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.     

SPATIAL COMPETITION À LA COURNOT: PRICE DISCRIMINATION BY QUANTITY-SETTING OLIGOPOLISTS*

In this paper, we consider oligopolistic competition in a spatial model when firms take care of goods' delivery and discriminate among consumers. Firms compete by setting quantity schedules independently over space. We show that under general conditions a Nash equilibrium in this game exists and is unique. In equilibrium, firms’ markets overlap, a feature which accords with intuition and empirical observations. Over the interval between two firms, the equilibrium spatial price schedule is quasi-concave (quasi-convex) when transport costs are concave (convex). With linear transport costs, the model predicts uniform delivered pricing. Uniform pricing could moreover be obtained by a combination of increasing returns to volume in transportation together with concavity of unit transport costs in distance.     

EMPIRICAL ANALYSIS OF OFFICE RENT AND AGGLOMERATION ECONOMIES: A CASE STUDY OF TORONTO*

ABSTRACT. An equilibrium model of office location is applied and tested in the Toronto metropolitan area. The model focuses on the role of communication among firms which is the driving force behind the spatial agglomeration of office firms. The model calculates the equilibrium floor rent in each district, given the existing building stock. The performance of the model is tested in terms of the goodness of fit between observed and estimated office rent in each district. By using the model, we estimate the value of agglomeration economies which is defined as changes in productivities caused by increases in the number of office firms. It is shown that the agglomeration economies in the office sector are much larger than those in manufacturing, and the external effects of agglomeration are considerably large.     

SPATIAL PRICING IN INTERDEPENDENT MARHETS*

ABSTRACT. Conditions for spatial price equilibrium are derived for a set of firms in oligopolistic spatial competition, distributed at fixed locations in a heterogeneous region where consumer purchasing patterns are a probabilistic function of the price distribution rather than a deterministic function of proximity to firms. The resulting prices vary with accessibility to consumers or with the degree of local spatial monopoly, and result in non-zero profits for firms. Conditions describing the existence and stability properties of this spatial price equilibrium are defined, and are shown to be equivalent for two different hypotheses concerning disequilibrium pricing behavior: a partial price adjustment model and a Bertrand game. For two different profit goals, total profit maximization and profit rate maximization, it is shown that a spatial price equilibrium exists and is at least locally quasi-stable.     

A SPATIAL COMPETITION APPROACH TO CENTRAL PLACE THEORY: SOME BASIC PRINCIPLES*

ABSTRACT. This paper investigates the potential offered by the model of spatial competition for the study of central place theory. We consider n firms selling m substitutable or complementary goods to a continuum of consumers evenly distributed along a linear segment. Consumers have the same income and the same utility function which is quadratic in the goods supplied by the firms and linear in the numeraire. The main results are as follows. (1) In any location equilibrium in which all goods are consumed everywhere, each good supplied by a single firm is sold at the market center. In Christaller's terminology, this means that when the exhaustive principle holds in equilibrium, highest-order goods are made available at the center. (2) When all goods (excluding the numéraire) are complements to each other and each good is sold by a single firm, there always exists an equilibrium in which all the firms locate coincidentally. (3) If the stores selling a given good are under the control of a single owner then, in any equilibrium for which the exhaustive principle holds, the stores are located in a way such that the total transport cost (borne by consumers) is minimized.     

PRODUCT DIFFERENTIATION,PRICING POLICY AND EQUILIBRIUM*

ABSTRACT. This paper studies the price-location equilibrium of duopolists supplying differentiated goods and competing in a spatial market with elastic demand. We show that a price-location equilibrium exists under all three pricing policies traditionally considered by the literature: f.o.b. mill, uniform delivered, and spatially discriminatory pricing. We also show that firms always cluster at the market center. The second part of the paper studies the endogenous choice of pricing policy. A surprising feature of the resulting equilibrium is asymmetry. The greater the extent to which the goods are substitutes, the more likely is it that one firm will choose f.o.b. pricing and the other price discrimination. Finally, the welfare consequences of the analysis show some interesting trade-offs.     

