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City size distributions: foundations of analysis Mulligan, Gordon Fredrick

Abstract

While many observers recognize the significance of the city size distribution topic, the resolution of several apparent inconsistencies in the body of literature has not yet been achieved. This may explain why geographers, sociologists, demographers, historians, economists, and planners essentially tend to describe intercity patterns, are biased toward ad hoc interpretations, and are prone to making intuitive statements in their research. The primary purpose of this thesis is to evolve a more consistent methodological viewpoint within the community size topic. Efforts are made to unite analytical statements resting upon a common premise, to qualify, in this light, the approaches prevalent in empirical research, and to relate theory and empiricism by adopting a flexible explanatory framework. The discussion necessarily involves a critique of existing arguments and certain extensions that, we can devise from those arguments. While there is considerable attention directed to presenting empirical methodologies, no original data analysis is included. Contending that the notions should be bound together within a systems framework, we naturally devote initial emphasis to the features of central place systems as outlined in the partial equilibrium theory of Christaller (1966) and Losch (1954). We place particular stress upon the Christaller model, the simpler and apparently more realistic of the two approaches. A major thrust of the paper is an integration of several city size models, all of which display a Christallarian hierarchy. The simplest models are shown to be special cases of a more general formulation given by Dacey (1966). Besides, we illustrate to what degree the characteristic property (that is, the constant proportionality factor) of the most elementary model (Beckmann, 1958) may be considered a limit of empirical generalization. Using the hierarchial concept, we also provide some rather novel views on the relation between community economic base and the distribution theme. It is felt that this subtopic may be useful in bridging the intra-and interurban scales. The widely expounded rank-size rule, essentially a consequence of empirical research, is then formally attached to the hierarchical models. At this stage our arguments become increasingly rigorous in order to qualify certain intuitive notions that seem accepted in the literature. The idea of hierarchical sets is crudely developed to complement the uni-hierarchy arguments. The basic conclusion here is that existing city size models hardly explain the rank-size phenomenon butt that the two notions cannot be considered totally incompatible. Empirical research methodologies are stressed as another fundamental subtopic. We suggest certain avenues along which empirical efforts must be strengthened before either (i) rigorous inductive generalizations or (ii) firm theory substantiation become more realizable. Particular attention is given to delimitation of the study area (and, therefore to the scale problem), the comparison of frequency curves, and the value of inferences we can make using rather crude statistical tools. At this stage we introduce other skew distributions that are genetically similar to the rank-size curve. Furthermore, the stochastic models that seemingly account for these distributions are taken to complement the deterministic theory mentioned above. Here we support the central place argument as the only existing source of models that explicate those factors inducing spatial differentiation of economic activities and, as a consequence, urban populations. Finally, we pursue the idea of growth within the interurban structure. At this time, however, discussion is certainly exploratory and so is limited to developing notions concerning the interrelations of growth variables (population, income, etc.) and hierarchal structure in the broadest sense. Within this analytic framework we can suggest only the most general factors that may be associated with low degrees of primacy (a quality of interurban structure that we view as a deviation from a characteristic skew distribution). This particular subtopic promises to be an exciting research theme in its own right as investigators move from equilibrium to dynamic modelling.

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