Urban agglomeration economies in a Linear City

A model of firms' spatial allocation and location is developed by explicit incorporation of urban agglomeration benefits using accessibility measure. In a linear and one-activity city, each firm is assumed to interact with each other for face-to-face transactions, and the unit construction cost of office building is considered to be proportional to firm density. It is shown that both the optimum and the equilibrium distributions of firms are cosine, quadratic or cosine-hyperbolic curves, that the latter is more dispersed, and that the equilibrium rent function is concave near the city center and convex near the boundaries.     

LOCATION OF VERTICALLY LINKED OLIGOPOLISTS

This paper examines the geographical equilibrium of location of N vertically linked firms and its relation to the creation of an industrial cluster. In a two-region spatial economy, a monopolist firm supplies an input to N consumer goods firms that compete in quantities. When the transport cost of the input increases, downstream firms prefer to agglomerate where the upstream firm is located, to save in production cost. However, simultaneous increases in the transport cost of the input and of the consumer good or increases in the number of downstream firms lead to a relative dispersion of these firms, to reduce competition and locate closer to the local final consumer. In contrast to Mayer (2000) , when both transport costs increase, the location decision of downstream firms is based more on the geographical point that maximizes accessibility to the local final consumer than on the geographical point that minimizes the production cost.     

Mixed oligopoly, foreign firms, and location choice

We investigate a mixed market in which a state-owned, welfare-maximizing public firm competes against n domestic private firms and m foreign private firms which are all profit-maximizing. A circular city model with quantity-setting competition is employed. We find that the equilibrium location pattern depends on m. All private firms agglomerate in the unique equilibrium if m is zero or one. Two foreign firms induce differentiation between domestic and foreign private firms. More than two foreign firms yield differentiation among the foreign firms. Regardless of n and m, agglomeration of all domestic private firms appears in equilibrium. We provide several conditions in which eliminating the public firm from the market enhances social welfare. We extend the basic model and investigate three issues concerning multiple public firms, inefficiency of the public firm, and entries by private firms. We obtain some additional implications of welfare and equilibrium locations.     

Multi-store competition: Market segmentation or interlacing?

This paper develops a model for multi-store competition between firms. Using the fact that different firms have different outlets and produce horizontally differentiated goods, we obtain a pure strategy equilibrium where firms choose a different location for each outlet and firms' locations are interlaced. The location decisions of multi-store firms are completely independent of each other. Firms choose locations that minimize transportation costs of consumers. Moreover, generically, the subgame perfect equilibrium is unique and when the firms have an equal number of outlets, prices are independent of the number of outlets.     

Spatial competition with free entry, Chamberlinian tangencies, and social efficiency

Free entry in Löschian spatial competition leads to a tangency between each firm's negatively sloped average revenue and the downsloping portion of average costs—as in Chamberlin's monopolistic competition. It is generally concluded that this equilibrium involves too many inefficiently small firms. However, this conclusion is incorrect. The difference between price and firm marginal production costs in spatial equilibrium is just sufficient to cover the additional marginal cost of output resulting from availability of multiple locations. This Chamberlinian tangency does not imply inefficiency, because it does not include all the social costs and benefits resulting from spatial competition.     

Communication technologies and spatial organization of multi-unit firms in metropolitan areas

Departing from traditional location theory (which treats a firm as a single-unit entity), in this paper we consider that each firm consists of multiple units that exchange information or services. Specifically, we develop a general equilibrium model of the city,in which each firm consists of a front-unit (e.g. business office) and back-unit (e.g. plant or back-office). Each front-unit interacts with all other front-units for the purpose of business communications, while each back-unit exchanges information or management services only with the front-unit of the same firm. Each firm must choose the location of its front-unit and back-unit optimally. The equilibrium spatial configuration of the city is determined as an outcome of interactions among all firms and households through competitive land and labor markets. We show that, depending on parameters, a variety of interesting patterns of metropolitan spatial organization emerges.     

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.     

Optimal zoning of managerial duopoly

This paper investigates optimal zoning of two managerial firms in an unconstrained linear city. Comparing with the case in which firms are not managerial type, the strategic delegation increases the incentives of one firm to locate farther from the rival. Then, a welfare function is introduced to highlight zoning regulation as an influential competition policy tool. Depending on the regulator's objective function and the timing of location choice, we provide a new mechanism that allows the regulator to attain the optimal locations of managerial firms and can lead to strong or weak competition.     