POLLUTION MOBILITY,PRODUCTIVITY DISPARITY,AND THE SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS

This paper first develops a model to characterize the equilibrium distribution of polluting and nonpolluting firms and then turns to the larger question of whether the equilibrium distribution is socially optimal. We find that the equilibrium distribution of polluting firms differs from the social optimum when they generate a large amount of stationary pollution and have much higher or lower productivity than clean firms. In these cases, conventional pollution control approaches generally do not bring about an optimal distribution. Consideration of transport costs along with productivity and pollution changes some of the classic results of the new economic geography literature.     

Competition and Efficiency in a Spatial Setting

In this paper our primary concern is with a spatial model of competing firms in a regional industry. The firms are producing for an extraregional market and are located so as to gain exclusive access to a dispersed raw-material input. After outlining the form of the industry long-run average cost curve, we specify the equilibrium outcome, both for the individual firm and the regional industry. We demonstrate that the industry long-run supply curve does not coincide with the industry long-run average cost curve. We further show that the outcome in the spatial model results from the separation of firms, each firm having its own domain, part or all of which becomes its supply area.     

Price Variation in Spatial Oligopolies

The “geography of price” is being given renewed attention by geographers and economists. This paper examines spatial price variation in both unbounded (circular) and bounded (linear) one-dimensional markets. Firms compete for consumers in the short run by adjusting price until the Bertrand equilibrium is reached in the market. While firms act as spatial oligopolists in specific market segments, the profit-maximizing price of any given firm depends directly and indirectly upon the spatial-economic properties (locations, marginal costs) of all other firms in the market.     

LOCATION AND ENTREPRENEURSHIP: INSIGHTS FROM A SPATIALLY‐EXPLICIT OCCUPATIONAL CHOICE MODEL WITH AN APPLICATION TO CHILE

Occupational choice and heterogeneous managerial ability enter a spatial Dixit‐Stiglitz setting, linking location, wages and regional entrepreneurship rates. Market potential has a positive partial effect and wages a negative partial effect on the regional supply of entrepreneurs, both balancing in equilibrium with endogenous wages. Market potential increases profits, but also the opportunity cost of entrepreneurship. In the long‐run equilibrium with perfect mobility, the cut‐off level of ability determining selection into entrepreneurship will be the same across regions; moreover, regional differences in entrepreneurship rates depend only in differences in average fixed costs of firms. An empirical application is provided for Chile.     

上海大都市区物联网产业集聚与空间演化

新兴技术产业的空间集聚与扩散对大都市区的空间结构有直接的影响,厘清新兴技术产业的空间分布和区位选择规律对新兴产业集群培育和大都市区空间结构调整都具有重要的政策意义。本文分析了上海市物联网企业的空间分布和集聚特征,结果发现初创期物联网企业在郊区集聚,随后向郊区其他区域扩散,并呈现出从单极向多极集聚转变的空间演化进程。通过构建负二项回归探究上海物联网企业的区位选择因素,结果表明制度因素和企业集聚效应对企业区位选择有重要影响。在产业发展初创期,企业区位选择受政府管制和市场机制双重影响,其中制度因素发挥了关键作用;而在随后的兴起期,产业集聚效应对新企业的入驻具有强大的吸引力。     

MILL PRICING AND SPATIAL PRICE DISCRIMINATION MONOPOLY PERFORMANCE AND LOCATION WITH SPATIAL RETAIL MARKETS*

ABSTRACT. Most of the monopoly spatial price discrimination literature explicitly assumes uniform population density over space. It also implicitly assumes that firms (plants) are spatially isolated from each other with production and retail points that coincide in location. While departures from these assumptions have been explored separately in the literature, it remains to examine performance and location when these assumptions are relaxed simultaneously. What emerges in this paper is a model where density functions approximate a pair of cities isolated from other cities. Each city has its own retail market, while the location of a single production or wholesale point is determined by characteristics of the two markets. Comparisons of mill pricing and spatial price discrimination found in the spatial monopoly literature can be interpreted as special cases of the more general framework provided here.     

