Löschian Spatial Competition in an Emerging Retail Industry

Löschian competition is traditionally thought to lead to a spatial equilibrium in which firms enter an industry and disperse across geographic space until each firm earns insufficient excess profit to attract net new entrants. This paper assesses the appropriateness of Löschian analysis using video (movie) rental establishments in Toronto as a case example. The video rental business, as we know it today, began to take shape around 1980 and has since seen much turnover. The paper describes the changing pattern of single‐site and chain stores between 1982 and 1999. I use logistic regression to predict the survival of existing establishments. Using survivorship as a proxy for profit, the paper draws conclusions about the extent to which temporal changes in video store location correspond to the tenets of Löschian competition. The coexistence of chain and single‐site stores suggests that there are distinct market niches and that single‐site stores have used a “swarming” strategy to compete against chains. Conclusions are drawn about how the retail sector might evolve in the future because of the locational competition between chains and single‐site stores.     

The Fractal Theory of Central Place Geometry: A Diophantine Analysis of Fractal Generators for Arbitrary Löschian Numbers

We develop material to determine whether or not an arbitrary number is Löschian; the procedure embodied in the theorems achieves the desired result more swiftly than do previous solutions to this problem. The correspondence between a partition of the central place lattice and a quadratic form permits the rapid determination of the lattice coordinates of an arbitrary Löschian number and of the exact shape of a single fractal generator used to form an entire central place hierarchy associated with an arbitrary Löschian number. Central place hierarchies may be generated geometrically using a single shape applied initially to a hexagon and subsequently, scaled appropriately, to resultant polygons. Fractional dimensions of arbitrary central place hierarchies, measuring their “space-filling” characteristics, follow naturally from this general procedure.     

The Lösch System of Market Areas: Derivation and Extension

Certain aspects of Lösch's classic work on the network of markets and the system of networks have not yet been clearly explained in the literature. Lösch did not describe his derivation procedures in full, and apparent printing errors in certain förmulae confuse the issue further, with the result that several recent texts reproduce Lösch's diagrams but offer no explanation of how they are constructed. Accepting the network of hexagonal market areas for a continuous system of markets, given an even but discrete distribution of population, the derivation from first principles of the complete system of different market areas is presented. Apparent errors in the translated text of Lösch's work are corrected. Limitations in some other authors' work and accordance with earlier empirically derived formulae are mentioned. The production of “city-rich” and “city-poor” sectors is shown to be a constraint on, rather than a result of, the system, and Lösch's statement that the coincidence of centers is maximized is clarified. The extension of the Lösch system to the internal tertiary structure of the city is presented and attention drawn to the empirical attractiveness of this approach.     

Spatial Mismatch and the Structure of American Metropolitan Areas, 1970–2000

Abstract.  This paper analyzes the impact of employment and population shifts in U.S. metropolitan areas from 1970 to 2000 on a spatial mismatch index to determine how metropolitan residents reacted to changes in metropolitan employment distributions. In particular, it seeks to determine whether suburban employment growth created new areas to which access is valued or whether it repelled metropolitan residents and sparked population growth in more distant suburban locations. The results show that residents tended to move away from areas gaining jobs. Black residents, on the other hand, appeared to be attracted to areas that are experiencing employment growth.     

Reality versus Policy: The Delineation and Testing of Local Labour Market and Spatial Policy Areas

As part of the empirical planning science, this article integrates theory, empirical findings and policy. It first deals with the question how to reach a theoretically well-grounded and empirical applicable delineation of local labour market areas. An inductive classification method is selected based on the behaviour of individual commuters without selecting a priori central places. By this, new urban forms like polynodality are included. In using this method for the Netherlands, 31 local labour market areas (LLAs) were distinguished. Moreover, the article elaborates some simple measures to test the optimality of LLA classifications. The 31 LLAs adequately reflect the 'reality' of actual functional labour market relationships. The article also investigates the matching between reality and the LLA classification as used in spatial policy. There is a large gap between reality and policy. This urges bringing the policy classification more in line with existing LLAs. Alternatively, if one considers the present policy classification as an instrument for future spatial structure, much additional effort will be required. The findings of the article can be easily applied to other European countries.     

Employment Densities, Spatial Autocorrelation, and Subcenters in Large Metropolitan Areas

Employment density functions are estimated for 62 large metropolitan areas. Estimated gradients are statistically significant for distance from the nearest subcenter as well as for distance from the traditional central business district. Lagrange Multiplier (LM) tests imply significant spatial autocorrelation under highly restrictive ordinary least squares (OLS) specifications. The LM test statistics fall dramatically when the models are estimated using flexible parametric and nonparametric methods. The results serve as a warning that functional form misspecification causes spatial autocorrelation.     

Identifying Domination and Resistance Through the Spatial Organization of Poonindie Mission,South Australia

One of the spaces where the interactions between Indigenous and non-Indigenous groups during the period of contact and cross-cultural interaction took place around the world, was at missions. In Australia, missions were founded, rearranged and closed down over a period of time in which the attitudes of Indigenous and non-Indigenous groups and official Government policy towards contact relationships were continually changing. By analyzing the use of these contested spaces at Australian Missions by both groups, archaeologists can begin to understand how the new relationships between these groups were negotiated, contested and played out over time. This paper analyses the use of space, using the theoretical frameworks of the archaeologies of capitalism, at Poonindie Mission in South Australia, which was established by the Anglican Church with support from the colonial government and operated between 1850 and 1896.     

A Location-Allocation Model of Lösch's Central Place Theory: Testing on a Uniform Lattice Network

This paper develops a location-allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. However, remaining inconsistencies appear to be due to the inability to express the consumer behavior laws as linear constraints, to the bounded and discrete nature of the network, and to the objective function being the sum of integer variables. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions.     

Association between Population Density and The Market Areas of Towns

This paper examines the relationship between population density and town spacing in four kinds of environment. These are: (1) linear curves of demand, transport and production costs and an even population distribution; (2) nonlinear transport cost curves over space; (3) variable population density within hinterlands; and (4) variation of transport costs with population density. Previously, it has been shown that the criterion of free entry does not uniquely determine town spacing. The implications of four stronger criteria are therefore examined in this paper. These location criteria are: (a) the number of towns is maximized; (b) the number of towns in minimized, subject to all consumers' being served; (c) the towns are all owned by one profit-maximizing monopolist; and (d) the average of some consumer utility function is maximized. In cases (a), (c), and (d) spacing decreases with density; in (b) spacing is an increasing function of density. Actual data are presented on the spacing of towns in Iowa and shopping centers in Chicago which indicate that spacing and population density are not associated. These results are consistent with the notion that entry is free but are not consistent with the stronger constraints employed in this paper.