OBNOXIOUS FACILITY LOCATION IN THE INTERIOR OF A PLANAR NETWORK*

ABSTRACT. The problem of locating a point that is as far as possible from arcs and nodes of a network is investigated. Each arc or node may have a different multiplicative factor (weight) for its distance. A graphical solution approach, as well as a computational algorithm, is presented.     

THE PURE THEORY OF HOUSEHOLD LOCATION AN AXIOMATIC APPROACH*

In this paper, I present an axiomatic basis for the neoclassical model of household location in a monocentric urban area. I generalize the existing framework and demonstrate that many of the conclusions derived using parametric models continue to hold even without the popularly assumed well-behaved utility and transportation cost functions.     

THE LOCATION THEORY OF THE PLANTATION*

ABSTRACT This paper develops a method for studying noninfinitesimal operational units, with the Thünen location and land use model. With constant returns to scale and perfect divisibility of nonland inputs, all operational units would occupy only a point on the landscape. The present model uses increasing returns to scale to generate large operational units, called “plantations” and studies the comparative statics. The setting of the model is an agricultural operation in which some processing of raw crop must be conducted prior to shipment to market. The processing is assumed to have increasing returns to scale.     

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.     

ON THE OPTIMUM LOCATION OF VERTICALLY RELATED FIRMS WITH SIMULTANEOUS ENTRY*

ABSTRACT This paper considers a case of bilateral monopoly and examines the possibility of an intermediate location for two vertically related firms under simultaneous entry, and then analyzes the welfare-maximizing location for both firms. It shows that whatever the case, an intermediate location for both firms is unlikely to occur and that the pattern of industrial location under welfare maximization is equivalent to the one under perfect competition, but is different from the one under bilateral monopoly under certain circumstances.     

LOCATION OF PUBLIC FACILITIES WITH SPILLOVER EFFECTS: VARIABLE LOCATION AND PARAMETRIC SCALE*

ABSTRACT This paper studies the location of public facilities of two neighboring local governments which consider not only the influence of the land market but also the spillover effects that each jurisdiction may have on the other. We obtain the following results: (1) in most cases, one of the cities behaves as an isolated city in choosing the facility location while the other enjoys the spillover effect as a free rider; (2) we also find that the equilibrium location in the two noncooperative city case is not socially optimal except for a special case.