STACKELBERG GAMES ON A NETWORK WITH COURNOT-NASH OLIGOPOLISTIC COMPETITORS

ABSTRACT. We formulate the spatial Stackelberg-Nash-Cournot competitive network equilibrium problem as a variational inequality constrained mathematical program. Our model differs from previous models of Stackelberg oligopolistic competition in that it employs explicit shipping decision variables and a general network topology. That is, the production and distribution decisions of the Stackelberg firm are determined simultaneously over a discrete network. We explore the existence of solutions to the proposed model, and we also numerically test a sensitivity analysis based algorithm. In particular, we illustrate how sensitivity analysis results can be used to generate the Cournot reaction necessary to solve the Stackelberg problem.     

COMPUTATIONAL COMPARISONS OF SPATIAL PRICE EQUILIBRIUM METHODS*

ABSTRACT. In this paper we propose new algorithms for the solution of both general and standard spatial price equilibrium problems, and test their performance with existing algorithms on randomly generated problems. For the standard problem, we propose decomposition schemes based on the concept of “equilibration operator” and compare their performance with the Frank-Wolfe method. For the general problem, we present alternative variational inequality formulations defined over Cartesian products of sets and then exploit these formulations to construct Gauss-Seidel-type serial decomposition methods. We then compare their performance with the projection method. Our computational tests suggest that the new schemes are substantially more efficient than earlier ones.     

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.     

THE LAW OF ONE PRICE IN A NETWORK: ARBITRAGE AND PRICE DYNAMICS IN NATURAL GAS CITY GATE MARKETS*

ABSTRACT. In this paper we develop a model of the law of one price in a network where many markets are linked with a structure of paths. We show that arbitrage-free prices depend on the structure of the network and so do price dynamics. Our estimates indicate that local bypass and open access pipeline transportation were instrumental in opening arbitrage paths to natural gas city markets and causing their prices to converge. Spot markets in the city gates, pipeline hubs, and production fields, that are scattered over distant points in the vast pipeline network in the United States, now form a single market.     

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.     

教育资源配置对住房价格影响的时空差异研究——以35个大中城市为例

本文以2002-2017年35个大中城市为数据基础,借鉴Rosen-Roback城市空间均衡模型,测度大中城市教育资源对住房价格的影响差异性。研究发现：①控制其他变量后,教育事业费支出水平每提高1%,住房价格水平平均上涨0.156个百分点;②空间维度上,沿海城市的教育资源对住房价格的影响,显著小于内陆城市;而政治级别的差异在大中城市间的影响较小;③时间维度来看,教育资源对住房价格的影响在各时期都是显著存在的,表明教育资源的影响具有长期累积特征;从影响程度绝对值来看,影响系数具有随时间递减的特征。     

SPATIAL DISEQUILIBRIUM

ABSTRACT. The well-known extremal principle for the solution of spatial equilibrium for a single commodity [Samuelson (1952)] is extended to deal with the case of disequilibrium caused by rigid prices and/or price controls. Both disequilibrium in consumer markets and in factor markets is covered.
The study of disequilibrium is well known in general interdependent economic systems (the so-called fixed-price model of interdependent systems). The present work extends this approach to the spatial dimension, and shows how it is possible to represent and solve disequilibrium models by mathematical programming rather than by fixed-point techniques.     

THE CORE OF A SPATIAL PRICE EQUILIBRIUM GAME*

ABSTRACT This paper presents a critical appraisal of the use of the core as a solution concept for games involving spatially separated producers. Starting from the classical Samuelson/Takayama-Judge spatial price equilibrium model, the core of a game between the producers of commodities in this economy is defined, the conditions ensuring the nonemptiness of the core are stated, and the problems surrounding the definition and computation of the characteristic function are addressed. An application to the eastern United States’coal market is then presented in order to illustrate the usefulness of the theoretical and algorithmic results of this paper.     

