Oligopolistic and competitive behavior of spatially separated markets

We examine the connection between Cournot oligopoly and perfect competition by showing that a fairly general oligopoly model with spatially separated markets generates a general spatial price equilibrium model as an extreme, limiting case. Our analysis depends crucially on the fact that the governing equilibrium conditions of both the oligopoly and the spatial price equilibrium problem can be formulated as variational inequalities.     

基于Multi-Agent技术的交通网络均衡模型

基于Multi-Agent技术,建立了一个交通网络均衡模拟模型。通过Agent的思想来描述网络中不同个体的行为决策,及其共同作用对整个网络产生的影响。模型结合经典均衡理论,为复杂的均衡点求解问题提供了直观、简洁的求解方式。     

SPATIAL PRICE EQUILIBRIUM AND THE TRANSPORT SECTOR: A TRADE‐CONSISTENT SCGE MODEL

In spatial computable general equilibrium models, interregional trade ought to play an important role in determining the spatial price equilibrium. Although the Armington assumption is commonly employed to describe cross‐hauling, many of the existing models do not explicitly consider the behavior of transport firms. This paper presents a framework that is compatible with the Armington assumption and explicitly considers transport activities. In the model, the trade coefficient takes the form of a potential function, and the equilibrium market price becomes similar to the price index in the context of new economic geography. The features of the model are investigated by using the minimal setting, which comprises two nontransport sectors and three regions. Because transport costs are given exogenously, the commodity prices are determined relative to them. The model can be described as a system of homogeneous equations, where an output in one region can arbitrarily be determined similarly as a price in the Walrasian equilibrium.     

Quality of Information and Oligopolistic Price Discrimination

Recent developments in information technology (IT) have resulted in the collection of a vast amount of customer-specific data. As IT advances, the quality of such information improves. We analyze a unifying spatial price discrimination model that encompasses the two most studied paradigms of two-group and perfect discrimination as special cases. Firms use the available information to classify the consumers into different groups. The number of identifiable consumer segments increases with the information quality. Among our findings (1) when the information quality is low, unilateral commitments not to price discriminate arise in equilibrium; (2) after a unique threshold of information precision such a commitment is a dominated strategy, and the game becomes a prisoners' dilemma; and (3) equilibrium profits exhibit a U-shaped relationship with the information quality.     

Stochastic Route Choice Equilibrium Assignment for Travelers with Heterogeneous Regret Aversions

Most route choice models assume that people are completely rational. Recently, regret theory has attracted researchers’ attentions because of its power to depict real travel behavior. This paper proposes a multiclass stochastic user equilibrium assignment model by using regret theory. All users are differentiated by their own regret aversion. The route travel disutility for users of each class is defined as a linear combination of the travel time and anticipated regret. The proposed model is formulated as a variational inequality problem and solved by using the self-regulated averaging method. The numerical results show that users’ regret aversion indeed influences their route choice behavior and that users with high regret aversion are more inclined to change route choice when the traffic congestion degree varies.     

Existence of equilibrium in a differential game of spatial competition with advertising

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.     

THE TRANSPORT SECTOR AND REGIONAL PRICE DIFFERENTIALS: A SPATIAL CGE MODEL FOR CHINESE PROVINCES

With regression formulas replaced by equilibrium conditions, a spatial CGE (Computable General Equilibrium) model can substantially reduce data requirements. Detailed regional analyses are thus possible in countries where only limited regional statistics are available. Alhough regional price differentials play important roles in multiregional settings, transport does not receive much attention in existing models. This paper formulates a spatial CGE model that explicitly considers the transport sector and FOB/CIF prices. After describing the model, the performance of our model is evaluated by comparing the benchmark equilibrium for China with a survey-based interregional I-O table for 1987. The structure of Chinese economies is summarized using information obtained from the benchmark equilibrium computation. This includes regional and sectoral production distributions and price differentials. The equilibrium for 1997 facilitates discussion of changes in regional economic structures that China has experienced in the decade.     

Existence of spatial cournot equilibria

Since the existence of equilibria in spatial price setting models is highly problematic, this paper suggests spatial Cournot competition to overcome the most severe existence problems. Sufficient conditions for existence are given for a general class of economic environments, and a linear model specification serves to illustrate the properties of a spatial Cournot-Nash equilibrium. Finally, the nature of the free entry equilibrium is discussed.     

具有价格干预的单产品流网络均衡

研究了由具有产能约束的多个相互竞争制造商以及面临随机需求和商品限制性价格上限的多个相互竞争零售商组成的供应链网络均衡问题。借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型。结合数值算例,分析了产能约束和限制性价格上限对网络均衡的影响。结果表明当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商和零售商的总利润减少;当存在产能限制时,将导致无价格限制的商品均衡价格更高以及消费市场中商品短缺量更大。     

No unbounded arbitrage,weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart’s securities exchange model. Journal of Economic Theory 41, 392–404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373–391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293–311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162]. In this note, we show that all these conditions are equivalent.     

The spatial price equilibrium problem with path variables

Most of the recent literature dealing with the solution of the spatial price equilibrium model has dealt with the arc variable formulation; that is, the situation where the flows on the paths connecting an origin-destination pair in a network with trans-shipment nodes are not explicitly considered. This paper presents a clarification of the main assumption underlying this arc formulation and presents an argument for the need for using a model with path variables in certain applications. After this discussion, a new solution algorithm for the model with path variables is stated and compared against the linear approximation algorithm first proposed by Florian and Los [1] for this problem. Numerical examples are presented which illustrate the features of this new algorithm.     

