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.     

LÖSCHIAN COMPETITION VERSUS SPATIAL COLLUSION: PRICE AND WELFARE COMPARISONS*

ABSTRACT. Löschian duopoly under heterogeneous cost conditions is examined to show that it is not equivalent, contra past findings, to spatial collusion. Moreover, within the confines of the assumed demand and cost conditions spatial collusion is shown to be superior to Loschian competition in terms of both (aggregate) consumer surplus and producer surplus, which implies a possible welfare gain from collusion. A general, if not the general, prices-and-welfare comparison of alternative pricing schema including collusive, Löschian, and optimal pricing is summarily presented in a table.     

A NOTE ON THE STABILITY PROPERTY OF SPATIAL COMPETITION*

ABSTRACT. Our study extends the standard comparative static analysis to allow for dynamic aspects of equilibrium in spatial competiton. We investigate dynamic stability properties via the Routh-Hurwitz criterion. Nontrivial equilibria in the so-called Löschian, Hotelling-Smithies, and Greenhut-Ohta models are shown to be stable even under heterogeneous cost conditions among competing firms, conditions not considered hitherto. We can thus provide powerful support to the comparative static analyses which can only be developed via equilibrium concepts with stability properties.     

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero-profit long-run equilibrium can occur in a space economy under conditions of increasing returns to scale.     

ON THE SHAPE OF MARKET AREAS IN LÖSCHIAN SPATIAL MODELS*

ABSTRACT. The paper analyzes the lattice shape of equilibrium configurations of firms in spatial models. Lösch's assertion that free entry will result in hexagonal market areas is proved for a variety of assumptions about the nature of the market equilibrium, and about the preferences of customers. All the models considered, however, incorporate rational entry behavior and identify the stable lattice as an entry deterring equilibrium. A simple proof is presented of the optimality of hexagonal market areas, at least among regular space-filling configurations.     

LÖWITH,LÖWITH'S HEIDEGGER,AND THE UNITY OF HISTORY

This article is about the problem of the unity of history as seen through the writings of Karl Löwith. By “unity of history” I understand the notion that all history constitutes one and only one range of kinds of objects and/or one field of knowledge. The article argues that the problem of the unity of history—though often neglected as a matter of mere argumentative infrastructure—is central to a number of wider problems, most prominently the possibility of a plural understanding of historicity and the possibility of ultimately avoiding a unified historical teleology. The article revisits Löwith's writings and proposes a variety of novel interpretations with the aim of evincing the centrality, and of exploring diverse aspects, of the problematic of the unity of history. This problematic is shown to have informed Löwith's work on the secularization thesis as well as his debate with Hans Blumenberg. The foundations of Löwith's discussion of the problem are pursued across his ambivalent critique and appropriation of Heidegger's model of an ontology of historicity as marked by inevitable internal conflict and thus disunity. The paper reconstructs the manner in which, after the Second World War, Löwith's philosophy of history sought to salvage basic traits of the Heideggerian model when it tried to establish the possibility of plural historicity from a notion of the natural cosmos. It is demonstrated that the motives for this salvage operation ultimately extended beyond the problem of Löwith's reception of Heidegger and concerned the possibility of continuing any debate on the philosophy of history.     

Classical Central Places as Protected Thresholds

Previous research efforts demonstrate the use of location covering in the spatial structuring of central places within a single-good context. In a multilevel context, this paper similarly develops a mathematical programming approach to the siting of central places based on the “protection” of inner (or threshold) markets. The objective function maximizes both market coverage of demand and market overlap, subject to an upper bound on market overlap; this allows the formation of different market structures consistent with the various K-valued central place systems of Christaller and Lösch. Siting examples serve to illustrate the working of the protected threshold model in isotropic settings. Furthermore, ways in which the present model might be extended for other situations are examined.     

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.     

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.     

Existentialism as a Political Problem in Karl Löwith's Thought

The aim of this paper is to make a case for the claim that Karl Löwith's thought is predominately preoccupied with one major philosophic–historical problem that may be broadly labelled existentialism. This notion is usually employed by Löwith in order to grasp the various phenomena and developments within the European (or Western) history in the modern age. I claim that the meaning assigned by Löwith to the notion of existentialism is inseparable from its political consequences. In other words, I attempt to reconstruct the notion of existentialism in Löwith's thought primarily as a political problem. By advancing this argument, I am inclined towards the view that Löwith’s ?uvre deserves more careful reception from political theorists than it has yet received.     

