Harold Hotelling Lindsay West

Meet Harold Goal: to apply a higher level of mathematics to the field of statistics a diverse man; he studied journalism, statistics, political science, population and food supply Studied at both Stamford and Columbia University founded a new statistics department at University of North Carolina at Chapel Hill was considered a pioneer in statistics and economics contributed to several theories including demand and utility, economics and taxation He completed several of his own papers on the topics of game-theory, resource exhaustion and many others Died in d-hotelling/g-6mfot524es8vkdb8frmuka0 September 29, 1895, Fulda, MN

Linear City this idea was developed in his article “Stability in Competition” the model was first a game in which each firm tries to set itself in the best location to maximize profits Each firm has to consider three different factors: competitors’ location customers’ distribution transportation costs this model has been inspiration for many pieces of literature as well as well as to other areas such as politics

How the Theory Works

Static Model (Firms choose their locations and prices Simultaneously) ● For profits to be both positive and maximized: ○ selling prices must be higher than marginal costs ○ also both firms cannot be located at the same point or else they would end up in Bertrand’s solution which is when the prices at both stands are equal to the marginal cost which means zero profit ● Conclusion: each stand will chose prices higher than their marginal costs and will choose a location that is not in the middle

dynamic Model additional assumptions Both firms have equal marginal production cost. Total cost for consumers depends both on the price of the goods and the distance to its location (t) at a certain point it is the same for customers to consume from either of the two firms subgame perfect Nash equilibriumsubgame perfect Nash equilibrium is when both firms have maximised their profits the demand effect decreases differentiation between the firms as they are inclined to move towards the center the strategiec effect is where both firms move towards the opposite extremes creating more differentiation (Firms determine price after determining location) this is the demand function for each firm Profits will be higher the less distance there is to the extremes, therefore maximum differentiation between stands will be given when A locates at 0 and the B at 1.

Optimal Location Within A Market page 391 in the textbook the book doesn’t give Harold any credit but the theory that is discussed is his theory “the best location is the one that minimizes the distance to the service for the largest number of people” the gravity model says that “the optimal location of a service is directly related to the number of people in the area and inversely related to the distance people must travel to access it

Bibliography Kruse, Megan. "Harold Hotelling." Amstat.org. N.p., n.d. Web. 19 Sept "Policonomics." Policonomics. Policonomics, n.d. Web. 19 Sept Rubenstein, James M. "Chapter 12." The Cultural Landscape: An Introduction to Human Geography. Upper Saddle River, NJ: Pearson/Prentice Hall, Print. Schenk, Robert. "Hotelling's Model." N.p., n.d. Web. 19 Sept