On the existence,uniqueness and stability of spatial equilibrium in an open city with externalities

This paper deals with the existence, uniqueness and stability of a spatial equilibrium in an open city with external diseconomies like air pollution generated by manufacturing activities. First, assuming that both production functions and utility functions are Cobb-Douglas, we prove the existence of a spatial equilibrium under some reasonable assumptions. It is shown, however, that the uniqueness and stability of the equilibrium may not be obtained, unless the degree of externality is sufficiently small. In fact, none of the equilibria will be stable for a certain set of speeds of adjustment in the labor market and the land market, if the degree of externality is relatively large. Finally, some implications of our results are derived in regard to the application of the hedonic price concept within the context of a spatial equilibrium model.     

Full or partial market coverage? A note on spatial competition with elastic demand

In this paper, a spatial model is used to endogenously determine product locations and prices when consumers have an elastic demand with a finite reservation price. I show under which condition a two‐stage Bertrand–Nash equilibrium yields maximal product differentiation with full market covering. Additionally, this paper highlights the effects of a change in the reservation price and in the utility loss rate on the equilibrium values of the model. The ambiguous effect of a change in the utility loss rate on prices constitutes a rather puzzling result. Copyright © 1999 John Wiley & Sons, Ltd.     

Spatial competition under uniform delivered pricing

A Hotelling-type model of spatial competition is considered, in which two firms compete in uniform delivered prices. First, it is shown that there exists no uniform delivered price–location equilibrium when the product sold by the firms is perfectly homogeneous andwhen consumers buy from the firm quoting the lower delivered price. Second, when the product is heterogeneous and when preferences are identically, independently Weibull-distributed with standard deviation μ, we prove that there exists a single uniform delivered price–location equilibrium iff μ≧1/8 times the transportation rate times the size of the market. In equilibrium, firms are located at the center of the market and charge the same uniform delivered price, which equals their average transportation cost, plus a mark-up of 2μ. Finally, we discuss how our result extends to the case of n firms and proceed to a comparison of equilibria under uniform mill and delivered pricing.     

Quality and Location Choices under Price Regulation

In a model of spatial competition, we analyze the equilibrium outcomes in markets where the product price is exogenous. Using an extended version of the Hotelling model, we assume that firms choose their locations and the quality of the product they supply. We derive the optimal price set by a welfarist regulator. If the regulator can commit to a price prior to the choice of locations, the optimal (second-best) price causes overinvestment in quality and an insufficient degree of horizontal differentiation (compared with the first-best solution) if the transportation cost of consumers is sufficiently high. Under partial commitment, where the regulator is not able to commit prior to location choices, the optimal price induces first-best quality, but horizontal differentiation is inefficiently high.     

Price and quantity competition among heterogeneous suppliers with two-part pricing: applications to clubs, local public goods, networks, and growth controls

Models of club goods, local public goods, and growth controls appear to have theoretical structures distinct from usual oligopoly models. This article shows, however, that they are special cases of a generalized oligopoly model that incorporates the possibility of two-part pricing and externalities between consumers (either congestion or network externalities). Our generalized two-part pricing model not only serves as a synthesis of a wide range of models but also allows us to obtain several new results on equilibrium prices. Another advantage of our model is that it can be interpreted as a reduced form of more complicated models that have spatial structures. This facilitates extension to the case where firms are heterogeneous and the number of firms is arbitrary.     

The implications of inflation in an estimated new Keynesian model

This paper studies the steady state and dynamic consequences of inflation in an estimated dynamic stochastic general equilibrium model of the U.S. economy. It is found that 10 percentage points of inflation entail a steady state welfare cost as high as 13% of annual consumption. This large cost is mainly driven by staggered price contracts and price indexation. The transition from high to low inflation inflicts a welfare loss equivalent to 0.53% of annual consumption. The role of nominal/real frictions as well as that of parameter uncertainty is also addressed.     

Precise computation of a competitive equilibrium of the discrete land market model

This paper provides a finite algorithm to compute a competitive equilibrium of the Alonso-type discrete land market model (known as bid-rent equilibrium) without assuming any condition on the spatial configuration such as monocentricity. The existence of the finite algorithm implies that the discrete land market model is sufficiently tractable for computer simulation analysis (sensitivity analysis) even if the spatial configuration is variable. Specifically, we can evaluate numerically the effects of new routes in a transportation network upon equilibrium rents and commuting mode.     

Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Lévy jumps

This paper presents an equilibrium formulation of asset pricing in an environment of mixed Poisson–Brownian information with recursive utility. The optimal portfolio choice problem is studied together with a derivation of Euler equation as necessary condition for optimality. It is further shown that the price processes governed by the Euler equation, together with the market clearing conditions, constitute the equilibrium price processes. Closed form formulas are derived for European call options and for other derivative securities in a particular parameterization of the economy. The derived option pricing formula contain many existing models as special cases, and is potentially useful in explaining the moneyness biasedness associated with Black–Scholes model.     

基于成本效益均衡的路网容量扩张问题

从交通供给的角度寻求解决城市路网供需矛盾问题。首先建立基于成本效益均衡的道路网络扩张模型,然后设计该模型的求解算法,最后给出了郑东新区路网容量扩张方案的应用实例。