Duopoly prices under congested access*

Abstract. Consider two firms, at different locations, supplying a homogenous good at constant marginal production cost. Consumers incur travel costs to the firm for each unit purchased, and the travel costs increase with the amount of travel to each firm (congestion). When all traffic and all congestion are generated by travel to a duopolist, both the Nash–Bertrand equilibrium prices and the Nash–Cournot equilibrium prices exceed the sum of the marginal production cost and the marginal external travel cost. However, when the road is shared by travelers to the duopolists' facilities and travelers in competitive markets, the Nash–Bertrand duopoly price equals the competitive price and the Nash–Cournot price contains a markup.     

UNCERTAIN INCOME AND HOUSING PRICE AND LOCATION CHOICE*

ABSTRACT. In this paper, we adapt recent developments in uncertainty modeling to the location choice paradigm. In particular, we analyze the impact of income and housing price uncertainty on housing demand and location demand characteristics in a partial equilibrium framework. We begin by recognizing that housing consumption cannot readily be altered in response to changes in income and price. We find that income and house price risk affect housing and location demands in different ways. Additionally, the spatial characteristics of price risk also affect consumer housing and location demands. For example, if housing price risk is lower farther from the central city, housing demand can be greater in those locations even with the higher transportation cost. Thus, over some locations, the expected price gradient could be positive.     

SPATIAL EQUILIBRIUM WITH FOOTLOOSE FIRMS*

ABSTRACT. We determine the location equilibria in a duopoly model under a novel solution concept. Typically, spatial equilibrium is described as either a simultaneous price and location game, or else as a two-stage location-then-price game. We introduce a new alternative, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the two standard solution concepts when products are homogeneous. We show this is also true for the new concept. We then provide numerical results for a specific functional form (the logit model) which introduces product heterogeneity into the standard framework, restoring equilibrium when the degree of substitutability between products is not too small.     

HOTELLING'S “MAIN STREET” WITH MORE THAN TWO COMPETITORS*

ABSTRACT. I analyze oligopolistic competition among three or more firms located on Hotelling's (1929) Main Street and show that in contrast with Hotelling's duopoly, the symmetric locational structure supports a noncooperative equilibrium in prices. However, in a two-stage game of location choice in the first stage, and price choice in the second stage, there exists no subgame-perfect equilibrium where the whole market is served. This is because, starting from any locational pattern, firms have incentives to move toward the central firm. This strong version of the Principle of Minimum Differentiation destroys the possibility of a locational equilibrium. The results are a direct consequence of the existence of boundaries in the space of location. The sharp difference between these results and those of the standard circular model (whose product space lacks boundaries) shows that the general use of the circular model as an approximation to the line interval model may be unwarranted.     

DRS. MUTH AND MILLS MEET DR. TIEBOUT: INTEGRATING LOCATION‐SPECIFIC AMENITIES INTO MULTI‐COMMUNITY EQUILIBRIUM MODELS*

ABSTRACT We consider the problem of integrating spatial amenities into locational equilibrium models with multiple jurisdictions. We provide sufficient conditions under which models that assume a single housing price in each community continue to apply in the presence of location‐specific amenities that vary both within and across communities. If these conditions are satisfied, the models, estimation methods, and results in Epple and Sieg (1999) are valid in the presence of (potentially unobserved) location‐specific amenities. We also show how to construct sufficient statistics that capture location specific spatial heterogeneity. We apply these techniques using data from the Pittsburgh metropolitan area. We find that these amenity measures capture proximity to important local employment centers as well as heterogeneity in school quality within a given school district.     

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.     

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.     

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.     

The Location Invariance Theorem in Weberian Space Under Uncertainty

This paper examines the validity of the location invariance theorem in Weberian space under various types of uncertainty. The main results are: Given that the firm's location is constrained to remain at a specified distance from the output market, the optimal location is invariant to any change in product demand if and only if the production function is homothetic for a firm facing demand price uncertainty, or if the production function is homothetic and both inputs are risk-neutral for a firm facing technological uncertainty. Alternatively, given that the distance from the firm's location to the output market is a variable, location invariance occurs for a firm facing demand price uncertainty if the production function is linear homogeneous. In the presence of input price uncertainty the optimal location always varies with a change in product demand. The results can include those previously obtained for linear stochastic location models as special cases and some are new contributions to the literature.     

构建汽车产业区位竞争优势——以长春市为例

区位建立竞争优势才能主动迎接经济全球化的挑战,由此,本文提出"区位竞争优势"这一概念。中国正处于工业社会向知识经济社会的转型过程中,制造业所需的区位竞争优势内容具有两种社会的交叉特点,极富代表性。本文选取受跨国公司影响巨大的汽车产业为分析对象,将区位竞争优势的内容分析落实到具体的产业;并以长春市为例,对条件并非最好的区位提出构建区位竞争优势的思路。     

AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

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.     

