In this paper we consider a Hotelling model on the linear city, where the location is not a free good. Brown, D.M. equilibrium. If In this respect, to reduce on the marginal cost of extraction, it would require that an industry be located close to the extraction point… Conclusion. 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. So this game was invented by an economic theorist, Harold Hotelling, and, therefore, it is sometimes called Hotelling's location game. Finally, the paper will endeavor to assess both Hotelling's contribution to location theory and identify some potentially fruitful avenues of future research activity. are independent of where the vendors locate. Locational interdependence refers to the impact of a business’s geographic location on its ability to operate and make a profit. Henry, are trying to decide where to locate along a stretch from the 1000-foot mark to the middle at 2000 feet, and For this reason, we must assume that both ice cream stands offer the exact same ice creams, and therefore consumers’ utility will be given only by the price of the ice cream and the distance to the stand. Keywords: agglomeration, linear city, location, principle of minimum differentiation According to Hotelling’s Law, there is an ‘undue tendency for competitors to imitate each other in quality of goods, in location, and in other essential ways’ (Hotelling, 1929: 41). This second condition implies that both stands can’t be located at the same point exactly in the middle of the beach. locations would minimize the average traveling costs of the two beaches. closer to him. google_color_url = "008000"; ex: Two ice-cream vendors moving … If this were the case it would be indifferent for the customers to go to either one. However, this solution would not be an Two conditions are necessary for profits to be positive and maximized in both stands: -Selling prices must be higher than marginal costs. If George moved from point A to point However, this model includes two different approaches, the first one being a static model consisting of a single stage were firms choose their location and prices simultaneously, and a dynamic model in which price is set after determining the location. In this first model,  is the exact middle of that beach, so consumers to its left would go to stand A while consumers to its right would go to stand B. At the 1000-foot Trained in mathematics, he participated in the early twentieth century movement to mathematize economics. 29 September 1895 - d. 26 December ... one in 1929 dealt with a problem of optimizing price and location in a competition between two entities in a spatial ... inverse of the population covariance matrix. google_ad_channel =""; economies 8. After Summary 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. consequence for presidential candidates, who must "sell" on The hot dog stands compete purely … This will lead us once again to the static model result, in which each stand sets its own price. unable or unwilling to reposition himself in the center. dimension. In Summary, the Hotelling theory has contributed to the economics of nonrenewable resources. 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. Empirical evidence 9. Harold HOTELLING. Industrial Organization-Matilde Machado The Hotelling Model 3 4.2. After properly analyzing statistical data, Sargent tried to ascertain the tendency of location of industries. google_ad_format = "120x600_as"; than 1000 feet away from any seller buy nothing. It is indifferent for customers whether to go to one or the other stand, as long as their utility is maximized. To gain the nomination, the candidate must It is a very useful model in that it enables us to The conclusions that can be drawn from this model are two opposite effects. Solutions for Problem Set 1 Game Theory for Strategic Advantage (15.025) Spring 2015. It also examines the extent to which the principle of minimum differentiation has stood the test of time and assesses both Hotelling's contribution to retail location theory … Yet similar cereals are viewed by consumers as good substitutes, and the standard model of this kind of situation is the Hotelling model. concerning location and product characteristics, the model If both stands’ prices were equal, the differential factor would be how close consumers are to each stand. Because the possess equilibria in pure strategies for only a limited set of location pairs. In American politics this tendency has a predictable Hotelling’s linear city model was developed by Harold Hotelling in his article “ Stability in Competition ”, in 1929. Suppose that initially the vendors locate at points and he will lose only 500 feet to Henry. //-->. Hotelling Model Graphically 0 1 1 Location of firm A Location of firm B Mass of consumers = 1 1 0 0 ∫1 1 0 1dz z= = − = x Industrial Organization-Matilde Machado The Hotelling Model 4 4.2. mark, he will sell to all people from 0 to 1000 feet. Here is a really well produced and clear visual explanation of the Hotelling model of spatial location. All consumers to left !store 1; all consumers to right !store 2. Hotelling’s model has been source of inspiration for a great amount of fruitful literature which does not only constrain to industrial organization theory but also to other sciences, such as politics, as some of its conclusion can be directly applied to them. He represented this notion through a line of fixed length. However, In politics we can observe how candidates follows this demand effect, as they tend to come from a specific ideology but tend to convey towards a moderate ideology with the objective of attracting as many voters as possible. sound quite different before nominations are decided. In this case, the model has two stages. Despite differences in prices, the stand with the lowest prices will not necessary attract all the demand since consumers will also consider the distance to the stand. Harold’s hotelling theory can be applied to the logistic industry. google_ad_type = "text_image"; Suppose further that there are 100 customers google_color_bg = "FFFFCC"; Only the candidate who attracts Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. With regards to the previous model there are two additional assumptions: Both stands have equal marginal production cost. attract votes from voters. 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. These Equilibrium in this case will occur only 1972, George McGovern won the Democratic nomination standing assumption. increasing traveling costs, it seems that we can have [more] This model has a high degree of generality and can be … Equating and equalising we get. Hotelling Model The transportation costs of consumer x: Of buying from … All consumers located to the left of a would go to stand A, and all consumers located to the right of 1-b would go to stand B. adding transport costs results in new efficiency problems. Both lost in landslides. He to buy the same amount no matter how far they are from the A and C in the illustration below. at the middle. For n = 4, two players occupy 1/4 and two players occupy … Each stand would decrease its prices in order to attract customers, and thus they would enter into what is referred to as a price war. will also sell to those people between him and Henry who are (This is the median voter theorem.) Furthermore, it would not be much harder to extend the theory to the third dimension as well if we used a planar space instead of a line. location decisions were not economically efficient. 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. While the first effect will reduce differentiation between the stands, the second one will increase it. 1979: The location decision of the firm: an overview of theory and evidence. they are greater—so that when the vendor gets far phenomena. On one hand, there is an incentive for both stands to locate at the centre of the beach in order to increase their market share by reaching out to the greatest amount of customers, in what is known as the demand effect. these rules, there is a strong tendency for each candidate