Location theory

Abstract: D IURING the past several decades there has been a growing interest in location theory in America. Building on the pioneering works of Thtinen, Weber, Lbsch, Palander, and others,2 a number of economists and geographers have extended the analysis to apply to a wide range of problems and have attempted to synthesize location theory with other fields of economics.3 However, very little work has been done in using the principles of location to analyze the historical growth of regions in America.4 While economists concerned with location theory sometimes point out the implications of their analysis for the growth of regions, they have not followed up these discrete observations with any systematic analysis. A fundamental difficulty has been that the theory of regional economic growth' has little relevance for the development of regions in America. Not only does the sequence of stages outlined by the theory bear little resemblance to American development but its policy implications are also fundamentally misleading. This paper will attempt to demonstrate the inadequacies of the existing theory of regional economic growth and will advance a number of propositions that may lead to a more useful theory, both for analyzing the historical development of the American economy and for understanding the contemporary problems associated with regional economic growth. The analytical propositions advanced in this paper, though explicitly oriented to America's development, would apply equally well to other areas that meet the following conditions: (1) regions that have grown up within a framework of capitalist institutions and have therefore responded to profit maximizing opportunities, in which factors of production have been relatively mobile,6 and (2) re1 I am indebted for criticisms and suggestions to several of my colleagues at the University of Washington, particularly Philip Cartwright, J. R. Huber, Franklyn Holzman, and Robert Lampman. Dean H. W. Stoke and the Research Committee of the Graduate School at the University of Washington generously provided financial assistance for research, part of which is used in this article.

Abstract: FOR more than four decades the construction of a general location theory has been a stimulating challenge to spatial theorists. Despite the productive efforts of Weber, Englander, Predohl, Ohlin, Palander, Hoover, Losch, and others, the goals of spinning a theoretical web and specifying the design of a corresponding operational model are still remote.2 However, the comparatively recent pioneering contributions of Leontief in developing input-output techniques for general equilibrium analysis are of consequence here. They permit an attack upon a specific set of significant problems which logically fall within the jurisdiction of a general theory of location and space-economy. The analysis of changing interregional economic bonds and flows can be approached from several directions. The input-output method as elaborated here implicitly assumes, for the most part, unchanging spatial relations between any producer and his suppliers. Only a limited amount of industrial relocation can be tolerated with any change in the basic parameters of the economic system at any given point of time. An alternative approach has been sketched for example in an unpublished memorandum by Koopmans.3 Such an approach would treat the space factor explicitly. It would permit major variation in the spatial extent of production for each firm and in the geographic pattern of production and resource utilization. It would be consistent with major relocation of industry and population. It would reveal how distance actively conditions interregional economic relations.4 An operational model following this alternative, more desirable, approach is yet to be developed. This paper is concerned with the much more limited assignment of regional and interregional analysis within the rigid spatial framework necessitated by the postulates of input-output analysis.5 'The analysis in this article has greatly benefited from discussions with Guy Freutel and with Wassily W. Leontief, James S. Duesenberry, Leon Moses, and other members of the Harvard Economic Research project. However, the shortcomings of the analysis and the views expressed herein are the author's only. The model to be developed through spatial aggregation is basically different from one constructed by Professor Leontief through national disaggregation (in his forthcoming Studies in the Structure of the American Economy, Chapter 4). Nevertheless, the two models should not be viewed as alternatives. Rather they are complements. The Leontief balanced regional model is particularly useful for determining regional implications of national projections; the pure interregional model, for determining national implications of regional projections. (For elaboration of this point, see W. Isard and G. Freutel, Regional and National Product Projections and Their Interrelations, sections 7 and 8, paper prepared for Conference on Research in Income and Wealth, National Bureau of Economic Research, May 195I,) Since one can proceed by degrees from one type of model to the other, it is likely that after considerable experimentation an hybrid model, involving elements of both, may prove to have the most general utility. The author's experience in directing the preparation and collection of the data and in carrying through the computations for the Leontief model has been of great value in setting up a feasible design for his own model. 'For a presentation and evaluation of these efforts see W. Isard, "The General Theory of Location and SpaceEconomy," Quarterly Journal of Economics, Vol. 63 (November I949), pp. 476-506. 3T. Koopmans, The Optimum Geographical Distribution of Population and Industry in the United States (Cowles Commission for Research in Economics, January I946). 'Though trade theory is basically concerned with geographic flows, it has by and large ignored or set aside the space factor. This is in line with the economic theorist's customary preoccupation with the time factor. ;;Treating space implicitly or as a passive factor has also been characteristic of the better regional development studies. Colin Clark in his excellent works on economic progress in the various regions and nations of the world (The Conditions of Economic Progress, London, I940, and The Economics of I960, London, I942) does not attempt at all to study the basic changes in the spatial interrelations and patterns of these nations or regions. Nor does he probe into the diverse spatial structures of nations and regions at a given point of time. To be sure, he makes spatial comparisons in the sense that he compares nations having different latitudinal and longitudinal positions. But such comparisons more accurately fall under the heading of geographic description, not spatial analysis. A. J. Brown (Industrialization and Trade, London, I943, and Applied Economics, London, I947), in ascribing a significant role to the world's uneven pattern of resources and its implications for geographic specialization and the global locational structure of industry, takes a major step forw7ard. But he does not transcend "geographic positional" analysis. He does not expose the fundamental spatial scaffolding of international relations. Nor do E. F. Staley (Woorld Economic Development, Montreal, I944), the

Abstract: Hubs are central facilities which act as switching points in networks connecting a set of interacting nodes. This paper develops several location models for hubs. The one-hub siting problem is equivalent to a Weber least cost location model. An empirical example demonstrates the relevance of this model for an understanding of contemporary express delivery networks. A new model describing the location of two hubs in a plane yields several interesting pairs of hub location under different assumptions about scale effects on the interfacility linkage: generally as these scale effects increase the locations of the hubs move apart.

Abstract: . Economies of scale, transportation costs, and factor mobility can interact to produce agglomerations even in the absence of any pure external economies. This paper offers a monopolistic competition model of a city that serves an agricultural hinterland; unlike most analyses in location theory, the model is fully general equilibrium, but it has strong links to older concepts in geography, notably the idea of “market potential.” The analysis shows that the forward and backward linkages that hold a population concentration together also allow that concentration to occur in a variety of possible sites—that is, there are multiple equilibria (indeed a continuum) for metropolitan location.