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.     

南京市住宅价格时空分异格局及其影响因素分析——基于地理加权回归模型的实证研究

以2009-2017年南京市“一主三副”商品房社区为基本研究单元,运用GIS地统计分析中的普通Kriging插值法对“一主三副”住宅价格空间分布进行模拟和估计,并利用地理加权回归（GWR）模型探究社区属性、商业区位、交通区位、服务区位和景观区位等类型变量对住宅价格的影响规律。研究结果表明：①南京市房价总体上呈现主城向副城递减的中心外围模式,“一主三副”住宅价格空间结构呈现出同心圆和扇形融合的混合模型。②中心位势对主城住宅价格影响相对下降,对副城影响相对提升,交通位势表现出相反的趋势,住宅房龄、绿化环境对住宅价格的影响由主城向副城递减,山水景观的影响由长江沿岸向外围递减。③主副城住宅价格影响因素具有空间异质性,其中主城受距CBD距离、住宅建筑年代和绿化率的影响较大,而副城主要受距地铁站距离、距景观资源距离的影响。     

我国西部城镇土地定级估价的特点——以西宁市为例

土地定级与估价是城市地产评估的两个方面,都是对城市土地利用适宜性和土地价格的评定,是以城市土地区位和土地使用效益的集聚程度及空间分布规律为依据。在城市土地定级估价研究中,根据城市特点选定不同的方法和因素及指标体系,对不同类型和特点的城镇,其因素的重要性和区位差异性有着较大的差别。因此在定级估价中,首先要针对城镇的特点进行分析,从而确定其方法路线和有关因素指标体系,才能得到客观理想的评估结果。本文以西宁市土地定级估价为例,对我国西部城镇土地定级估价特点和方法进行了分析。     

THE SCOPE FOR PURE PROFITS IN A STANDARD LOCATION MODEL*

ABSTRACT. This paper examines the possibility of sustaining a collusive equilibrium in a standard location model. Drawing on recent developments in game theory, it is suggested that collusion is only feasible if market areas lie within a certain range. When market areas are large the threat of entry is likely to undermine any collusive agreement. In contrast when market areas are small, defection from the cartel is shown to be profitable. Thus collusion is shown to be feasible only when market areas and demand lie within certain bounds. More generally, this result appears to be consistent with the somewhat ambiguous empirical evidence which suggests that competitive pricing behavior is likely to prevail in periods of excessively high demand and during recessions.     

Mode Choice,Commuting Cost,and Urban Household Behavior*

Abstract. In this paper, we extend the partial equilibrium urban model of DeSalvo (1985) to include mode choice. DeSalvo demonstrated that the urban model of Muth (1969) was robust to the extension to leisure choice. We show that the model is robust to mode choice as well. In addition, we derive the comparative static results that commuters choose higher speed modes for longer commutes, at higher wage rates, with greater tastes for housing, and with lower housing prices. Also, for a given distance commuted, we derive the comparative static result that commuters chose shorter duration commutes at higher wage rates. Whereas it is typically assumed that marginal commuting cost is positive and non‐increasing with distance, we derive these results. Moreover, we derive the results that marginal commuting cost rises with an exogenous increase in housing price and falls with increased tastes for housing. We also explore the effects of exogenous commuting‐cost changes on the endogenous variables of the model. The remaining comparative static results on housing consumption and location are qualitatively the same as in DeSalvo.     

SENSITIVITY ANALYSIS FOR GENERAL SPATIAL PRICE EQUILIBRIA

ABSTRACT. General spatial price equilibrium models are formulated as variational inequalities. Sensitivity analysis results recently developed for variational inequalities are reviewed which give conditions for existence and equations for calculating the derivatives of solution variables with respect to perturbation parameters. These results are applied to the variational inequality formulations of general spatial price equilibria, and derivatives of supplies, demands, flows, and prices with respect to perturbations of supply functions, demand functions, and transportation-cost functions are calculated.     

城镇地价水平的相关分析——以石家庄市为例

城镇土地存在着级差收益,土地价格受多种因素的影响。本文以地租地价理论为依据,分析了石家庄市辖县地价水平与城镇区位、社会经济发展水平的相关关系,初步探讨了城镇地价水平的一般分布规律。     

THE EFFECT OF RETAIL FIRM OWNERSHIP ON PRICE EQUILIBRIUM*

ABSTRACT. This paper examines the effect of retail firm ownership on price equilibrium using a simple linear-city model. It is shown that price divergence emerges due to the differences in retail firm ownership, because retail firms under different ownership internalize shopping externalities differently. It is also shown that if a commercial center has two specialized retail firms, these stores charge the same markup for different goods at the equilibrium.