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.     

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.     

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.     

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.     

The Forgotten Semantics of Regression Modeling in Geography

This article is concerned with the semantics associated with the statistical analysis of spatial data. It takes the simplest case of the prediction of variable y as a function of covariate(s) x, in which predicted y is always an approximation of y and only ever a function of x, thus, inheriting many of the spatial characteristics of x, and illustrates several core issues using “synthetic” remote sensing and “real” soils case studies. The outputs of regression models and, therefore, the meaning of predicted y, are shown to vary due to (1) choices about data: the specification of x (which covariates to include), the support of x (measurement scales and granularity), the measurement of x and the error of x, and (2) choices about the model including its functional form and the method of model identification. Some of these issues are more widely recognized than others. Thus, the study provides definition to the multiple ways in which regression prediction and inference are affected by data and model choices. The article invites researchers to pause and consider the semantic meaning of predicted y, which is often nothing more than a scaled version of covariate(s) x, and argues that it is naïve to ignore this.     

LANDSCAPES OUT OF ORDER: STUDYING THE INNER URBAN FRINGE BEYOND THE RURAL – URBAN DIVIDE

Contemporary accounts of the inner urban fringe tend to focus on the transition from rural to urban land use and rural–urban conflicts, rather than highlighting the landscape at the city edge in its own right. It is argued in this paper that such dichotomous accounts neglect the complexity, values and conflicts of fringe landscapes. The study illustrates that an investigation into the relationship between attempts within spatial planning to design orderly places for urban expansion and the evolvement of places out of order offers a way to analyse landscape transformations at the fringe beyond the rural–urban divide. This approach will offer a multifaceted analysis of the landscape, which in turn will facilitate a more open discussion on land use and values within planning. A theoretical discussion on the interplay between ordered and disordered places is followed by a case study of the interactions between a disordered place and the ambitions within spatial planning to create order. The study has been conducted at the fringe of Burlöv (in southernmost Sweden). By way of conclusion, the findings of the case study are summarized, along with arguments that underline the need for further case studies of fringe landscapes.     

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 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.     

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.     

A Persistent Place for Hunter-Gatherers During the Late Holocene: The Case of Burials in Pit on the Coast of Lángara Bay,Argentine Patagonia

In Argentine Patagonia, the type of archaeological burial “in pit” has been only identified on the coast of Lángara Bay. This modality is characterized by the presence of single and multiple primary burials. Studies on five human burials in pits are presented in this article. The aim is to compare the contexts of burials in pit at the site level and the spatial characteristics of their distribution in the Lángara Bay locality from a diachronic perspective. The approach focuses on mortuary practices and social relations of hunter-gatherer groups during the Late Holocene. A characterization of the burials, their chronologies, bioarchaeological determinations, stable isotope studies, and their spatial distribution are included. The results allow us to chronologically place the contexts between ca. 3000 and 2000 cal BP. A spatial pattern in the distribution of burials in the coastal landscape was identified. Finally, it is proposed that this part of the Patagonian coast was a persistent place of burials in pit.     

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.     

The Assessment of Spatial Autocorrelation through Constrained Multiple Regression

Most published measures of spatial autocorrelation (SA) can be recast as a (normalized) cross-product statistic that indexes the degree of relationship between corresponding entries from two matrices—one specifying the spatial connections among a set of n locations, and the other reflecting a very explicit definition of similarity between the set of values on some variable x realized over the n locations. We first give a very brief sketch of the basic cross-product approach to the evaluation of SA, and then generalize this strategy to include less restrictive specifications for the notion of similarity between the values on x. Using constrained multiple regression, the characterization of variate similarity basic to any assessment of SA can itself be framed according to the information present in the measure of spatial separation. These extensions obviate the inherent arbitrariness in how SA is usually evaluated, which now results from the requirement of a very restrictive definition of variate similarity before a cross-product index can be obtained.     

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.     

