Spatial equilibrium with local public goods: Urban land rent,optimal city size and the Tiebout hypothesis

This paper extends the standard model of urban land rent to consider the spatial equilibrium conditions in a local public goods market as hypothesized by Charles M. Tiebout. An analysis is made of the spatial dimensions of public goods, their degree of ‘localness’ and their impact on land values. It is shown that the optimal population size of the community (Tiebout's sixth assumption) is simultaneously derived with the optimal supply of local public goods and local taxes. It is also shown that land rent is a poor output indicator of Tiebout's equilibrium conditions and that the capitalization assumption is not the appropriate test for his hypothesis.     

On the existence,uniqueness and stability of spatial equilibrium in an open city with externalities

This paper deals with the existence, uniqueness and stability of a spatial equilibrium in an open city with external diseconomies like air pollution generated by manufacturing activities. First, assuming that both production functions and utility functions are Cobb-Douglas, we prove the existence of a spatial equilibrium under some reasonable assumptions. It is shown, however, that the uniqueness and stability of the equilibrium may not be obtained, unless the degree of externality is sufficiently small. In fact, none of the equilibria will be stable for a certain set of speeds of adjustment in the labor market and the land market, if the degree of externality is relatively large. Finally, some implications of our results are derived in regard to the application of the hedonic price concept within the context of a spatial equilibrium model.     

Communication technologies and spatial organization of multi-unit firms in metropolitan areas

Departing from traditional location theory (which treats a firm as a single-unit entity), in this paper we consider that each firm consists of multiple units that exchange information or services. Specifically, we develop a general equilibrium model of the city,in which each firm consists of a front-unit (e.g. business office) and back-unit (e.g. plant or back-office). Each front-unit interacts with all other front-units for the purpose of business communications, while each back-unit exchanges information or management services only with the front-unit of the same firm. Each firm must choose the location of its front-unit and back-unit optimally. The equilibrium spatial configuration of the city is determined as an outcome of interactions among all firms and households through competitive land and labor markets. We show that, depending on parameters, a variety of interesting patterns of metropolitan spatial organization emerges.     

Existence of equilibrium configurations of competitive firms on an infinite two-dimensional space

This paper analytically examines the existence of equilibrium configurations of competitive firms on an infinite two-dimensional space. It is shown that the Löschian configuration (a regular-hexagonal lattice) and a square lattice are in global equilibrium; the Löschian configuration is in the strongest global equilibrium among the regular lattices (in this sense, spatial competition leads to the social optimum); and the so-called back-to-back configuration is not in equilibrium. These results are in marked contrast to those obtained from a one-dimensional model, implying that spatial equilibrium configurations in a two-dimensional space should not be inferred only from one-dimensional models frequently employed in spatial economics.     

Thick market externalities in a spatial model

It is natural to think of thick market externalities as spatial phenomena. When agents are in close physical proximity, potential trading partners are more numerous and less costly to reach. Counteracting such agglomeration benefits is the dispersion force due to land being an essential input in production. The distribution of economic activities over space is an outcome of how decisions on location, land demand, and the search strategy of agents interact in spatial equilibrium. More desirable locations are those that allow their occupants more abundant and less costly access to potential trading partners. In spatial equilibrium, these are the densest locations, the occupants of which benefit from the strongest thick market externalities.     

Spatial patterns of urban growth: Optimum and market

The optimum spatial pattern of urban growth for a problem which is essentially a dynamic version of von Thünen model of land use is first studied by using a notion of bid land price curves, which is a dynamic extension of bid rent curves by Alonso [1]. Then a competitive market of which equilibrium growth path coincides with this optimum one is obtained by examining demand side properties. It is hoped in this way to throw some light for the future development of dynamic theory of urban land use.     

