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.     

An Empirical Analysis of Retailer Participation Decisions in a Downtown Parking Coupon Program

Parking coupon programs help downtown shopping areas attract consumers away from suburban shopping centers. Here we conduct an empirical analysis of retailer participation in such a program. Consistent with expectations, participation was higher for stores in shopping centers than for street-front retailers, for stores receiving subsidies for coupon purchase, and for stores selling comparison-shopping goods than for stores selling goods bought on one-stop, single-purpose or multipurpose-shopping trips. Participation also varied with numbers of competitors, chain membership, and store vintage. Apparently, participation is a local public good for downtown retailers and stores are inclined to free ride.     

Löschian Spatial Competition in an Emerging Retail Industry

Löschian competition is traditionally thought to lead to a spatial equilibrium in which firms enter an industry and disperse across geographic space until each firm earns insufficient excess profit to attract net new entrants. This paper assesses the appropriateness of Löschian analysis using video (movie) rental establishments in Toronto as a case example. The video rental business, as we know it today, began to take shape around 1980 and has since seen much turnover. The paper describes the changing pattern of single‐site and chain stores between 1982 and 1999. I use logistic regression to predict the survival of existing establishments. Using survivorship as a proxy for profit, the paper draws conclusions about the extent to which temporal changes in video store location correspond to the tenets of Löschian competition. The coexistence of chain and single‐site stores suggests that there are distinct market niches and that single‐site stores have used a “swarming” strategy to compete against chains. Conclusions are drawn about how the retail sector might evolve in the future because of the locational competition between chains and single‐site stores.     

PRODUCT DIFFERENTIATION,PRICING POLICY AND EQUILIBRIUM*

ABSTRACT. This paper studies the price-location equilibrium of duopolists supplying differentiated goods and competing in a spatial market with elastic demand. We show that a price-location equilibrium exists under all three pricing policies traditionally considered by the literature: f.o.b. mill, uniform delivered, and spatially discriminatory pricing. We also show that firms always cluster at the market center. The second part of the paper studies the endogenous choice of pricing policy. A surprising feature of the resulting equilibrium is asymmetry. The greater the extent to which the goods are substitutes, the more likely is it that one firm will choose f.o.b. pricing and the other price discrimination. Finally, the welfare consequences of the analysis show some interesting trade-offs.     

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.     

Competition in a Repeated Spatial Auction Market with an Application to Timber Sales

In this paper we develop a model of a repeated spatial auction market. The auction model contributes to the literature on spatial competition by considering the sale of goods in a market with spatial and temporal dimensions, and in which goods are sold by an auction institution instead of a posted-price institution. In the Nash equilibrium of the spatial auction model, each bidder is found to have a dominance solvable strategy to bid below his net (of transportation costs) valuation for the first unit of the good because there is an option value to not winning, namely that the following units may be locationally preferred to the first unit. The equilibrium bidding strategies lead to the possibility of non–Pareto-efficient outcomes. The auction model is applied to data from U.S. Forest Service timber sales.     

The Max-Min-Min Principle of Product Differentiation

We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importances on each product attribute; these are measured by weights on the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all such equilibria have maximal differentiation in one dimension only; in all other dimensions they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of these, or all three.     

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.     

ZONING A CROSS‐BORDER CITY

This paper investigates zoning in a cross‐border linear city that consists of two bordering towns. In each town, a local regulator has a say in the location of the local firm. We find that local regulators may use zoning strategically. The incentive to gain consumers from the other town, or not to lose local consumers, may push regulators to approve only locations for firms close enough to the frontier. When zoning is costly an asymmetric equilibrium may emerge: only one regulator resorts to zoning. In the case of towns of different sizes, the regulator of the larger town is the only one that zones in an asymmetric equilibrium.     

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.     

Location Equilibrium for Cournot Oligopoly in Spatially Separated Markets

Consider a two-stage non-cooperative Cournot game with location choice involving n≥ 2 firms each with several facilities. There are m≥ 2 spatially separated markets constituting the vertices of a network. Each firm first selects the locations of their facilities and then selects the quantities to supply to the markets to maximize its profit. There exists a Nash equilibrium in the quantities offered by each firm at the markets. Furthermore, when the demand in each market is sufficiently large, each firm chooses to locate its facilities only at vertices. With linear demand in each market, there exists a Nash location equilibrium.     

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.     

International activity in Antarctica 1955–56

Small farmers in the Crofting Counties receive relatively low prices for their store stock partly because most of them are bought by dealers. Dealers rather than farmers purchase the stores because they are marketed in small diverse lots and because many of them are sold at centres far removed from the main areas of demand. Suggested improvements in the marketing system include grouping stock prior to sale and selling them at large accessible markets rather than at small remote ones.     

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 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.     

The Importance of the Distribution of Consumers in Horizontal Product Differentiation

This paper examines the importance of the distribution of consumers in Hotelling's circle on the comparison between the optimal and the market equilibrium levels of diversity. It finds that when most consumers are located very close to the firms, the result of Salop—that the equilibrium number of firms is larger than the optimal one (surplus maximizing)—can be reversed.     

UNIVERSITY GEOGRAPHY INSTRUCTION WITHIN BUNTEP: A DREE PROGRAM IN NORTHERN MANITOBA

The BUNTEP programme has established itself as a successful innovator and purveyor of higher education to a hitherto neglected segment of the Canadian mosaic the isolated lndian reserves of northern Manitoba. BUNTEP comes at a time, however, when the reserves isolation from the outside world is breaking down. Combined with the stresses imposed by the post-war nuclear settlement policy of the government and the stresses of the population explosion, the formerly isolated bands are confronting challenges they are ill-equipped to meet. Television (which reached some reserves as recently as December 1977). the telephone, airplanes, motorboats, snowmobiles, and all the convenience goods sold at the local Hudson's Bay Company stores are steadily undermining whatever traditional culture is left. It is hoped that BUNTEP, and the successful graduates of BUNTEP, may provide these isolated communities with a means of coming to terms with the increasingly intrusive greater Canadian society.     

Multi-Firm City Versus Company Town: A Micro Foundation Model of Localization Economies

When do we have a company town and when do we have a multi‐firm city? In this paper I analyze the impact of public infrastructure investment decisions on types of cities in a decentralized urban system. This is done in a one‐sector spatial general equilibrium model of a closed economy. Investment in public infrastructures reduces the fixed set up cost of all firms within the city resulting in multi‐firm cities. Thus, in this approach localization economies are modelled explicitly instead of assuming that larger industrial size within the city enhances productivity. On the other hand, when the infrastructure is not provided, a company town will be formed by a developer because of the fixed cost required by each firm. The decision of whether to invest in the provision of public infrastructures depends on the type of city that will provide households with the highest utility. This paper characterizes the conditions that lead to each of the two equilibrium configurations.     

THE EFFECTS OF ZONING IN SPATIAL COMPETITION

ABSTRACT This paper considers a location model to illustrate the effect of zoning on competition. A planner is in charge of designing a city in a circular space where firms and consumers are located on different sides. With this type of market configuration, equilibrium in location under concave transport costs is proved. Then, a welfare function with different weights attached to consumer and firm surpluses is introduced to highlight zoning regulation as an influential competition policy tool. Depending on the regulator's political profiles and the demand, it is shown that zoning can lead to strong, weak, or moderate competition.     

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.