Nonminimal product differentiation as a bargaining outcome

It is well known that in a duopoly model of product choice with quadratic transportation cost, the firms locate at the extreme endpoints of the market. Jehiel (1992, Int. J. Ind. Organ, 10, 633–641) has examined this model in an infinite horizon setting where in the initial period the firms choose location and in subsequent periods charge the Nash bargaining solution prices. Then, in the unique equilibrium both firms locate at the center of the market. This paper examines the case when the firms instead charge the prices determined by either the egalitarian bargaining solution or the Kalai–Smorodinski bargaining solution. It is shown that central agglomeration is an equilibrium. Furthermore, there is a continuum of symmetric equilibria in addition where the firms locate apart from each other. So the products are not necessarily minimally differentiated. Thus different bargaining solutions provide quite different outcomes.     

An Unequal Spatial Structure of Location and Price with Consumer Density*

This paper incorporates the interdependent relationship of firms and the increasing consumer density into a framework of spatial equilibrium analysis, and studies the location of firms and the price system on a plane market. As consumer density increases, symmetric equilibrium is established initially for the first- and the second-round entry of firms, but this equilibrium becomes unequal later for the third and the fourth rounds. This fact means that in spatial equilibrium, even if all firms sell identical goods on a plane market, mill prices and market area sizes will differ.     

Tax Effects in a Model of Product Differentiation: A Note

We investigate how unit (or specific) tax and ad valorem tax affect equilibrium location choice in a model of product differentiation, which includes Hotelling (linear-city) and Vickrey-Salop (circular-city) spatial models as special cases. We find that neither tax affects equilibrium location patterns as long as each firm has the same production cost. Two taxes can yield different location patterns under cost heterogeneity among firms.     

Preemptive entry in differentiated product markets

Summary. Models of spatial competition are typically static, and exhibit multiple free-entry equilibria. Incumbent firms can earn rents in equilibrium because any potential entrant expects a significantly lower market share (since it must fit into a niche between incumbent firms) along with fiercer price competition. Previous research has usually concentrated on the zero-profit equilibrium, at which there is normally excessive entry, and so an entry tax would improve the allocation of resources. At the other extreme, the equilibrium with the greatest rent per firm normally entails insufficient entry, so an entry subsidy should be prescribed. A model of sequential firm entry (with an exogenous order of moves) resolves the multiplicity problem but raises a new difficulty: firms that enter earlier can expect higher spatial rents, and so firms prefer to be earlier in the entry order. This tension disappears when firms can compete for entry positions. We therefore suppose that firms can commit capital early to the market in order to lay claim to a particular location. This temporal competition dissipates spatial rents in equilibrium and justifies the sequential move structure. However, the policy implications are quite different once time is introduced. An atemporal analysis of the sequential entry process would prescribe an entry subsidy, but once proper account is taken of the entry dynamics, a tax may be preferable. Received: April 26, 1999; revised version: September 22, 1999     

Spatial price discrimination in the unidirectional Hotelling model with elastic demand

The unidirectional Hotelling model is extended to allow for elastic demand functions. A two-stage Bertrand-type model and a two-stage Cournot-type model are considered. If firms choose location and then set prices, agglomeration never arises; instead, if firms choose location and then set quantities, agglomeration arises at one endpoint of the segment when the transportation costs are low enough. Instead, when the transportation costs are high enough, a dispersed equilibrium arises in Cournot. The equilibrium distance between the firms is lower in Cournot than in Bertrand. When the transportation costs are high (low) the Bertrand equilibrium is welfare superior (inferior) to the Cournot equilibrium.     

Consumer flexibility,data quality and location choice

We analyze firms’ location choices in a Hotelling model with two-dimensional consumer heterogeneity, along addresses and transport cost parameters (flexibility). Firms can price discriminate based on perfect data on consumer addresses and (possibly) imperfect data on consumer flexibility. We show that firms’ location choices depend on how strongly consumers differ in flexibility. Precisely, when consumers are relatively homogeneous, equilibrium locations are socially optimal regardless of the quality of customer flexibility data. However, when consumers are relatively differentiated, firms make socially optimal location choices only when customer flexibility data becomes perfect. These results are driven by the optimal strategy of a firm on its turf, monopolization or market-sharing, which in turn depends on consumer heterogeneity in flexibility. Our analysis is motivated by the availability of customer data, which allows firms to practice third-degree price discrimination based on both consumer characteristics relevant in spatial competition, addresses and transport cost parameters.     

