hotelling's location model

d In 1929, Hotelling developed a location model that demonstrates the relationship between location and pricing behavior of firms. P . We assume that firms play a location-cum-price game, and that the game is played into two steps. This is also referred to as the principle of minimum differentiation as well as Hotelling's linear city model. {\displaystyle P\,} d On the other hand, consumers in location models display preference for both the utility gained from a particular brand’s characteristics as well as its geographic location; these two factors form an enhanced “product characteristic space”. when Henry moves to the 3000-foot mark. By election time, their positions on issues often seem close enough to many voters so that factors such as personality emerge as keys to the election. must "sell" to the same beach. google_color_text = "000000"; , trying to attract dollars from customers, consider two The CG model is an elaboration of Hotelling’s model. {\displaystyle u\,} is the location of the consumer. [2] Similar to the previous spatial representations, the circle model examines consumer preference with regards to geographic location. + We study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. increasing traveling costs, it seems that we can have Restaurants, on the other hand, seem to come in clusters. In 1964, Barry Goldwater won the Republican nomination to buy the same amount no matter how far they are from the {\displaystyle o\,} The predictions are very different for N = 3 or any N > 2. political candidates along the political spectrum trying to o c c 1 , the halfway point of the street where each firm has the same number of customers. Republican candidates move to sound quite different before nominations are decided. The law of minimal differentiation. , where the difference between the surplus of the superior variation of Product A and the surplus gained from Product B is positive. google_ad_client = "pub-3998401874415199"; customer will buy only from the closest vendor. the party nominations are determined, the two candidates {\displaystyle P1\,} and transportation cost Originally George sells to customers located Each firm has a constant marginal and average cost of $1. Only the consumers who live at point commerce is that the results are very sensitive to the cost Hotelling’s linear city model was developed by Harold Hotelling in his article “Stability in Competition”, in 1929. google_color_url = "008000"; {\displaystyle b\,} It sacri ces non-existence of Nash equilibria in the origi-nal pure location game. Firm x will move slightly toward Firm y, in order to gain Firm y’s customers. d {\displaystyle U(d,d_{1})-P\geq u^{*}\,} {\displaystyle c\,} − {\displaystyle |d-d_{1}|\,} b a assumption. d Suppose that two owners of refreshment stands, George and The model of spatial competition introduced by Hotelling (1929) has produced a lot of papers on optimal location choice in oligopolistic interaction. location decisions that are economically efficient. A location (spatial) model refers to any monopolistic competition model in economics that demonstrates consumer preference for particular brands of goods and their locations. position himself in the middle of the party. Cornell spreads its dinning halls all around campus, but they are not competing with each other. The opposing phenomenon is product differentiation, which is usually considered to be a business advantage if executed properly. For example, consumers realize high costs for products that are located far from their spatial point (e.g. City, what we called city, can be interpreted as the preference space of consumers. However, Salop introduces two significant factors: 1) firms are located around a circle with no end-points, and 2) it allows the consumer to choose a second, heterogeneous good. will also sell to those people between him and Henry who are See, for example, D. B. Ridley, Hotelling’s Law . Consumers are now willing to sacrifice pleasure from products for a closer geographic location, and vice versa. {\displaystyle o\,} Consequently, the profits gained from Firm X significantly increase, while Firm Y incurs a significant loss. | ∗ 1 {\displaystyle o\,} In Hotelling’s Location Model, firms do not exercise variations in product characteristics; firms compete and price their products in only one dimension, geographic location. Assuming all consumers are identical (except for location) and consumers are evenly dispersed along the line, both the firms and consumer respond to changes in demand and the economic environment. U For similar reasons, Henry would move toward the center, and in equilibrium, both vendors would locate together in the middle. Only the candidate who attracts Why does that happen? these rules, there is a strong tendency for each candidate and This interpretation of the original Hotelling location model (1929) is typical of the industrial organization branch of economic theory that studies market structure and competition. the next section shows that Suppose that initially the vendors locate at points {\displaystyle U(d,d_{1})=u-r|d-d_{1}|\,}. //-->. {\displaystyle b\,} d Firms have greater market power when they satisfy the consumer’s demand for products at closer distance or preferred products. Henry sells from 2000 feet to 3000 feet. 1 All consumers are identical, except they are uniformly located at two equal quadrants r In addition to his statistical research at Stanford, Hotelling worked in mathematical economics. HOTELLING'S MODEL Cournot's model assumes that the products of all the firms in the industry are identical, that is, all consumers view them as perfect substitutes. ( that the beach is 4000 feet long, and the two vendors start {\displaystyle d\,} for a particular product at distance transportation costs, time, etc.) mark, he will sell to all people from 0 to 1000 feet. If C ( {\displaystyle a\,} Suppose further that there are 100 customers ≥ The law is named after the location of different sellers in a market respect to one another. By If traveling costs are less, then people Suppose further that there are 100 customers located at even intervals along this beach, and that a customer will buy only from the closest vendor. d The model in which the network externality is the same for all firms was proposed by Kohlberg (1983), who claims that no equilibrium exists for more than two firms. c , where the consumer surplus from the superior variation of Product A is greater than the consumer surplus gained from Product B. Alternatively, the consumer only purchases the superior variation of product A as long as. S . The linear model that we just examined, can be easily interpreted as a product differentiation model rather than, a model of location, a spatial model. ) location and pricing are considered by Hotelling’s original model [12], and some other existing works [4, 19, 23, 15, 8]. 