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Conclusions The techniques defined in this paper will divide a set of cities into subgroups which specify a central place and its subordinate hierarchy. The association between cities is not the only system which may be defined as a network of points and lines. Nations or states may be thought of as points with migrations or commodity flows as lines. The important step in the employment of abstract linear graph analysis is the assignment of plausible meaning to the points and lines, preferably in terms of some real world phenomena. The usefulness of the attributes and the interpretation of the resulting hierarchy depends on the correspondence between an empirical example using graph theory analysis and other knowledge of the phenomena. The procedure described in this paper may be employed in a variety of ways, but the application is valid only when significant theoretical conclusions are produced and verified empirically.

Summary Central place theory is the theory pertaining to the spatial aspects of retail and service business. Among these spatial aspects are the location and groupings of central functions, the consequent size and spacing of central places, consumer travel behavior, and the size, shape, and arrangement of trade areas. This paper has attempted to view these aspects in their interdependence at both the aggregate and elemental levels of inquiry, and to present some theoretical implications of the findings. Of interest are the recognition that the basic requirements of the theory (thresholds and ranges) are satisfied in the Iowa case, and the verification of the major postulate of the theory (the hierarchy). While the spatial pattern of centers conforms to a particular set of location principles (the principles of transportation), the nesting of trade areas does not, due to the importance of the information content of central places (number of central functions performed) in consumers' shopping and travel be havior.

Conclusion The ideas outlined in this paper are tentative and only partially developed. They have arisen very much as a response to the deficiencies in existing regional models. Whether this particular structure can lead to added order and power in such models remains to be demonstrated. But with increasing demands for analysis at a regional level, a substantial theoretical basis for regional models is manifestly needed.

Summary In this paper it has been argued that there are several important variables to consider in explaining the distribution of residential neighborhoods. These include (1) the overall tendency for urban populations to be concentrated about central places and along major transportation facilities, (2) the pattern of social relations which exist among the subgroups which comprise the community's population, (3) the major (common) residential values held by members of the community, and (4) the community power structure. It has been noted that the first of these factors has received more than its share of attention, and that, indeed, most attempts to explain residential structure seek to associate compositional characteristics in a fixed way to the settlement density and competition for land. Because the relationship between composition and density is mediated by many institutional and social variables, however, this approach is not considered very promising. Instead, it is suggested that attention be directed to all four elements, and especially to the second, dealing with the social relations that exist among the subgroups of the community. The careful study of these relations should provide an important key to the understanding of the residential structure of the modern American metropolis.

Summary This paper delves into a more explicit analysis of demand in space than has been undertaken heretofore. Utility theory is used to develop the concepts of spatial income-distribution effect, spatial-induced income effect, and spatial substitution effect, the effects on demand of changes or differences in location. Indifference curve analysis is employed to give a graphical interpretation to these concepts.

Conclusion In this paper, I have tried two things: (1) to develop a formal mathematical description of the innovation diffusion process under the simplest conditions and (2) to do the same for expenditure streams, migration, and price movements considered as spatial diffusion processes. My aim has been to demonstrate similarities and differences among these processes. The theoretical study of diffusion models appears to me to be fruitful as an extension of economic stability analysis to spatial situations and also as an alternative approach to predicting the movement in space of economic phenomena.

Conclusion The result of this paper is to suggest that the Koopmans-Beckmann conclusion quoted earlier depends crucially on the indivisibility assumed in their model.

Summary This paper is concerned with the formulation of a research design for measuring and evaluating the impact of a federal-provincial regional development program upon the Interlake Area of Manitoba. The evaluation process is approached through a comprehensive system of social accounts formulated after the two-region input-output model. The system of social accounts includes both current and capital accounts for business and government and provides the basis for the development of a dynamic model of the economy. The accounts also have special provisions for relating the development program expenditures to the public and private sectors of the two regions.

Conclusion According to the transition theory, the transformation of an agricultural society into an industrial urbanized society is associated with a decline of the death rate and with a lagged decline of the birth rate. A variety of mathematical formulations of these trends are conceivable. In this paper, the following assumptions were adopted: (1) that the rate of change of the death rate is a maximum when the death rate is midway between an upper and a lower equilibrium level, and that it is the closer to zero, the closer the death rate is to the equilibrium levels, and (2) that the birth rate follows the death rate after a time lag. This formulation of the transition theory yields a doubly asymptotic population trend corresponding to a modified logistic curve.

Conclusions The over-all conclusion of this paper is that the effec of delivery cost on the price policy of a monopolist depends systematically upon the shape of the demand curves of the consumers in his market area. In drawing the specific conclusions of propositions I–IV, we have used the simplifying assumptions of constant marginal production costs and identity of all consumer demand schedules. Our results are also dependent upon conditions that the convexity of the individual demand curve nowhere varies beyond well defined limits. Therefore, the results of our analysis are not as general as those which might be derived at the cost of a more involved analysis.