CENTER POINTS, EQUILIBRIUM POSITIONS, AND THE OBNOXIOUS LOCATION PROBLEM

ABSTRACT. Real variable analysis has een used to great benefit in a variety of classical problems in location theory. In this paper we explore basic complex variable techniques in one formulation of the obnoxious location problem. A general definition of center points is first given and used to formulate several alternate versions of the obnoxious location problem. A logarithmic transformation is then used to demonstrate some equivalences between these families of distinct location problems (defined via center points). A prototype logarithmic potential function which results from this formulation is then investigated, and it is demonstrated that the extremal solutions with this objective reside on the boundary of its domain of definition. An application using zero- and one-dimensional centers is discussed, and a generalization to the spatial obnoxious problem is also briefly examined. We define a zero-dimensional center as a critical point of the logarithmic potential function, and it is shown that these centers are equivalent to the solutions of the Complex Moment Problem.     

LOCATIONAL SIGNALING AND AGGLOMERATION

Agglomeration can be caused by asymmetric information and a locational signaling effect: The location choice of workers signals their productivity to potential employers. The cost of a signal is the cost of housing at that location. When workers' marginal willingness to pay for housing is negatively correlated with their productivity, only the core‐periphery (partially stratified) equilibria are stable. When workers' marginal willingness to pay for housing and their productivity are positively correlated, there is no core‐periphery equilibrium. The urban wage premium is explained when there is a core‐periphery equilibrium. Furthermore, location can at best be an approximate rather than a precise sieve for high‐skill workers.     

AUTOMOBILE USE AND LOCATIONAL INTERDEPENDENCIES

ABSTRACT. Congestion and pollution externalities from automobile use are simultaneously included in an urban monocentric model. The externalities enter household utility functions directly, and result in a complex interdependency in household location decisions in the city. Implications of the model are drawn out by a simulation and complete sensitivity analysis. The two unpriced externalities are examined for their impact on urban structure, and contrasted with each other. Also, the effect of changes in speed of travel are examined for the impact on urban structure. Speed affects the level of both external effects, and is affected by location decisions.     

AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

EXPLORING LOCATIONAL EQUILIBRIA IN A COMPETITIVE BROADBAND ACCESS MARKET: THEORETICAL MODELING APPROACH

ABSTRACT Due to strong local competition in the broadband access market, strategic locational planning is very important for service providers. In this paper, we explore locational equilibria in a competitive broadband market under several situations: with and without customer loyalty and under different initial market conditions. To do this, we propose a competitive broadband location model based on probabilistic patronage behavior, explicitly considering the characteristics of the broadband market and competitive structures. Also, we suggest iterative algorithms to identify spatial equilibria. We show that competing location strategies may lead to a stable spatial configuration of market share.     

STRUCTURAL DIMENSIONS IN THE GEOGRAPHY OF LOCATIONAL CONFLICTS

L ocational c onflict is a frequent by-product of efforts to change the physical structure of man-made environments. Within the geography discipline, theoretical and empirical interests in the conflict basis of public and private decisions on the use of land were stimulated in the early 1970s by the work of Julian Wolpert and his associates.¹ The resolution of conflicts over the locations of specific activities is seen as an important means of allocating benefits among locations² and has led to considerable variations in the distribution of necessary services and amenities among residents of the city.³ Indeed, irrespective of overt evidences of conflict occurrence, David Harvey has characterized the land-use pattern itself as an important indicator of the socio-political rules which direct urban development.⁴