城市空间结构理论——单中心城市静态模型

首先介绍了在西方城市经济理论中被广泛接受的单中心城市空间结构静态模型。然后,利用比较静态分析方法(comparativestaticanalysis),分析区位、居民收入及交通费用(区位,居民收入及交通费用为模型的外生变量(exogenousvariable))对价格和房屋消费量(价格和房屋消费量为模型的内生变量(endogenousvariable))的影响。最后,理论模型通过引进一般住房生产函数,推导出土地价格及资本密度(即建筑高度)的空间变化规律。通过对城市经济模型进一步分析(对极值条件或解的微分解析分析)得出地价(地租),资本密度(或称容积率),人口密度的空间分布规律,这些规律对城市规划,城市政策,引进市场原则和价格机制来提高城市土地利用效率都有理论指导意义。     

Land use dynamics and the environment

This paper builds a benchmark framework to study optimal land use, encompassing land use activities and environmental degradation. We focus on the spatial externalities of land use as drivers of spatial patterns: land is immobile by nature, but local actions affect the whole space since pollution flows across locations resulting in both local and global damages. We prove that the decision maker problem has a solution, and characterize the corresponding social optimum trajectories by means of the Pontryagin conditions. We also show that the existence and uniqueness of time-invariant solutions are not in general guaranteed. Finally, a global dynamic algorithm is proposed in order to illustrate the spatial-dynamic richness of the model. We find that our simple set-up already reproduces a great variety of spatial patterns related to the interaction between land use activities and the environment. In particular, abatement technology turns out to play a central role as pollution stabilizer, allowing the economy to reach a time-invariant equilibrium that can be spatially heterogeneous.     

Congestion,agglomeration, and the structure of cities

Congestion costs in urban areas are significant and clearly represent a negative externality. Nonetheless, economists also recognize the production advantages of urban density in the form of positive agglomeration externalities. The long-run equilibrium outcomes in economies with multiple correlated but offsetting externalities have yet to be fully explored in the literature. Therefore, I develop a spatial equilibrium model of urban structure that includes both congestion costs and agglomeration externalities. I then estimate the structural parameters of the model using a computational algorithm to match the spatial distribution of employment, population, land use, land rents, and commute times in the data. Policy simulations based on the estimates suggest that congestion pricing may have ambiguous consequences for economic welfare.     

On the foundations of land use theory : Discrete versus continuous populations

Urban economists and location theorists have long employed land use models with a continuum of agents distributed over a continuum of locations. However, these continous models have been criticized on behavioral grounds in that individual households can consume only zero amounts of land in equilibrium. Hence the central purpose of this paper is to propose an alternative interpretation of these continous models as limiting approximations of discrete population models. In particular, it is shown that for large population sizes, the population distributions of the classical continuous model uniformly approximate the equilibrium population distributions generated by an appropriately defined class of discrete population models.     

Discrete-space agglomeration model with social interactions: Multiplicity,stability, and continuous limit of equilibria

This study examines the properties of equilibrium, including the stability, of discrete-space agglomeration models with social interactions. The findings reveal that while the corresponding continuous-space model has a unique equilibrium, the equilibrium in discrete space can be non-unique for any finite degree of discretization by characterizing the discrete-space model as a potential game. Furthermore, it indicates that despite the above result, any sequence of discrete-space models’ equilibria converges to the continuous-space model’s unique equilibrium as the discretization of space is refined.     

Full or partial market coverage? A note on spatial competition with elastic demand

In this paper, a spatial model is used to endogenously determine product locations and prices when consumers have an elastic demand with a finite reservation price. I show under which condition a two‐stage Bertrand–Nash equilibrium yields maximal product differentiation with full market covering. Additionally, this paper highlights the effects of a change in the reservation price and in the utility loss rate on the equilibrium values of the model. The ambiguous effect of a change in the utility loss rate on prices constitutes a rather puzzling result. Copyright © 1999 John Wiley & Sons, Ltd.     

The spatial structure of production with a Leontief technology

The structure of the optimal spatial pattern of production is studied when there are interdependencies among production units which can be described by a Leontief technology, and when there is a single marketplace of final demand, the CBD. Transportation cost is proportional to distance. It is shown that the various goods are produced in rings which can be ranked by distance from the CBD independently of the levels of final demand. Furthermore shipment of goods for meeting intermediate and final demand can only be in the direction of the CBD and no shipment of goods towards the periphery can occur. A finite algorithm is given for the construction of the optimal pattern and for determining a system of f.o.b. prices and land rents which sustain it as a competitive equilibrium.     