TRAUMA DELEGITIMIZED: KARL LÖWITH AND THE COSMIC VIEW OF HISTORY

This article uncovers the work of trauma in Karl Löwith's historical thought. Although best known for his critique of the philosophy of history and for the conception of secularization in his 1949 book, Meaning in History, Löwith deepened his positive historical vision in several essays that he wrote in the 1950s and 1960s. From these texts emerges a unique historical orientation, which I call the “cosmic view of history.” This perspective was at once a critique of modern historical consciousness and an embodied corrective to that consciousness, one in which the catastrophes of the twentieth century were relativized and made endurable. In both the origin and structure of this historical orientation and in its textual expression in Löwith's work, trauma is a residual force that links Löwith's language, his experiences, and the postwar context. The role of trauma in Löwith's thought further reveals a process of delegitimization in which historical consciousness and historical events lose their power to determine historical meaning, thus enabling a response to and an escape from catastrophe. This article also explores the significance of this cosmic view of history for contemporary theoretical concerns related to the Anthropocene and its consequences for historical theory.     

Spinners and weavers of auffay. Rural industry and the sexual division of labour in a French village, 1750–1850

German scholars of Jewish origin who were students of Martin Heidegger in the 1920s and 1930s are frequently criticized for their supposed postwar refusal to ‘disavow earlier liaisons with Heidegger.’ These scholars are thus indicted for being fundamentally anti-liberal or apolitical, and for those reasons dangerous disciples of Heidegger. By examining the works of Karl Löwith and Hans Jonas, two of Heidegger's influential former students, the following paper presents a more nuanced reading of the relationship between master and disciples, namely that Jonas and Löwith operate with Heidegger's philosophical grammar in order to turn against Heidegger, philosophically and politically. Within this framework, the article fleshes out the crucial importance of theology to the understanding of Jonas’ and Löwith's philosophical critique of Heidegger's thought. Following this theological turn, the paper demonstrates the complexity of Jonas’ and Löwith's postwar approach, that is an anti-Heideggerian ethical and political quest which is anchored nonetheless in Heidegger's philosophy. As such, Jonas’ and Löwith's political projects demonstrate the manner in which Heideggerian categories are not exhausted by Heidegger's own political interpretation; they grippingly denotes the aptitude to steer Heideggerian philosophy towards new ethical and political shores.     

A WOMAN'S PLACE: SPACE,MEETING PLACES AND GENDER IN 16TH‐CENTURY NYA LÖDÖSE,SWEDEN

In this article, archaeological and archival data are used to discuss gender in 16^th‐century Nya Lödöse in western Sweeden with a focus on women. Four areas for social space are identified and analysed. The result shows that women seem to have had a somewhat higher degree of agency in Nya Lödöse compared with the surrounding countryside and smaller towns.     

THE PUZZLE OF THE BANQUET HALL OF THE DUKES: THE PROFESSIONALIZATION OF SWEDISH HISTORICAL RESEARCH STUDIED THROUGH LUDWIK FLECK'S “THOUGHT COLLECTIVE” AND “THOUGHT STYLE”

In 1312, the Swedish dukes Erik and Valdemar Magnusson married the Norwegian princesses Ingeborg Haakonsdaughter and Ingeborg Eriksdaughter at a ceremony in Oslo, Norway. In 1313, the two couples were reunited at a purpose-built banquet hall, believed to have been located in the medieval Swedish town of Lödöse. The main source of information concerning these events is the Swedish medieval rhyme chronicle The Chronicle of Duke Erik. However, a closer reading of the chronicle reveals that Lödöse is never mentioned in relation to the banquet hall. The article discusses the passing down of knowledge through generations of the same professional collective, in this case the professional collective of Swedish historians during the twentieth century, and demonstrates how the validity of once-established prescientific knowledge persists. To achieve its goal, the article applies Ludwik Fleck's terms “thought collective,” “thought style,” and “tenacity in science,” as well as Thomas Kuhn's concept of the “paradigm,” to a historiographical case study of how the proto-idea of the banquet hall being located at Lödöse has survived to become an established scientific fact. The location of the banquet hall concerns but a minor detail in the turbulent political situation of the Swedish kingdom during the first decades of the fourteenth century. However, the continuing reiteration of this minor detail is evidence of a larger phenomenon, namely how contemporary historical research is influenced by scholars in the prescientific past.     

