periphery model are investigated in this paper. Possible agglomeration patterns for a system of cities spread uniformly on a circle are set forth theoretically. For example, a possible and most likely course predicted for eight cities is a gradual and successive one---concentration into four cities and then into two cities en route to a single city. The existence of this course is ensured by numerical simulation for the model. Such gradual and successive agglomeration, which is called spatial-period doubling, presents a sharp contrast with the agglomeration of two cities, for which spontaneous concentration to a single city is observed in models of various kinds. It exercises caution about the adequacy of the two cities as a platform of the spatial agglomerations and demonstrates the need of the study on a system of cities

Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities

The orientation and progress of spatial agglomeration for Krugman's core--periphery model are investigated in this paper. Possible agglomeration patterns for a system of cities spread uniformly on a circle are set forth theoretically. For example, a possible and most likely course predicted for eight cities is a gradual and successive one---concentration into four cities and then into two cities en route to a single city. The existence of this course is ensured by numerical simulation for the model. Such gradual and successive agglomeration, which is called spatial-period doubling, presents a sharp contrast with the agglomeration of two cities, for which spontaneous concentration to a single city is observed in models of various kinds. It exercises caution about the adequacy of the two cities as a platform of the spatial agglomerations and demonstrates the need of the study on a system of cities.Agglomeration of population; Bifurcation; Core-periphery model; Group theory; Spatial period doubling

Travel Cost Method Considering Trip-day Counts as Integers

The Travel Cost Method (TCM) is a typical benefit measurement method, using the fact that people substitute the benefit of visiting some sites for their travel cost. However, in the case of tourist sites, travelers do not choose the number of days spent in a tourist city as continuous numbers but integer numbers. We investigate how a bias could arise from ignoring integer numbers of nights in TCM. We derive the formula of what factors constitute the bias. Next, we numerically show that when measuring benefits of improving quality at sites, the maximum bias could be around 20%

Cities and biodiversity: Spatial efficiency of land use

Biologically important but dangerous wildlife creatures encroach into cities, which causes human-wildlife conflicts. To explore the effect of the encroachment of wildlife into cities on equilibrium land use and its efficiency, we develop an equilibrium theory of land used for humans and wildlife by combining an ecosystem model with urban economics model. Humans choose their housing location and size in response to the risk of encountering wildlife in cities, and animals optimize their food intake by spreading out in response to heterogeneous feeding grounds in both urban areas and natural habitats, which determines the spatial heterogeneous distribution of both agents. We first prove the existence and uniqueness of the spatial equilibrium in a linear city adjacent to natural habitats. Next, our theory provides new insights for the wildlife conservation: (i) this spatial heterogeneity generates inefficient predator-prey interactions, leading to an inefficient steady state population equilibrium of animals; (ii) With the spatial inefficiency, the equilibrium city size is not always too big. We numerically demonstrate how both the equilibrium and the optimal solution are affected by the scale of conflicts and the value of wildlife

Transportation Improvement and Hollowing-out of Urban Commercial Center: Do They Harm Consumer Welfare?

Concentration or dispersion of retail stores is the result of market interactions. If it involves market failures, then the spatial location equilibrium of retail stores is not optimal in terms of social welfare. We investigate two important market failures involving retail store location: “monopolistic competition among retail stores” and “shopping externality caused by multipurpose shopping”. Retail store locations in market equilibrium and those in a social optimum are derived. Next, we show that the degree of hollowing-out of urban centers is not always excessive from the perspective of the social optimum. It is believed that hollowing-out of urban commercial centers harms social welfare. But on the contrary, if the accessibility of suburban areas from residential areas is lower than that of the urban center, we confirm that hollowing-out of urban commercial centers is desirable. In this case, promotion of retail stores’ location in urban center, such as subsidies to locate in the city center or restrictions on location in suburbs, decreases social welfare. Instead, promotion of stores’ location in the suburbs is preferred

Travel Cost Method Considering Trip-day Counts as Integers

The Travel Cost Method (TCM) is a typical benefit measurement method, using the fact that people substitute the benefit of visiting some sites for their travel cost. However, in the case of tourist sites, travelers do not choose the number of days spent in a tourist city as continuous numbers but integer numbers. We investigate how a bias could arise from ignoring integer numbers of nights in TCM. We derive the formula of what factors constitute the bias. Next, we numerically show that when measuring benefits of improving quality at sites, the maximum bias could be around 20%

Transportation Improvement and Hollowing-out of Urban Commercial Center: Do They Harm Consumer Welfare?