Mixed Duopoly with Subcontracting

Existing literature on mixed oligopoly focuses on competition among different types of firms but ignores their possible cooperation. We allow cooperation between a public firm and a private firm through subcontracting in a Hotelling mixed‐duopoly model. We find that when subcontracting is possible, the equilibrium without subcontracting is not socially optimal because subcontracting can lower total production costs. And if both firms engage in subcontracting, the existence of a public firm can guarantee the first best equilibrium, whether it is the low‐cost firm or not. But when a private firm is the low‐cost firm, it is more profitable for it to choose vertical foreclosure. And the consequent equilibrium is not socially desirable anymore. Copyright © 2014 John Wiley & Sons, Ltd.     

The role of debt and bankruptcy statutes in facilitating tacit collusion

Using a two‐period model this paper examines the quantity decisions of leveraged duopolists that are vulnerable to bankruptcy in the first period. When the firms have symmetric costs, a bankrupt firm reorganizes under Chapter 11. If a Chapter 11 firm experiences marginal cost relief, each firm produces a collusive output in period one in order to prevent its rival's financial demise. When the firms have asymmetric costs, the less efficient firm is liquidated under Chapter 7 upon bankruptcy. A predatory equilibrium exists, whereby the inefficient firm is driven from the market. Copyright © 1999 John Wiley & Sons, Ltd.     

Product choice with economies of scope

This paper develops a model in which two competing firms on a bounded line each sell two products. Production costs for each firm are lower the closer are its two products. It is shown that there may be anywhere from zero to three possible equilibrium configurations. Equilibrium may entail market segmentation, market interlacing or an intermediate case. The paper contributes to two bodies of literature: (i) Industrial organization. When the line is interpreted as a one-dimensional characteristic space, the model provides an appealing explanation of economies of scope in multi-product firms. (ii) Firm location theory. The model relaxes the unrealistic assumption made in spatial models that each firm has a single outlet and obtains significantly different results.     

Price and quality competition with quality positions

In this study, we investigate price and quality decisions in a duopoly in the presence of firms’ quality positions , which are determined by the quality levels of their existing core products. Into a standard model of vertical differentiation, we incorporate a “repositioning cost” that is proportional to the quality differences between firms’ current and new products. By varying the levels of quality positions, we analyze the impact of this cost on the equilibrium outcomes. Our results show that the presence of repositioning costs restricts firms’ abilities to improve profitability and differentiate themselves vertically. As a result, a high‐positioned firm does not necessarily have a competitive advantage over a low‐positioned firm, even if the former offers a superior new product in equilibrium. In addition, if a low‐positioned firm is significantly cost‐efficient compared with its rival with regard to repositioning, then that firm can earn higher profits than those of a high‐positioned firm by strategically offering its low‐end product. These results contrast sharply with those based on the standard vertical differentiation model.     

Allocating Ideas: Horizontal Competition in Tournaments

We develop a stylized model of horizontal and vertical competition in tournaments with two competing firms. The sponsor cares not only about the quality of the design but also about the design location. A priori not even the sponsor knows his preferred design location, which is only discovered once he has seen the actual proposals. We show that the more efficient firm is more likely to be conservative when choosing the design location. Also, to get some differentiation in design locations, the cost difference between contestants can be neither too small nor too big. Therefore, if the sponsor mainly cares about the design location, participation in the tournaments by the two lowest-cost contestants cannot be optimal for the sponsor.     

Nonlinear pricing in spatial oligopoly

A model of duopoly competition in nonlinear pricing when firms are imperfectly informed about consumer locations is analyzed. A continuum of consumers purchase a variable amount of a product from one of two firms located at the endpoints of the market. At the Nash equilibrium in quantity-outlay schedules, consumers buy the same quantities as they would from the same firm if it were a monopolist facing the same informational asymmetries, but they receive greater surplus. Hence, no efficiency gains result from competition. If consumers have the option to reveal their locations and have the firms deliver the goods, all consumers choose to reveal their locations in equilibrium. Thus, the inefficiencies from information asymmetries may not arise because firms can deliver the good to consumers. In contrast, with a monopoly seller, consumers have no incentives to reveal their locations.     

