Hotelling Games with Three,Four, and More Players*

Abstract. This paper extends the interval Hotelling model with quadratic transport costs to the n‐player case. For a large set of locations including potential equilibrium configurations, we show for n > 2 that firms neither maximize differentiation—as in the duopoly model—nor minimize differentiation—as in the multi‐firm game with linear transport cost. Subgame perfect equilibria for games with up to nine players are characterized by a U‐shaped price structure and interior corner firm locations. Results are driven by an asymmetry between firms. Interior firms are weaker competitors than their rivals at the corners. Increasing the number of firms shifts even more power to the corner firms. As a result, there is too much differentiation from the social perspective if n ≤ 3, while adding firms leads to a level of differentiation in equilibrium below the social optimum.     

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.     

FRAGMENTATION AND CLUSTERING IN VERTICALLY LINKED INDUSTRIES*

ABSTRACT This paper models the location of two vertically related firms in a low labor cost country and in a country with a large market. The upstream industry is more labor intensive than the downstream industry. We find that spatial fragmentation occurs for low values of the input‐output coefficient and intermediate values of the transport rate, particularly if the countries are very asymmetric in size. Otherwise, we obtain agglomeration either in the low cost country (when the transport rate is low) or in the large market (when the transport rate is high). Multiple agglomerated equilibria arise when the transport cost of the intermediate good is significant.     

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.     

Spatial Agglomeration of Manufacturing in Greece: Sectoral Patterns and Determinants

This article aims to demonstrate how the industry characteristics of manufacturing sectors affect the patterns of their spatial agglomeration. It also addresses several intricate issues concerning the measurement of localization economies and estimation of their main determinants in manufacturing industries. The original empirical analysis employs annual industrial data from the Hellenic Statistical Authority (ELSTAT) during the period 1993–2006 in Greece at the prefecture level, i.e. for 51 prefectures. The data processing reveals three important findings. The first is the temporal persistence of localization economies in the Greek manufacturing. The second refers to the high level of agglomeration associated with the high-technology industries as well as the resource- and scale-intensive industries. Lastly, there are significant effects of industry characteristics related to knowledge externalities, labour skills and productivity, scale economies and own-transport expenditure on spatial agglomeration, as resulted from the use of alternative geographic concentration indices and panel data models. Results obtained have implications for policy-makers, who can enhance the regional manufacturing activity by affecting these industry-specific factors. Amongst others, planning measures and policies which aim at promoting the local development and regional convergence should focus on reducing transport costs for firms or sectors, by improving the infrastructure capacity, interconnectivity and quality of services.     

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。     

EXTERNALITIES AND PARTIAL TAX REFORM: DOES IT MAKE SENSE TO TAX ROAD FREIGHT (BUT NOT PASSENGER) TRANSPORT?*

ABSTRACT Externalities such as pollution and road congestion are jointly produced by the use of intermediate inputs by firms and the consumption of final goods by households. To cope with such externalities, policy proposals often suggest partial tax reforms. This paper uses a simple general equilibrium model to explore the effects of a reform of taxes on freight transport in a second‐best setting. The theoretical model shows that the welfare effect of higher freight taxes is positive, unless passenger transport is severely under‐taxed and the tax reform attracts substantially more passenger transport. Moreover, the optimal freight tax may be below or above marginal external cost. Budgetary neutral tax reform exercises with a numerical simulation model for the U.K. suggest that, under a wide variety of parameter values, higher freight transport taxes are indeed welfare increasing. The welfare gain of freight tax reform rises with the level of the passenger tax, but the optimal freight tax declines at higher taxes on passenger transport. Substantial net benefits of tax reform are obtained only under labor tax recycling of the revenues.     

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.     

PRICING POLICY REACTIONS TO AGGLOMERATION IN A MARKET WITH SPATIAL SEARCH*

ABSTRACT. Price dispersion (variation) and agglomeration are common characteristics of spatial markets, in particular, markets with imperfect consumer information and search. However, pricing and location strategies in these markets are not well analyzed since spatial search is difficult to model without restricting the spatial dimension of the problem. This paper analyzes pricing and location strategies in a market with spatid search using a probabilistic modeling strategy that does not restrict search patterns in the plane. Specifically, the analysis considers the pricing strategy of an isolated firm in response to the agglomeration of competing firms. Results indicate that spatial and temporal price dispersion are effective responses to competitors'agglomeration. However, the relative effectiveness of these strategies varies with market conditions. In addition, agglomeration can have some counterintuitive effects. This paper also provides insights into existing theories of spatial search and spatial competition in spatially-restricted (linear and circular) markets.     

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.     

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.     

The Max-Min-Min Principle of Product Differentiation

We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importances on each product attribute; these are measured by weights on the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all such equilibria have maximal differentiation in one dimension only; in all other dimensions they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of these, or all three.     