Concentration or dispersion of retail stores is the result of market interactions. If it involves market failures, then the spatial location equilibrium of retail stores is not optimal in terms of social welfare. We investigate two important market failures involving retail store location: “monopolistic competition among retail stores” and “shopping externality caused by multipurpose shopping”. Retail store locations in market equilibrium and those in a social optimum are derived. Next, we show that the degree of hollowing-out of urban centers is not always excessive from the perspective of the social optimum. It is believed that hollowing-out of urban commercial centers harms social welfare. But on the contrary, if the accessibility of suburban areas from residential areas is lower than that of the urban center, we confirm that hollowing-out of urban commercial centers is desirable. In this case, promotion of retail stores’ location in urban center, such as subsidies to locate in the city center or restrictions on location in suburbs, decreases social welfare. Instead, promotion of stores’ location in the suburbs is preferred

Heterogeneous Households’ Choices of Departure Time and Residential Location in a Multiple-origin Single-destination Rail System: Market Equilibrium and the First-best Solution

This paper explores heterogenous commuters’ train choices with different arrival times and residential locations in a city composed of a single CBD and multiple residential zones. First, we analyze the relation between the cost of train overcrowding and train choice, given three residential location patterns according to income level, which are discussed in Fujita (1989) and Tabuchi (2019). Next, we analyze the necessary conditions for the existence of the residential location patterns on the basis of the relation between train overcrowding and train choice in equilibrium. The obtained necessary conditions depend on the values of time, housing lot sizes, and the overcrowding costs. The overcrowding costs depend on the choices of trains with different arrival times in equilibrium. Finally, in quantitative analysis, we showhowmuch the socialwelfare improves due to the first-best congestion fares, depending on the residential location patterns. In any residential pattern, households with the lowest income increase their utilities the most among all households with different incomes, whereas households with the highest income lose their utilities

Quantitative evaluation of benefits of place-based policies for retail agglomeration

Local governments have recently adopted place-based policies in order to revitalize decayed shopping areas in downtown areas. Developing a multipurpose shopping model, we quantitatively evaluate the welfare impacts of place-based policies for downtown retail agglomeration. In the model, retail stores are under monopolistic competition, and households are free to choose where to reside. Results show that, whether or not place-based policies are efficient depends on the recipients of government subsidies, even if the policies promote retail agglomeration in downtown areas. We show that the total benefits of location subsidies to households and location subsidies to stores are 566 and −342 million JPY per year, respectively

Residential Land Use and Utilities of Multiple Generations with Lifespan Perspectives and Demographic Dynamics

Demographic dynamics and spatial distribution of urban amenities bring about spatially different benefits to young, middle-aged, and elderly people, thereby affecting residential location patterns. Using an overlapping generations model in a closed city with two zones with different amenity levels, we demonstrate how young, middle-aged, and elderly generations with lifespan perspectives reside in the two zones with their interplay across periods and locations and analyze the residents’ welfare levels. We find that, unlike a static situation, there is no steady residential pattern in which middle-aged or elderly households live in both of the two zones when they optimize their residential locations throughout their life. Our numerical simulation reveals two findings useful for policy making: first, urban amenities should be unevenly distributed across the city from a perspective of lifetime utility; second, different demographic changes lead to different desirable residential patterns in terms of utility. Finally, we check the robustness of these findings for the case of the expansion of remote work