Investment in a New Technology as a Signal of Firm Value Under Regulatory Opportunism

We examine the question of whether a regulated firm that makes a long-term investment in infrastructure can credibly signal its private information regarding the future demand for its output to the capital market. We show that necessary conditions for a separating equilibrium in which the magnitude of investment signals high future demand may include a low degree of managerial myopia, large variability of future demand, a lenient regulatory climate, and low sunk cost. Our model suggests that in estimating valuation models of regulated firms it is important to separate firms into two groups: firms for which a separating equilibrium is likely to obtain and firms for which the equilibrium is likely to be pooling. The market value of a firm in the first group is positively correlated with its level of investment, but uncorrelated with the level of actual demand, whereas for the second group the opposite holds.     

The combined equilibrium of travel networks and residential location markets

The combined ‘user’ equilibrium of travel networks and residential location markets is shown to exist and to be unique in the expected allocation of households to residential locations and to the routes and links of the network, in the vacancies and rents of residential locations and in the congested travel time and cost of each network link. The formulation combines a multinomial logit model of households' location and route choices derived from utility maximization, a binary logit model of house owners' offer decisions derived from profit maximization and the standard model of network congestion. A travel disutility measure (consistent with utility maximization) replaces the standard ‘generalized cost function’. The proof utilizes a non-linear programming formulation which reproduces the simultaneous equilibrium conditions of the behavioral formulation. The stability of the unique equilibrium position is briefly discussed, a computational algorithm is proposed and hints for generalized formulations are provided.     

Vertical differentiation,product innovation,and dynamic competition

This paper presents an infinite horizon dynamic model in which two firms compete in a market vertically differentiated by the qualities of their products and consumers have heterogeneous preferences for quality. Given the product qualities offered, the firms engage in price competition that segments the market. In each period each firm can spend on product innovation that if successful increases the quality of its product. Three types of Markov perfect equilibria are identified. A running–coasting equilibrium exhibits increasing quality dominance with one firm undertaking innovation and the other coasting to free ride on the innovation by the first firm. The firm that coasts can have the larger dynamic payoff, so quality dominance does not imply payoff dominance. A second is a leap‐frog equilibrium in which the trailing firm undertakes innovation to leap into the lead. The trailing firm never innovates solely to narrow the gap with the leader, so catch up strategies are never used. In the third both firms undertake innovation, but if both have innovation successes, product differentiation remains the same and profits are reduced by the cost of innovation. The rivalry between Intel and AMD in microprocessors for personal computers provides a motivating example.     

Price Dispersion and Consumer Reservation Prices

We describe firm pricing when consumers follow simple reservation price rules. In stark contrast to other models in the literature, this approach yields price dispersion in pure strategies even when firms have the same marginal costs. At the equilibrium, lower price firms earn higher profits. The range of price dispersion increases with the number of firms: the highest price is the monopoly price, while the lowest price tends to marginal cost. The average transaction price remains substantially above marginal cost even with many firms. The equilibrium pricing pattern is the same when prices are chosen sequentially.     

Spatial Price Discrimination in the Spokes Model

The spokes model allows to address nonlocalized spatial competition between firms. In a spatial context, firms can price discriminate using location‐contingent pricing. Nonlocalized competition implies that neighboring effects are not relevant to firms. This paper analyzes spatial price discrimination and location choices in the spokes model. Highly asymmetric location patterns are one outcome if the number of firms is sufficiently high: in that case, one firm supplies a generally appealing product whereas others focus on a specific niche. Moreover, multiple equilibria arise for intermediate values of the number of firms. In this case, the location patterns do not always globally minimize the sum of transport costs: asymmetric configurations distribute more efficiently the cost between firms.     

Managerial overconfidence,overinvestment, and R&D spillover

This paper examines whether a firm will select an overoptimistic manager when a cost‐reduction investment has a spillover effect. We consider a Cournot competition model where R&D investment ex ante occurs before the process of product market competition. Our analysis reveals that there exists a unique and symmetric equilibrium for firms to delegate overoptimistic managers. We show that only when the spillover effect is sufficiently high do firms benefit from delegation. Furthermore, the equilibrium confidence level and investment decision first decrease and then increase as the spillover parameter changes. As the initial production cost increases, the equilibrium performance becomes worse.