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.     

PRICE AND LOCATION CONJECTURES IN MEDIUM- AND LONG-RUN SPATIAL COMPETITION MODELS*

ABSTRACT. This paper examines medium-run and long-run equilibria in unbounded (circular) and bounded (linear) one-dimensional multifirm markets. A price-location adjustment model is outlined that dows simulation of the spatial equilibrium when these firms anticipate reactions from their nearest spatial rivals. Thus, the market equilibrium is derived from the interdependent but atomistic decisions of the competing firms and is not imposed by some outside observer or agency. Ail conjectures are exogenous; the three well-known price conjectures (Greenhut-Ohta, Hotelling-Smithies, and Losch) are highlighted; and the relevant comparative statics are provided.     

资本、权力与空间:“空间的生产”解析

全球化时期的生产方式从根本上决定了资本和权力是城市空间产生和演化的主要动力。它们分别展现了不同的作用范围、形式及效果:资本主要作用于物质的、社会—经济空间的生产,而权力主要作用于抽象的、政治—制度空间的生产。这两个过程相互影响、相互交织。本文将"空间的生产"理论与城市空间实践结合起来进行转型中国语境下的解析,尝试提供一个研究我国城市与区域空间重构问题的马克思主义政治经济学视角。     

TWO-DIMENSIONAL BERTRAND COMPETITION: BLOCK METRIC,EUCLIDEAN METRIC,AND WAVES OF ENTRY*

This paper examines two-dimensional spatial competition, with Bertrand price determination. With a block metric, equilibrium prices are significantly lower when market areas are squares than when they are diamonds (rotated squares) of the same size. If demand density grows, waves of entry occur, and the shapes of market areas change from squares to diamonds and back to squares again. The former change leaves prim unchanged, whereas the latter cuts prices in half. Results are also derived for a Euclidean metric, with square and hexagonal market areas. Optimal waves of entry are examined with the block metric. With either metric, the socially optimal market shape becomes suboptimal if market areas are constrained to be of the zero-profit size.     

SPATIAL COMPETITION AND THE JOINT CONSUMPTION OF SERVICES*

In Hotelling location models, an implicit assumption has been made that a customer uses the service provided by the firm, independent of other customers. However, for firms that supply meeting rooms, wedding halls, tennis courts, and golf links it is essential to incorporate the fact that the customer only uses the service in conjunction with other customers. The objective of this paper is to formulate the Hotelling location model n consideration of the interdependence among customers in one-dimensional space, and to characterize the state of equilibrium. In our model, each group of members within a given distance enjoys a fixed amount of service of the firms, under the assumption that the travel cost incurred by each group is defined as the travel cost of the farthest customer in the group.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

SPATIAL ADJUSTMENTS IN GRAIN PRODUCTION IN LATE TSARIST RUSSIA

The late nineteenth century world grain market expanded as prices declined and trade increased. As competition increased, Russian producers adapted to market conditions. Russian grain output increased, first by the extension of arable southward and eastward and later as a result of land reform. Analysis of grain output data using information statistics demonstrated dispersed patterns of production from 1885 to 1909. Among individual grain types, rye and oats displayed dispersed output patterns, while wheat and barley output became more concentrated. Changes in these patterns are evidence of adaptation to world market conditions and changes in Russia's socioeconomic system.     

3. SPACE,PLACE, AND GENDER: THE SEXUAL AND SPATIAL DIVISION OF LABOR IN THE EARLY MODERN HOUSEHOLD

Much has been written about the history of the work of men and women in the premodern past. It is now generally acknowledged that early modern ideological assumptions about a strict division of work and space between men and productive work outside the house on the one hand, and women and reproduction and consumption inside the house, on the other, bore little relation to reality. Household work strategies, out of necessity, were diverse. Yet what this spatial complexity meant in particular households on a day‐to‐day basis and its consequences for gender relationships is less clear and has received relatively little historical attention. The aim of this paper is to add to our knowledge through a case study of the way that men and women used and organized space for work in the county of Essex during the “long seventeenth century”. Drawing on critiques of the concept of “separate spheres” and the models of economic change to which it relates, together with local/micro historical methods, it places evidence within an appropriate regional context to argue that spatial patterns were enormously varied in early modern England and a number of factors—time, place, occupation, and status, as well as gender—determined them. Understanding of the dynamic, complex, uneven purchase of patriarchy upon the organization, imagination, and experience of space has important implications for approaches to gender relations in early modern England. It raises additional doubts about the utility of the separate spheres analogy, and particularly the use of binary oppositions of male/female and public/private, to describe gender relations and their changes in this period and shows that a deeper understanding demands more research into the local contexts in which the gendered division and meaning of work was negotiated.     