城市规划视角下西安市主城区住宅空间结构演变研究

近年来,住宅市场的空间分异逐渐受到学界关注。本文以西安市主城区为研究区域,以2003年至2009年区内住宅资料为基础数据,分析了西安市主城区住宅空间结构的动态演变规律,并从城市规划视角对住宅空间结构演变机制做以探究。结果认为:西安市主城区内住宅空间结构呈现出数量上向轴线和板块集聚、价格上向多核均衡演变的趋势。住宅空间结构的演变受城市规划的空间战略、产业布局、交通建设和设施配套等影响较大。科学的城市规划能够引导住宅结构逐步优化,使之从单一极化结构向多极多层次的网络化均衡结构演变。     

南京市对外交通节点与酒店之间游客流动空间特征分析

利用旅游攻略数据,构建关系网络,探讨南京市对外交通节点与酒店之间游客流动这一特殊旅游流的空间特征,研究表明:1在节点方面,酒店的流入度、流出度和中心度均呈现出较为明显的圈层结构,高数值区域分布在城市中心的南北两端,外围区域数值较低,游客选择的酒店集中于夫子庙街道、健康路街道、梅园新村街道、玄武门街道;对外交通节点中,南京火车站中心度最高,铁路在南京旅游对外交通中作用突出。2在网络方面,随着流量阀值增加,整个网络的连通性不断增强,且流量分布更加均衡;核心对外交通节点与酒店集中分布街道在整个网络中起着重要的支配作用。3游客选择酒店并非集聚在对外交通节点周边,距离在酒店选择中所起作用不强,而与景点空间分布存在较强相关性。     

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.     

The Expected Maximum Distance Objective in Facility Location

Abstract In this paper we introduce a new objective function for the minimax location problem. Every demand point generates demand for service with a given probability (during a given period of time) and the objective is to minimize the expected maximum distance. The planar problem is proven to be convex and thus standard solution techniques such as using the Solver in Excel can be applied for its solution. Properties for the problem on the network are proven and an efficient algorithm proposed for its solution.     

WHERE IS THE ECONOMICS IN SPATIAL ECONOMETRICS?*

ABSTRACT Spatial econometrics has been criticized by some economists because some model specifications have been driven by data‐analytic considerations rather than having a firm foundation in economic theory. In particular, this applies to the so‐called W matrix, which is integral to the structure of endogenous and exogenous spatial lags, and to spatial error processes, and which are almost the sine qua non of spatial econometrics. Moreover, it has been suggested that the significance of a spatially lagged dependent variable involving W may be misleading, since it may be simply picking up the effects of omitted spatially dependent variables, incorrectly suggesting the existence of a spillover mechanism. In this paper, we review the theoretical and empirical rationale for network dependence and spatial externalities as embodied in spatially lagged variables, arguing that failing to acknowledge their presence at least leads to biased inference, can be a cause of inconsistent estimation, and leads to an incorrect understanding of true causal processes.     

SPATIAL MONOPSONY AND MONOPOLY PRICING IN A STOCHASTIC ENVIRONMENT*

ABSTRACT. In this paper some of the important properties of the behavior of a spatial monopsonist (monopolist) facing a stochastic supply (demand) curve are derived. Under uncertainty, price setting and quantity setting behavior are no longer equivalent. Hence, spatial price discrimination has to be compared with spatial quantity discrimination with respect to expected profits. I prove three general theorems on how the ranking of the behavioral modes, in terms of expected profit, depends on how the stochastic component enters the supply (demand) and supply (demand) price functions. In particular, I prove that under monopsony one would expect a high probability of excess demand, in the sense that the firm would accept all deliveries at the preset price.     

沈阳市住房价格空间分异格局及其影响因素研究

本文以我国典型的老工业城市沈阳为例来分析其住房价格空间分异特征与影响机理。通过大数据方法获取该市1450个住宅小区的房价及特征数据，利用Kriging空间插值法模拟其房价空间分布格局，并从社区、公共配套设施和交通出行等方面构建地理加权回归模型，探究各因子对房价空间分布的影响机理。结果表明：①沈阳市住房价格呈现出多中心的空间结构，且长白区域已成为新的价格峰值区。②特征因素对住房价格的影响具有显著的空间异质性，其中，公共配套设施和地铁站对房价表现出较高的影响力，并对住房价格的作用程度呈现明显空间差异性。③受“强政府、弱市场”等的长期影响，政府调控下的城市资源分配不均衡成为沈阳等老工业城市住房价格空间分异的根本原因。     

