Competitive Location and Pricing on Networks

In this paper we consider a location and pricing model for a retail firm that wants to enter a spatial market where a competitor firm is already operating as a monopoly with several outlets. The entering firm seeks to determine the optimal uniform mill price and its servers' locations that maximize profits given the reaction in price of the competitor firm to its entrance. A tabu search procedure is presented to solve the model together with computational experience and an example.     

MARKET CAPTURE BY TWO COMPETITORS: THE PREEMPTIVE LOCATION PROBLEM*

ABSTRACT. We consider a location and allocation game for two competitor firms, A and B, that each seek to locate p facilities in a network. A market is captured by a particular firm if that market's closest facility belongs to that firm rather than a competitor. The question is as follows: Firm A wants to locate its p facilities so that B, which enters also with p facilities after Firm A has located its facilities, will capture the minimum market value possible. That is, Firm A wishes to preempt Firm B in its bid to capture market share to the maximum extent possible. A model is presented that addresses this issue, together with solution methods and computing times.     

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.     

Spatial Price Discrimination in Two-Dimensional Competitive Markets

Intuition suggests that firms that can apply price discrimination make higher profits than firms that are restricted in their pricing policy. In this paper, we show that, in general, this is not the case. In the framework of a two-dimensional spatial model with elastic demand à la Lösch, we further investigate the interplay of transport costs, competition, and price policy. One of our results is that under realistic specifications of parameters each firm gains a monopolistic area in the center of its market that has the same shape as the entire market, but with a convexly or concavely distorted separating line, depending on the extension of the market.     

Competitive Multifacility Location on Networks: the (r∣Xp)‐Medianoid Problem

Abstract.  We investigate the ( r ∣ X _p )‐medianoid problem for networks. This is a competitive location problem that consists of determining the locations of r facilities belonging to a firm in order to maximize its market share in a space where a competitor is already operating with p facilities. We consider six scenarios resulting from the combination of three customer choice rules (binary, partially binary, and proportional) with two types of services (essential and unessential).
Known discretization results about the existence of a solution for the set of nodes are extended. Some examples and computational experience using heuristic algorithms are presented.     

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.     

阿米巴经营与市场型企业

京瓷公司阿米巴经营取得了极大的成功,其原因在于构建了独特的组织形式与运行机制,即在阿米巴的组织基础上,通过核算机制引入了市场价格,再利用其独特的权威机制来克服企业部价格机制的不足。这样,使得企业的外部激励部化,低能激励高能化,从而提高了企业对市场的反应速度与企业的竞争力。我们称这种引入市场机制的企业为市场型企业,但我们也发现,随着企业的增大,企业部的价格机制就越难以发挥作用,故阿米巴经营也有它的局限性。     

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero-profit long-run equilibrium can occur in a space economy under conditions of increasing returns to scale.     

UNIFORM SPATIAL PRICING

ABSTRACT Uniform spatial pricing means that a firm delivers its product to any customer at a fixed price, independent of location. Economic theory explains the use of uniform pricing by the added profit generated by absorbing freight charges of distant customers. I extend this insight by demonstrating that when demand elasticity and transportation cost are positively enough correlated, uniform pricing generates higher profits than mill pricing. I show that this result can better explain observed patterns of price policy choice by mail order and web firms. A second result is application of this idea to firms with many shipping facilities.     

Marketing as Diffusion in a Single Population

The paper examines the optimal advertising policy for a profit-maximizing firm in a single market area. The results are first derived for a spaceless market, indicating the steady-state equilibrium advertising policy and market size. The model is then extended to account for the costs of overcoming distance. It is shown that there is an outward limit to marketing, and that this distance is dependent on the market price and retirement rate of the good and the interest rate. The minimal price necessary for covering any given distance is derived, along with the minimal advertising effort necessary to reach the steady-state market size. It is shown that the steady-state market size, advertising policy, and switching time are all monotonic functions of distance.     

ZONE PRICING*

ABSTRACT. Our purpose is to study a spatial price policy often encountered in the real world, known as zone pricing. This price policy consists in determining simultaneously several delivered prices together with the geographical zones in which they apply. It is shown that zone pricing approximates perfect spatial price discrimination and that the firm's profit increases with the number of zones. Furthermore, the number of markets supplied by the firm rises with the number of zones. Finally, zone pricing is compared to other standard spatial price policies and possible extensions are discussed.     

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.     

Hotelling Games with Three,Four, and More Players*

Abstract. This paper extends the interval Hotelling model with quadratic transport costs to the n‐player case. For a large set of locations including potential equilibrium configurations, we show for n > 2 that firms neither maximize differentiation—as in the duopoly model—nor minimize differentiation—as in the multi‐firm game with linear transport cost. Subgame perfect equilibria for games with up to nine players are characterized by a U‐shaped price structure and interior corner firm locations. Results are driven by an asymmetry between firms. Interior firms are weaker competitors than their rivals at the corners. Increasing the number of firms shifts even more power to the corner firms. As a result, there is too much differentiation from the social perspective if n ≤ 3, while adding firms leads to a level of differentiation in equilibrium below the social optimum.     

OPENNESS TO TRADE AND INDUSTRY COST DISPERSION: EVIDENCE FROM A PANEL OF ITALIAN FIRMS*

ABSTRACT We use Italian firm‐level data to investigate the impact of trade openness on the distribution of firms across marginal cost levels. In so doing, we implement a procedure that allows us to control not only for the standard transmission bias identified in firm‐level TFP regressions but also for the omitted price bias due to imperfect competition. We find that more open industries are characterized by a smaller dispersion of costs across active firms. Moreover, in those industries the average cost is also smaller.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

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.     

Competition and Efficiency in a Spatial Setting

In this paper our primary concern is with a spatial model of competing firms in a regional industry. The firms are producing for an extraregional market and are located so as to gain exclusive access to a dispersed raw-material input. After outlining the form of the industry long-run average cost curve, we specify the equilibrium outcome, both for the individual firm and the regional industry. We demonstrate that the industry long-run supply curve does not coincide with the industry long-run average cost curve. We further show that the outcome in the spatial model results from the separation of firms, each firm having its own domain, part or all of which becomes its supply area.     

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.     

Price Variation in Spatial Oligopolies

The “geography of price” is being given renewed attention by geographers and economists. This paper examines spatial price variation in both unbounded (circular) and bounded (linear) one-dimensional markets. Firms compete for consumers in the short run by adjusting price until the Bertrand equilibrium is reached in the market. While firms act as spatial oligopolists in specific market segments, the profit-maximizing price of any given firm depends directly and indirectly upon the spatial-economic properties (locations, marginal costs) of all other firms in the market.     

Surviving in a Competitive Spatial Market: The Threshold Capture Model

Many facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a firm that wishes to enter a spatial market where there are several competitors already located. This market is such that for each outlet there is a demand threshold level that has to be achieved in order to survive. The firm wishes to know where to locate its outlets so as to maximize its market share taking into account the threshold level. It may happen that due to this new entrance, some competitors will not be able to meet the threshold and therefore will disappear. A formulation is presented together with a heuristic solution method and computational experience.