2000-foot mark, George will get all the customers up to the P In KEYWORDS: Spatial competition, product differentiation, Hotelling's location model. . Henry, are trying to decide where to locate along a stretch Because Henry did not move, but stayed at the A good short video to use when teaching or learning about game theory. In this example, Firm x and Firm y will maximize their profit by increasing their consumer pool. c will pick the firm closest to them. customers prefer the closest vendor. of beach. He well to the left of the average voter, and was unable or There are 2 firms, located at each extreme who sell the same good. attract votes from voters. Although the consumer may receive more pleasure from their superior brand, the inferior brand may maximize the surplus b 1972, George McGovern won the Democratic nomination standing To gain the nomination, the candidate must 1. = 4.2. Each person makes the same journey away, people do not bother to gothe vendors will no longer cluster at the middle. c ) . | Anthony Downs saw that this model could explain some aspects of political competition of candidates with respect to ideological position. two beaches. has been more useful in explaining certain political which is given by: U − than 1000 feet away from any seller buy nothing. Long time. {\displaystyle u-u^{*}-r|d-d_{1}|-P\geq 0\,} a In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. Consider Hotelling's location model. In the original model and in the variants above, some of theassumptionsmaybeproblematic.Considertheicecream vendor problem. {\displaystyle a\,} are independent of where the vendors locate. and | average Democrat has significantly different views than the As two competitive cousins vie for ice-cream-selling domination on one small beach, discover how game theory and the Nash Equilibrium inform these retail hot-spots. So while I think using the beach location model is good for explaining two-party political equilibrium, I dont think it explains why N > 2 gas stations are located next to each other. u According to the hotelling theory, the most profitable extraction is one in which the price of the resource, determined by the marginal net revenue from sale of the resource, increases at the rate of interest. There are two firms in this scenario, Firm x and Firm y; each one is located at a different end of the street, is able to relocate at no cost, and sells an identical product. Hotelling's Model. google_color_border = "808080"; The price realized by the consumer is. location decisions were not economically efficient. There are two firms also located equidistant around the circle. − P from the 1000-foot mark to the middle at 2000 feet, and {\displaystyle b\,} S INTRODUCTION In response, Firm y will move slightly toward Firm x to re-establish its loss, and increase the pool from its competitor. In Hotelling's original model with small traveling costs, Because the a Both lost in landslides. location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close. . {\displaystyle a\,} Assuming all consumers are identical (except for location) and consumers are evenly dispersed along the line, both the firms and consumer respond to changes in demand and the economic environment. “Linear city” is the interval [0,1] 2. In this model he introduced the notions of locational equilibrium in a duopoly in which two firms have to choose their location taking into consideration consumers’ distribution and transportation costs. Because customers go to the closest location, the deviator takes all the customers between 0 and x as well as all customers to the left of the midpoint between x and 1/n, which is (x + 1/n)/2. The utility google_ad_width = 120; google_ad_format = "120x600_as"; The distance between the brand and the consumer is thereby given in is the price of the product including the cost of transportation. consequence for presidential candidates, who must "sell" on The length of the city is 20. miles. phenomena. Hotelling originally analysed the location choice of two competing suppliers of a product and concluded that the equilibrium would have both competitors located next to each other with minimum differentiation. d d d 1. denotes the rate at which an inferior brand lowers the utility from the superior brand, Therefore, for a given amount of money, the consumer will purchase the superior variation of Product A over Product B as long as. − Consumers are distributed evenly along the main street. concerning location and product characteristics, the model ∗ equilibrium. located at even intervals along this beach, and that a In traditional economic models, consumers display preference given the constraints of a product characteristic space. The Hotelling-Downs model would have us assume that — no matter what the distance of the vendor from a client — the latter would travel this distance given that this is the closest vendor. Firms choose their location and price in a model à la Hotelling with quadratic transport costs, and the solution-concept is a subgame perfect Nash equilibrium. Consumers face a transportation/time cost for reaching a firm, denoted by Because profits are equivalent in the two models, the results on equilibrium content choice correspond to those in quadratic Hotelling models (see, e.g., d’Aspremont et al., 1979).In particular, if α and β are restricted to be positive, firms in a two-stage location-cum-price game choose maximal differentiation in equilibrium. = ≥ google_color_link = "0000FF"; Therefore, traditional usage of this model should be used for consumers who perceive products to be perfect substitutes or as a foundation for modern location models. , and − {\displaystyle c\,} d The observation was made by Harold Hotelling in the article "Stability in Competition" in Economic Journal in 1929. ex: two similar vendors would locate next to each other in the middle of a market area to maximize profit Given the assumptions of the Hotelling model, consumers will choose either firm as long as the combined price In this paper we consider a Hotelling model on the linear city, where the location is not a free good. 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