Spatial equilibrium in deviations: An application to skill‐premium and skill‐mix heterogeneity

In this paper, we propose a novel—and general‐purpose—modeling approach. We give a linear representation of the spatial general equilibrium, expressed in terms of local percentage deviations from the benchmark case of symmetry, where all the areas in the economy are taken to be initially identical. To illustrate the flexibility of our approach, we revisit the literature on the spatial heterogeneity of local skill premia and local skill mix. We show that our approach is able to encompass a variety of alternative explanations in a simple “unifying framework.” Finally, we exploit a graphical version of the model to show how to implement empirical tests.     

GRAVITY AND SPATIAL STRUCTURE: THE CASE OF INTERSTATE MIGRATION IN MEXICO*

ABSTRACT The estimation of gravity models of internal (aggregate) place‐to‐place migration is plagued with endogeneity (omitted‐variable) biases if the unobserved effects of spatial structure are not accounted for. To address this econometric problem, this paper presents a more general specification of the gravity model, which allows for (bilateral) parameter heterogeneity across individual migration paths—along with (unilateral) origin‐ and destination‐specific effects. The resultant “three‐way fixed‐effects” (3FE) model is applied for an analysis of interstate migration in Mexico based on cross‐sectional data. To overcome parameter‐dimensionality problems (due to limited or incomplete information), the 3FE model is estimated using the Generalized Maximum Entropy (GME) estimator. The empirical implications of this new modeling strategy are illustrated by contrasting the 3FE‐GME estimates with those for the traditional and two‐way fixed‐effects (2FE) models. The former are far more plausible and intuitively interpretable than their traditional and 2FE counterparts, with parameter estimates changing in expected directions. The (average) effect of the migrant stock is markedly smaller than usually estimated, providing a more realistic measure of network‐induced migration. Migration outflows from centrally located origins have significantly steeper distance decay. Path‐specific distance effects exhibit directional asymmetries and spatial similarities.     

基于GWR模型的合肥居住地价影响因素研究

以合肥市主城区为例,基于2010-2014年居住用地的出让数据,运用地统计法、GWR模型等方法,对合肥市居住地价的空间异质性及其影响因素进行研究。研究表明：①合肥市居住地价的空间分布呈现出显著的多中心的空间结构,地价的峰值区分别以老城区、政务区天鹅湖及滨湖新区塘西河公园为中心呈现圈层式分布;②不同的地价影响因素表现出不同的空间分布特征,其中容积率对居住地价的贡献度空间差异最大,其次是宗地面积,主干路次之,交通站点对居住地价的贡献度最小;③厘清各影响因素对地价的作用机制,建立动态的数字地价模型,不仅能促进土地资源的集约利用,重塑城市的空间结构,而且能为城市整体价值的发挥提供重要的理论支撑。     

THE REPRODUCTION OF GENDER RELATIONS OVER SPACE: A MODEL APPLIED TO THE CASE OF CHARTERED SURVEYORS

Chartered surveyors are one of the main groups of property professions in Britain involved in all aspects of land use and development: but only five percent are women. This paper discusses the dimensions of a conceptual model, expressed as a diagram, developed to demonstrate the role of surveyors in the reproduction over space of social relations: in this case the imprint of gender relations on the built environment through the development process. In seeking to trace empirically the transmission paths, it is concluded that one is dealing with a complex network of processes in which gender and class cannot be easily separated, but inter-react to produce the end product.     

THE FUTURE OF SPATIAL ECONOMETRICS*

ABSTRACT The purpose of this paper is threefold. First, we give an overview of the general direction the spatial econometrics literature has taken without attempting to provide a representative survey of all interesting work that has appeared. Second, we identify a number of problems in spatial econometrics that are as yet unresolved. Finally, we provide advocacy for the notion that new spatial econometric theory should be inspired by actual empirical applications as opposed to being directed by what appears to be the most obvious extension of what is currently available.