Spatial Price Discrimination in Two-Dimensional Competitive Markets

Intuition suggests that firms that can apply price discrimination make higher profits than firms that are restricted in their pricing policy. In this paper, we show that, in general, this is not the case. In the framework of a two-dimensional spatial model with elastic demand à la Lösch, we further investigate the interplay of transport costs, competition, and price policy. One of our results is that under realistic specifications of parameters each firm gains a monopolistic area in the center of its market that has the same shape as the entire market, but with a convexly or concavely distorted separating line, depending on the extension of the market.     

LOCATING OUTSIDE A LINEAR CITY CAN BENEFIT CONSUMERS*

ABSTRACT We investigate the effects of restricting the locations of firms in Hotelling duopoly models. In standard location‐price models, the equilibrium distance between firms is too great from the viewpoint of consumer welfare. Thus, restricting the locations of firms and shortening the distance between them improves consumer welfare by reducing prices and transport costs. We introduce strategic reward contracts into location‐price models and find that, in contrast to the above result, restrictions on the locations of firms reduce consumer welfare. These restrictions reduce transport costs but increase prices by changing the strategic commitments of the firms.     

Spatial Organization of Fortune Global 500 Corporations in China: An Empirical Study of Multinationals from Japan,the United States,and European Union

Using data on investments in China from Fortune Global 500 multinational corporations (MNCs) based in Japan, the United States, and European Union over a three-decade period, the authors document the gradual expansion of MNCs in China both functionally and geographically. Statistical analysis suggests the existence of significant intra-firm clustering as a result of sequential investments, as well as country-of-origin agglomeration in the case of MNCs from Japan. Disaggregated analysis, however, reveals that functional and cross-functional mutual avoidance (e.g., intra- and inter-firm competition) in the location of MNC subsidiary firms tends to mitigate country-of-origin agglomeration effects. Journal of Economic Literature, Classification Numbers: D200, D800, G320, L200. 5 tables, 5 figures, 68 references.     

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.     

The Role of Leading Firms in the Evolution of SME Clusters: Evidence from the Leather Products Cluster in Florence

Clusters that emerged in the past have changed during the latest decades, so that today the research challenge in economic geography is on their evolution over time. The aim of this paper is to update the evolutionary path of SME Italian clusters, which faced the economic crisis are undergoing a process of decline in the number of firms. Furthermore, changes in the techno-economic landscape and in the competitive environment have generated new challenges. In this context, some leading firms, able to connect local resources (and firms) to global networks, have emerged over time and today they act as a gatekeeper. The focus will be on local networks interacting with leading firms and particular attention will be devoted to the pattern of co-evolution and to the geographical dimension of this co-evolutionary process. To empirically verify if other firms in the cluster may co-evolve with the leading firm over time, a deep analysis of the Gucci network in the leather products cluster in Florence will be carried out.     

中国电子机械制造业出口产品贸易网络研究——基于产品内分工与贸易视角

在区分中间/最终产品、一般/加工贸易后，描述了中国电子机械制造业出口产品贸易网络，并探讨了出口经验和产品关联如何影响企业进入网络从事出口和拓展优势贸易伙伴。结果表明：①出口地、目的国、出口地-目的国维度出口经验和产品关联可以显著地促进4种电子机械制造业产品企业进入特定贸易网络进行出口。②在位出口企业扩展优势伙伴方面，出口地-目的国维度出口经验对4种企业均有促进作用；目的国出口经验、出口地产品关联的促进作用集中在中间产品企业；出口地出口经验则集中在一般贸易企业。     

CAN REGIONALIZATION OF LOCAL PUBLIC SERVICES INCREASE A REGION'S WEALTH?*

ABSTRACT. In the presence of agglomeration and congestion externalities the sequence of location choices made by firms results in an inefficient distribution of economic activity, since individual firms do not bear the congestion costs they impose on other firms. In this paper, we model the interaction of public authority service strategies and firm location choices. We show that a self-interested regional authority can effect a welfare-improving distribution of economic activity when compared with an economy without an authority or an economy with local authorities. However, we also show that the conditions under which the authority would induce a welfare enhancing distribution depends on the authority's strategic posture, as well as the nature and size of public subsidies for the authority. The conditions necessary for a regional authority to choose an efficiency enhancing strategy may be difficult to achieve.     

COMPETITIVE LOCATION UNDER UNCERTAINTY OF COSTS

ABSTRACT. In this paper, we study the centroid problem from competitive location theory for a linear market with uniform demand, assuming that the leader has imperfect information about the follower's fixed and marginal costs. It is shown that the general version of this problem can be formulated as a nonlinear programming problem and the exact solution can be obtained analytically in a special case. A simple strategy is also given for the general problem, and it is proven that this strategy has a guaranteed error bound. It is demonstrated that uncertainty of costs might lead to market failure in the centroid problem, but this disappears if the game is repeated and the firms learn from observing each other's moves. It is also shown that it is possible for the leader to obtain optimal expected profit at a low perceived risk, with only sufficient, and not necessarily perfect, information. These two observations lead to our primary conclusion from the study that although cost uncertainty is a realistic feature of most competitive location models, there are very effective ways of dealing with it.