SPATIAL COMPETITION WITH LOCATION-DEPENDENT COSTS*

This paper investigates the behavior of spatially-competitive firms whose costs depend on their locations. Necessary and sufficient conditions for optimum locations are derived. Comparative-statistics analysis of the equilibrium shows that the responses of firms to changes in input and output transport rates depend on the properties of consumer demand curves or are ambiguous in sign.     

RURAL AND REGIONAL RESTRUCTURING OF APARTHEID: IDEOLOGY, DEVELOPMENT POLICY AND THE COMPETITION FOR SPACE

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SPATIAL COMPETITION WITH CONSISTENT CONJECTURES*

ABSTRACT Equilibrium in spatial models invariably depends on firms' conjectures about how competitors will react to their price changes. This paper analyzes spatial price and location equilibrium when firms hold consistent (i.e. correct) conjectures. Most spatial models assume an exogenous conjecture. Consistent conjectures are one method, albeit a controversial one, for endogenizing the conjecture. We show that the consistent conjecture about a competitor's reaction to a price change in the simplest case is 1/3. When demand is elastic the consistent conjecture is a decreasing function of the radius. It is always below 1/3 and can be negative. In the third model, we show that the consistent conjecture declines as the number of dimensions and the number of competitors increases.     

THE SPATIAL ORGANIZATION OF MILK PRODUCTION IN THE MOSCOW REGION AND WAYS OF IMPROVING IT

Ways of improving the locational pattern of milk production and processing facilities in Moscow Oblast are investigated in order to: (a) reduce the volume of long-distance whole milk imports during winter; (b) increase the size of the dairy herd in the Moscow Region, especially in the west, through more effective utilization of natural pasture and cultivated fodder; and (c) promote a shift in animal husbandry toward dairy stock in areas fringing the capital. Milk processing facilities are compared in terms of production capacity, direct sales versus shipments to higher-order processors, and percentage of output consumed within the oblast and by Moscow (translated by Andrew R. Bond).     

SPATIAL PRICE COMPETITION WITH CONSUIMERS ON A PLANE,AT INTERSECTIONS,AND ALONG MAIN ROADWAYS*

ABSTRACT. This paper examines two-dimensional price competition on a plane, with a block metric and a square grid of main roadways. One store is located at each intersection of main roadways. Consumer locations include a uniform distribution over the plane, linear concentrations along main roadways, and point concentrations at intersections. Bertrmd-Nash mill price competition is examined first. The equilibrium price depends on the relative numbers of consumers in the three types of locations (and on travel costs per mile and the spacing between stores). If too many consumers are in each point concentration, then the price equilibrium is undermined by a high-price strategy or by mill-price undercutting. Spatial competition with price discrimination is examined next, and compared to Bertrand-Nash mill price competition.     

THE NONCHERNOZEM DEVELOPMENT PROGRAM AND PROSPECTIVE SPATIAL SHIFTS IN GRAIN PRODUCTION IN THE AGRICULTURAL TRIANGLE OF THE SOVIET UNION

The Soviet program to proceed from further expansion of the grain area in the semi-arid steppe zone to intensification of graingrowing in the humid Nonchernozem Zone after decades of neglect is considered a landmark decision in the history of Soviet agriculture. If successfully carried out, the Nonchernozem program might yield by the late 1980s a grain increment equivalent to the amount now being imported by the Soviet Union for its own needs and for re-export to its allies. The implementation of the Non-chernozem program would also have consequences for regional grain-production patterns in the Soviet Union. The Nonchernozem Zone would be in a position to make a more significant contribution to the demand for grain in the industrial centers of European Russia, thus easing the pressure on the virgin lands of northern Kazakhstan and reducing the need for the present long grain hauls. Finally, a greater shift of grain production into the humid Nonchernozem would be in keeping with a program of water economies since grain output in the humid zone requires less than half of the water needed for grain production in the arid zone. The success of the Nonchernozem program is conditioned on greater attention to the development of rural infrastructure, particularly roads, which the author considers a key element in upgrading the agriculture of the region.     

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.     

SPATIAL DEPENDENCE AND SPATIAL STRUCTURAL INSTABILITY IN APPLIED REGRESSION ANALYSIS*

The stability of regression coefficients over the observation set (“regional homogeneity”) is typically assessed by means of a Chow test or within a seemingly unrelated regression (SUR) framework. When spatial error autocorrelation is present in cross-sectional equations the traditional tests are no longer applicable. I evaluate this both in formal terms as well as empirically. I introduce a taxonomy of spatial effects in models for structural instability, and discuss its implication for testing. I compare the performance of traditional tests, robust approaches, maximum-likelihood procedures and pretest techniques by means of a series of simple Monte Carlo experiments.     

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