An equilibrium existence result for an economy with land

This research uses a different set of assumptions for land than those used in the standard general equilibrium framework. In particular, land is modelled explicitly as a subset of the plane with anything immobile, from flowers and trees to houses, embedded in it. There is a finite number of consumers with preference orderings over land parcels satisfying certain axioms along with endowments of land that partition this subset of the plane. Allowing for recombinations of parcels, the main result demonstrates the existence of prices in L¹ and a partition of land among consumers so that the land market clears.     

The accuracy of changes of urban land values as a measure of social benefits from public programs

This paper extends the standard model of urban land rent to consider the impact of the output of public programs on the spatial equilibrium and to analyze the accuracy of changes of urban land values as a measure of social benefits from public investment. Two consistent output indicators of public investment are advanced: the individual's welfare and total land values. The general results of the comparative analysis are that there is a lack of correspondence between both output indicators, and that changes in land values are, in general, not an accurate measure of the benefits of such programs.     

A multiobjective integer programming model for the land acquisition problem

The purpose of this paper is to present a multiobjective integer programming formulation for the analysis of the land acquisition problem. There are two important contributions of this paper. First, the model incorporates the discrete and multiobjective nature of land acquisition. Second, we present an efficient, specialized algorithm for finding non-inferior solutions of a multiobjective integer program, a problem for which a general-purpose algorithm, applicable to moderately sized problems, does not exist.     

Revealed Preference and Location Choice

The assumption that population and structural densities are defined over parcels of land with zero area is problematic when interpreting the standard residential land use model as approximating a large finite economy. This paper extends revealed preference theory to depict a spatial economy with land parcels of finite area. The model generalizes the standard utility function approach, allowing for many consumer types with different tastes and incomes and labor-leisure choice, to show that the most important predictions of the standard theory hold in the general finite framework studied here.     

Urban search models under high-relocation costs. Theory and application to spatial mismatch

We develop a search-matching model in which mobility costs are so high that it is too costly for workers to relocate when a change in their employment status occurs. We show that, in equilibrium, wages increase with distance to jobs and commuting costs because firms need to compensate the transportation cost difference between the employed and unemployed workers at each location in the city. We also show that the equilibrium land rent is negatively affected by the unemployment benefit because an increase in the latter induce firms to create less jobs, which, in turn, reduces the competition in the land market. We then use this model to provide a mechanism for the observed spatial mismatch between where black workers live and where jobs are. We finally show that a transportation policy consisting in subsidizing the commuting costs of black workers can increase job creation and reduce unemployment if the level of the subsidy is set at a sufficiently high level.     

Efficiency of markets for heterogeneous,indivisible housing

A rental housing market with a finite number of traders is presented. Tenants trade money to landlords for the use of an indivisible, heterogeneous house. Equilibrium is defined as the outcome of a competitive bidding arrangement among agents, the bid rent approach. Using this bidding arrangement, the two fundamental welfare theorems are shown to apply to this market. The second welfare theorem is verified via an algorithm which constructs equilibrium prices for Pareto-efficient allocations.     

土地财政与最优城市规模

土地是有限的,完全依靠土地收入的发展模式是不可持续的。本文主要考察土地财政作为地方政府的一种融资渠道,城市建设用地规模的使用是否与城市人口规模的增加相协调,是否存在过度扩张城市面积促进地区经济发展的现象。为了分析土地出让收入(地租)、公共品供给以及城市规模之间的关系,本文以乔治亨利定理为基础,并引入林达尔均衡条件建立起最优城市人口密度理论模型。采用1999～2009年31个省面板数据对中国城市成本收益模型进行计量分析,结果表明全国26个省低于估算的最优城市人口密度,验证了中国存在城市面积的扩张与人口的增加不协调发展的情况。