Groundwater discharges in the Baltic Sea: survey and quantification using a schlieren technique application

Groundwater seeps are known to occur in Eckernförde Bay, Baltic Sea. Their discharge rate and dispersion were investigated with a new schlieren technique application, which is able to visualize heterogeneous water parcels with density anomalies down to Δσ_t = 0.049 on the scale of millimeters. With the use of an inverted funnel, discharged fluids can be captured and the outflow velocity can be determined. Overall, 46 stations could be categorized by three different cases: active vent sites, seep‐influenced sites, and non‐seep sites. New seep locations were discovered, even at shallow near‐shore sites, lacking prominent sediment depression, which indicate submarine springs. The detection of numerous seeps was possible and the groundwater‐influenced area was defined to be approximately 6.3 km². Flow rates of between 0.05 and 0.71 l m^?2 min^?1 were measured. A single focused fluid plume, which was not disturbed by the funnel was recorded and revealed a flux of 59.6 ± 20 ml cm^?2 min^?1 and it was calculated that this single focused plume would be strong enough to produce a flow rate through the funnel of 1.32 ± 0.44 l m^?2 min^?1. The effect of different seep‐meter funnel sizes is discussed.     

Analysis of a Distribution of Point Events Using the Network‐Based Quadrat Method

This study proposes a new quadrat method that can be applied to the study of point distributions in a network space. While the conventional planar quadrat method remains one of the most fundamental spatial analytical methods on a two‐dimensional plane, its quadrats are usually identified by regular, square grids. However, assuming that they are observed along a network, points in a single quadrat are not necessarily close to each other in terms of their network distance. Using planar quadrats in such cases may distort the representation of the distribution pattern of points on a network. The network‐based units used in this article, on the other hand, consist of subsets of the actual network, providing more accurate aggregation of the data points along the network. The performance of the network‐based quadrat method is compared with that of the conventional quadrat method through a case study on a point distribution on a network. The χ² statistic and Moran's I statistic of the two quadrat types indicate that (1) the conventional planar quadrat method tends to overestimate the overall degree of dispersion and (2) the network‐based quadrat method derives a more accurate estimate on the local similarity. The article also performs sensitivity analysis on network and planar quadrats across different scales and with different spatial arrangements, in which the abovementioned statistical tendencies are also confirmed.     

Storytelling as Method in Spatial Planning

Abstract

Drawing on the case of the Wageningse Eng in the Netherlands, this paper considers the role of “storytelling” within spatial planning practices. It moves away, though, from seeing it as merely a model of spatial planning, where “storytelling” is sometimes used to justify planners' ideals for the landscape, or a model for spatial planning, which pushes for a normative use of “storytelling” as a means of encapsulating local knowledge and the views of those who live in, and use, the landscape. Rather, the paper engages “storytelling” as a method for revealing how formal planning practices may be destabilized by more vernacular narratives seeking to subvert dominant discourses and processes. In doing so, it seeks to not only show the contested nature of participatory planning within the Netherlands, but also the ways in which narratives—as revealed via such a method—construct specific positionalities with real implications for notions of inclusivity within planning practices.     

NORDEN AND THE "SUBSTANTIVE LANDSCAPE": A PERSONAL ACCOUNT

This commentary takes its point of departure in the debate provoked by the landscape theory that Denis Cosgrove presented in his seminal book, Social Formation and Symbolic Landscape (1984), in which he defined landscape in terms of scenic, spatial forms of representation. By unpacking the evolution of the concept of landscape the author proposed an alternative interpretation to Cosgrove's, emphasizing differing conceptions of lawfulness, in which the “substantive” platial landscape was introduced as a counterpoint to the scenic spatial concept. Initially, and for two particular reasons, the substantive landscape became theoretically placed in Norden: first, due to the historical and contemporary territorial/platial connotations of the term in the Nordic realm, and second, because the interest in a substantive landscape has been considerable among Nordic scholars. Today, this interest goes well beyond a Nordic context. In commenting on the contributions in this special issue the paper points at how different engagements with a “substantive landscape” might inform present and future scholarly debate concerning the role and meaning of landscape.     

The Historic Landscape of the Saga of the People of Vatnsdalur: Exploring the Saga Writer's Use of the Landscape and Archaeological Remains to Serve Political Interests

Abstract

The saga of the People of Vatnsdalur (Vatnsdaelasaga) provides a case study for a new approach to the Sagas of Icelanders (Íslendingasögur). This treats the saga as a cultural product of the 13th century that can give insights into its creator's ideas and worldviews. Fieldwork at five sites in the Vatnsdalur valley in NW Iceland seeks to establish what these places were like in the 13th century. This knowledge, alongside the saga and place-name evidence, illustrates how the saga writer, presumed to come from a powerful 13th-century family, systematically used the landscape and archaeological remains in the valley to serve his political interests when describing 10th-century events.