CAPITALIZATION OF LOCAL AND REGIONAL ATTRIBUTES INTO WAGES AND RENTS: DIFFERENCES ACROSS RESIDENTIAL,COMMERCIAL AND MIXED-USE COMMUNITIES*

ABSTRACT. The extent to which the value of locational attributes is capitalized into wages rather than rents is analyzed in a general equilibrium framework. This paper differs from earlier work by taking into account local and regional attributes and makes distinctions among residential, commercial, and mixed-use communities. The theory implies that in localities with both individuals and firms, wages and rents are simultaneously determined, while in exclusively residential localities the model is recursive. The major theoretical insights are consistent with estimations of the model using data from the University of Michigan's Panel Study of Income Dynamics.     

PREFERENCE HETEROGENEITY AND ECONOMIC GEOGRAPHY*

ABSTRACT We investigate the effect of preference heterogeneity between skilled and unskilled workers on agglomeration, and we identify a new source of dependence of equilibrium prices on the demand properties shaped by the inter‐regional distribution of workers. We find a new preference effect, and we show that when the intensity of skilled workers' preference for the modern good and its variety is strong enough, prices charged by firms may even increase when the mass of local firms increases, therefore acting as a new dispersion force when trade costs are low or as a new agglomeration force when trade costs are high.     

PRICE UNCERTAINTY AND PRODUCTION-LOCATION DECISIONS UNDER FREE ENTRY OLIGOPOLY*

ABSTRACT. This paper departs from earlier work on location theory under uncertainty by considering an oligopoly case where the symmetric Cournot-Nash equilibrium of imperfectly competitive and identical firms are examined. It will be shown that once a Cournot competitive equilibrium is introduced, the demand function plays a central role in the choice of location, and the effects of changes in fixed costs, mean product price and price variability on the firm's optimum location and output are independent of absolute and/or relative risk aversion. These striking results are in sharp contrast with the well-known results obtained in previous contributions to the location literature.     

Regional Competition for Mobile Oligopolistic Firms: Does Public Provision of Local Inputs Lead to Agglomeration?

We develop a model in which two regional governments compete for two mobile oligopolistic firms. Regional governments provide local infrastructure to attract mobile firms in order to increase regional employment and income. Firms face the trade-off between better regional infrastructure and fiercer competition for local workers. Strategic interaction prevails at the regional level as well as at the firm level. We show that an equilibrium with spatial concentration of firms as well as an equilibrium with spatial diversification of firms exists. In almost all cases regional competition leads to a suboptimal provision of local infrastructure.     

Cournot Retail Chains

In this paper a model of spatial Cournot competition among retail firms is devised and used to assess the effect of a variety of structural factors on retail prices and profits. The model illustrates the spatial chain of interaction that firms must anticipate to reach equilibrium when organized in chains or as independents. It shows the sensitivity of price to the location of stores, the number of stores per location, and transportation cost.     

THE SPATIAL STRUCTURE OF HIERARCHICAL INTER-URBAN SYSTEMS: EQUILIBRIUM AND OPTIMUM*

In this paper, I model a simple hierarchical inter-urban system in which the location of business firms is considered together with the determination of residential land-use patterns. By supposing a spatial externality between the business firms and all the residents of the region, three spatial structures are obtained: monocentricity, multicentricity, and a separate pattern where cities are spatially split with an agricultural land existing between them. It is also shown that the spatial structures of monocentric and multicentric patterns formed by the market principle tend to be more concentrated than the optimum.     

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.     

Evaluating the geographic concentration of industries using distance-based methods

We propose new methods for evaluating the spatial distributionof firms. To assess whether firms are concentrated or dispersed,economists have tradi-tionally used indices that analyse theheterogeneity of a spatial structure at a single geographiclevel. We introduce distance-based methods, Besag's L function(derived from Ripley's K function) and Diggle and Chetwynd'sD function to describe simultaneously spatial distribution atdifferent geographical scales. Our empirical applications considerthe distribution of French manufacturing firms in the Parisarea and in France generally. For some geographic levels, resultsshow significant concentration or dispersion of firms accordingto their sector of activity.