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.     

ON THE VARIABLE SHAPE OF THE FREE SPATIAL DEMAND FUNCTION*

ABSTRACT Analytical evidence is presented confirming variations in the shape of the free spatial demand function under different market conditions. For some simple spatial configurations of consumers, the transformation from convexity to concavity may be conveniently observed using graphical methods. The key criteria for concavity of the free spatial demand function are certain combinations of concave consumer demand, nonuniform consumer density, and/or nonlinear transportation costs. Although findings are confined to free spatial demand, similar variations may be expected to hold for the competitive case.     

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.     

ADDITIVE-INTERACTION MODELS OF SPATIAL AGGLOMERATION*

A wide variety of existing models of spatial agglomeration postulate additive-interaction effects among agents. In this paper, a synthesis of such models is achieved by establishing certain mathematical equivalences between them. In particular, it is shown that Rockafellar's conjugacy theory of concave functions yields a symmetric one-to-one correspondence between three classes of existing models, here designated as spatial-accessibility models, endogenous-contact models, and fixed-contact models. These correspondences not only allow the transference of results between models, but also suggest new economic interpretations of each model in terms of its conjugate model. A series of examples are drawn from the literature to illustrate these results.     

POISSON GRAVITY MODELS OF SPATIAL FLOWS*

ABSTRACT The purpose of this paper is to bring together a number of results on spatial flow models, and to reformulate them within a unified probability framework based on Poisson frequencies. To do so, a class of discrete stochastic processes, designated as independent flow processes, is developed which not only yields a complete characterization of Poisson flow frequencies, but also allows a wide range of gravity-type flow models to be formulated within this distributional framework. In particular, a hierarchical classification of 12 model types is developed, and each model type is shown to be characterizable directly in terms of behavioral axioms on independent flow processes.     

THE ECONOMIC LAW OF MARKET AREAS: A FURTHER DISCUSSION*

ABSTRACT. The Economic Law of Market Areas, so named by Fetter, is concerned with the division of a territory between two competing centers. It is argued that this Law can be conveniently examined in terms of six cases, each of which is specified by a combination of differentials in freight rates and prices at the two centers. The locational significance of each case is considered, along with the form and dimensions of the market-area boundary between the two centers. Three of the cases are each shown to subsume a special case. It is further shown that for any case except one, a reversal of the differentials between the two centers, while resulting in a symmetrically-equivalent outcome, requires a different (and usually substantial) respecification of the case.     

NON-NESTED TESTS ON THE WEIGHT STRUCTURE IN SPATIAL AUTOREGRESSIVE MODELS: SOME MONTE CARLO RESULTS*

ABSTRACT. This paper presents some further results with respect to hypothesis tests for the appropriate structure of dependence in mixed regressive/spatial-autoregressive relations. Three tests on non-nested hypotheses are considered, which are based on the use of augmented regressions, and their small sample performance is compared in a number of Monte Carlo simulation experiments.     

K. H. RAU AND THE ECONOMIC LAW OF MARKET AREAS*

It is well-known that the economic law of market areas was first discovered by Launhardt (1882, 1885, 1900-1902) in Europe and independently discovered by Fetter (1924) in the United States. This paper shows that the seeds of the law of market areas are contained in a letter of K. H. Rau to M. Quintelet published in 1841, and that Rau's name deserves to be mentioned alongside those of Launhardt, Cheysson, and Fetter, as writers who contributed substantially to the developments of the law of market areas.     

UPPER BOUNDS ON THE SIZES OF INTERREGIONAL FEEDBACKS IN MULTIREGIONAL INPUT-OUTPUT MODELS*

ABSTRACT. Upper bounds are presented for a measure of the overall percentage error caused in a multiregional input-output model when interregional feedback effects are ignored. This error figure is thus a measure of the magnitude of interregional linkages. The upper bounds are expressed as a function of the levels of self-sufficiency in the regions in the model and of the norms of the regional technical coefficients matrices. Experimental results are presented for a variety of examples that are thought to reflect real-world situations, and it is clear that in many cases the upper bound (and hence the error) is extremely small. The implication is that single-region input-output models may be adequate for a variety of questions.     

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.