COMPETITION‐ACCELERATING PUBLIC INVESTMENTS*

We investigate the effects of infrastructure investments that reduce transport costs. We use a spatial model of Salop (1979). It is well known that the number of firms is excessive at free‐entry equilibrium (excess entry theorem). We find that the optimal investment level exceeds the ex post cost‐minimising level because investments accelerate competition and reduce the number of entering firms; resulting in the improvement of welfare. We also show that, in cases where the excess‐entry theorem is true, the desirable policy is the one accelerating, rather than restricting, competition.     

Spatial Cournot competition in a circular city with more than two dispatches

This paper investigates spatial Cournot competition in a circular city, where the maximal service range of a vehicle is less than half of the perimeter, and a firm needs to initiate more than two dispatches to serve the whole market. We examine a multi‐stage game of location and transportation mode choices, and the subsequent quantity competition between duopoly firms. The findings reveal that non‐maximum dispersion is the unique location equilibrium when duopoly firms deliver products in different transportation modes or when the transportation mode decisions are made endogenously and the fixed cost of a transportation instrument is relatively high.     

Innovation and evolution as a dynamic game with rational behaviour

In the recent literature about the explanation of the behaviour of innovating firms there coexist two basically different approaches. To so calledneoclassical approach assumes maximising behaviour relating to an exogenously given innovation technology and theevolutionary approach postulates time constant routine decisions. Both explanations are supported by well known arguments. Nevertheless they seem to be completely separated in the literature. The evolutionary approach even defines itself by the separation of the neo-classical approach. In this paper the two methods or philosophies are linked in a simple duopolistic model. It will be shown, that the strategic maximising behaviour of innovating firms leads in a dynamic model to routine decisions as equilibrium strategies.     

TAX COMPETITION IN A SIMPLE MODEL WITH HETEROGENEOUS FIRMS: HOW LARGER MARKETS REDUCE PROFIT TAXES*

We set up a simple two‐country model of tax competition where firms with different productivity decide in which location to produce and sell output. In this model, a unique, asymmetric Nash equilibrium is shown to exist, provided that countries are sufficiently different with respect to their exogenous market size. Sorting of firms occurs in equilibrium, as the smaller country levies the lower tax rate and attracts the low‐cost firms. A simultaneous expansion of both markets that raises the profitability of firms intensifies tax competition and causes both countries to reduce their tax rates, despite higher corporate tax bases.     

Performance Pay and Adverse Selection*

It is well known in personnel economics that firms may improve the quality of their workforce by offering performance pay. We analyze an equilibrium model where worker productivity is private information and show that the firms’ gain from worker self‐selection may not be matched by a corresponding social gain. In particular, the equilibrium incentive contracts are excessively high‐powered, thereby inducing the more productive workers to exert too much effort and increasing agency costs stemming from the misallocation of effort.     

Cartel Stability in a Delivered Pricing Oligopoly

Using the spatial price discrimination framework, the relationship between the locations of firms and their ability to collude is investigated. Gupta and Venkatu (2002) show that in a duopoly model agglomeration at one point is the most stable location. We find that agglomeration stabilizes the cartel when there are three firms, too. When there are more than three firms, however, agglomeration of all firms is never the most stable location. With four firms, the following location pattern produces the most stable cartel: two firms at one point and the other two at the farthest point from the first two.     

The role of indifference in sequential models of spatial competition: An example

This note shows how indifference expands the set of subgame-perfect equilibria in an illustrative model of spatial competition. The model concerns sequential location for three firms on a unit segment, with consumers buying the good from the nearest firm. Indifference occurs because, when the third firm enters in-between the first two, it gets the same payoff independently of its particular location. The note ends with a discussion of a particular equilibrium outcome, the one where the indifferent player is allowed to use his indifference optimally, in order to influence other players' strategies.     

Trade and Location with Horizontal and Vertical Multi-region Firms

We analyse the effect on agglomeration tendencies of allowing multi-region firms in a standard trade and location model, the core–periphery (CP) model developed by Kurgman (1991). The introduction of horizontal multi-region firms mitigates the agglomeration effects found in the CP model by reducing the range of trade costs for which the core–periphery equilibrium occurs. The introduction of vertical multi-region firms that separate the location of headquarters and plants has two counteracting effects. While headquarters exhibit a strong tendency to concentrate, plants tend to spread out. The equilibrium is always asymmetric in spite of the underlying symmetry of the model.     