Jüdischer alltag in Deutschland, 1933–1945

While discussions of the debate between Karl Löwith and Hans Blumenberg over ‘secularisation’ focus primarily on the methodological utility of the concept, the difference between them was also one of the philosophical commitments and substantive claims about modernity. This difference is not always obvious. One way of bringing it out is to address the different contexts in which they produced their most famous statements about secularisation. But another, and one that will be pursued here, is to consider the critical dialogue that both thinkers engaged in with Nietzsche. Put briefly, while Löwith thought that Nietzsche misunderstood the ancients, Blumenberg thought that he misunderstood the moderns. For Löwith, Nietzsche's doctrine of the eternal return is not Greek, but an aggressive countergospel that owes much to the Christian culture it seeks to oppose; for Blumenberg, Nietzsche assumes, wrongly, that the self-belittlement of man by theology has been succeeded by the self-belittlement of man by science. In addition, Blumenberg – unlike both Nietzsche and Löwith – thinks that he can mount a robust defence of both modern science and progress.     

The City as a Focus for Human Capital Migration: Towards a Dynamic Analysis of University Human Capital Contributions

Universities’ contributions to urban development frequently focus on their micro- or macro-scale effects, ignoring the meso-scale effects they have on inter-territorial relationships. Although universities are seen as an essential part of the recipe for successful urban development, there is a lacuna to understanding how they make places and shape urban hierarchies, and this article addresses this question. This article focuses on one university–urban development process, the creation and embedding of highly skilled graduates, to explore what the aggregate effects of universities on places are; it develops a set of indicators to measure graduate attraction and retention as well as the overall composite place effect. The article develops a typology based on these three indicator sets, and tests this using a data set developed from a Polish social media website. It finds that these indicators are a good way of measuring the effects of human capital creation and mobility at the urban scale. The article concludes by arguing that a greater focus is required in studying the roles that universities play in fostering through-flow in places, changing these places’ nature as nodes within wider urban systems and hierarchies, in the context of university–regional development.     

ECONOMIES OF SCALE AND ENTRY IN SPATIAL MARKETS

For the purposes of simplicity, short-run cost functions are widely used in spatial markets literature, even when the long-run effects of entry are in question. In this paper, I show that if a long-run cost function is incorporated into a Löschian model, counter-intuitive and novel performance characteristics can result. Under some circumstances welfare per area can decrease as cost levels decrease.     

Gendered spheres: theorizing space in the English printing house

The English printing house was initially conceived, legally, as a printing house, with public work taking place in a private setting. This private space emphasised the traditional hierarchies of political and legal order: Women’s work that took place within the printing house thus fell into the traditional role of household labours. This erasure of labour is one that foregrounds the erasure of women’s writing from history; women who worked in essence as publishers, as printers and booksellers, are very clearly present in the historical records but invisible in our narratives of book history. How did this erasure happen, and why is their presence, and work, overlooked? If we consider the language of space in theory and reread Moxon’s Mechanickal Exercises closely, we see the ways in which the ideas of space itself can be implicitly gendered, and how this might shape our idea of the printing house.     

‘Resemblances to archaeological finds’: Guido Boggiani,Claude Lévi-Strauss and Caduveo body painting

In 1942, Claude Lévi-Strauss published an article on Caduveo body painting in the first number of the surrealist magazine VVV, with the editorial assistance of André Breton and cover by Max Ernst. In the article, Lévi-Strauss uses the photographs of the Caduveo women taken during his fieldtrip in 1935–36, together with drawings of facial designs collected to reflect on their ‘strong originality’, which ‘evokes a very ancient culture, and one full of preciosities’. Amongst these illustrations, there is an engraving taken from Guido Boggiani’s book, I Caduvei, published in 1895. Boggiani, an Italian landscape painter who visited South America in 1887–93, was captivated by the Caduveo graphic art, which he sketched in detail. In 1896 he returned, travelling to Paraguay, this time equipped with a new tool to help his ethnographic research: a photographic camera. Over a period of five years, Boggiani completed more than 400 photographs on glass gelatin plates of various sizes. For Lévi-Strauss, as for Boggiani, the originality of the Caduveo graphic art remained enigmatic, evoking a very ancient culture; it was a topic to which he would return in several of his most influential works. In this article, I focus on the visual images (engraved, drawn, photographed and filmed) that depict the body painting of the Caduveo people in central Brazil by Boggiani and Lévi-Strauss in order to explore the ways in which they enabled an ephemeral art – delicate arabesques painted on skin – to be studied as archaeological vestiges. In the process, I trace the aesthetic sensibility of Boggiani and Lévi-Strauss that provided them with the imaginative tools to do so.