Forward looking dynamics in spatial CGE modelling

This paper sets up a spatial dynamic CGE framework by combining the optimal growth model of saving and investment under adjustment costs and the spatial CGE model with Dixit–Stiglitz structure in the modern sector. Because of increasing product diversity on the dynamic equilibrium path, the model belongs to the category of semi-endogenous growth models. We overcome the difficulty of existing multiregional models to correctly approximate the infinite horizon equilibrium by employing a theoretically consistent terminal condition. The distinction of goods, factors, firms, and households by location, and the incorporation of trade costs in the model allow to study a variety of issues in regional and transport economics. We describe the model calibration and a tailor-made solution algorithm. The functionality is demonstrated using two illustrative examples.     

A Noncooperative Analysis of Hotelling's Location Game

We study the location equilibrium in Hotelling's model of spatial competition. As d'Aspremontet al.have shown, with quadratic consumer transportation cost the two sellers will seek to move as far away from each other as possible. We show that the location game possesses an infinity of mixed strategy Nash equilibria. In these equilibria coordination failure invalidates the principle of “maximum differentiation” and firms may even locate at the same point.Journal of Economic LiteratureClassification Numbers: C72, D43, L11.     

跨国多期技术授权方式选择及社会福利分析--基于空间数量歧视竞争的框架

跨国技术授权作为企业获得竞争优势的重要途径已经受到理论界的关注。与以往的内部技术授权研究不同,文章构建了一个外国拥有技术的企业与东道国企业的空间数量歧视竞争模型,考察多期技术授权存在技术泄露、关税内生及空间竞争对外国拥有技术的企业的最优授权策略选择以及东道国社会福利的影响。研究表明：(1)外国拥有技术的企业偏好双重收费方式,且固定收费方式优于特许权收费方式;(2)双重收费方式不能同时实现拥有技术的企业和社会福利的最优,但可以实现社会福利的次优;(3)外国企业应该通过双重收费方式或固定收费方式进行技术授权,而东道国政府不应一味地提高关税水平,适当地降低进口关税有利于跨国技术授权的实现。文章的结论对于发展中国家的技术引进以及技术出口政策的制定具有一定的现实意义。     

企业异质性对制造业新建企业区位选择的影响

本文运用2005-2013年长三角制造业新建企业微观数据,结合离散选择模型,探究企业异质性对区位选择的影响,并分析了不同特征制造业企业的空间分布.研究从企业异质性的角度合理解释了中国新建制造业企业区位选择的影响机制.结果表明:不同特征的企业之间,区位因素的作用存在差异,企业异质性对区位选择的影响是多样的.随着企业员工数量的增加,新建制造业企业倾向于选择中等水平的城市,在竞争激烈的发达城市选址的可能性降低;国有所有制对企业的区位选择没有显著影响,而外商投资企业则倾向于选择较发达和外资制造业企业相对集中的城市;与外商投资企业相似,高技术企业也具有明显的集聚特征.     

欧美跨国公司在华离岸研发的空间区位战略比较研究*——基于城市层面集群网络的视角

本文基于研发子公司空间分布的城市集群网络特征,构建了跨国公司离岸研发“集群寻求型”战略框架,并采用离散选择模型对这一理论视角进行实证检验。样本包含了1992-2012年期间在华275家美国研发子公司和207家欧洲研发子公司跨越27个城市的区位战略。实证结果揭示了欧美在华离岸研发的差异化空间区位战略：美国公司采用“知识集群寻求型”战略,即一个城市的知识资源和技术基础设施是重要的区位因素;欧洲公司则采用“工业集群寻求型”战略,例如,一个城市的制造业基础、产业专业化以及公司内部的前向关联显著地影响其区位选择。此外,母国公司规模和欧洲公司母国的异质性的影响也得到证实。     

Optimism and firm formation

This paper analyses firm formation and innovation in an economy where agents differ with respect to their optimism in the face of ambiguity. Individuals choose between starting a firm or working in one; and also between employing a traditional technology or a new technology about which little is known. In the face of ambiguity, decision-makers are either optimistic or pessimistic. We study the innovation-proof equilibria of the economy: wages clear all labor markets when agents make optimal occupational choices, and no mutually beneficial opportunity for innovation remains unexploited. In equilibrium, optimists are more likely to form firms, but also more likely to be workers in firms using the ambiguous technology. This phenomenon sheds new light on the relationship between firm culture and technology. We find that three types of firms emerge in equilibrium: entrepreneurial firms, where both owners and workers are optimists operating a highly ambiguous technology; traditional firms, where an optimistic owner employs a pessimistic worker and uses a less ambiguous technology; and bureaucratic firms where both owners and workers are pessimists employing a well-known technology. We also suggest how the relative scarcity of the optimists may help to explain the commonly observed S-shaped diffusion profile for successful innovations.