Hotelling’s Model of Spatial Competition: How does a Location of the Firm Affect Market Competition?

By Saloni Gala | Edited by Ruth D’Souza 

Ever wondered why Starbucks and Barista are located next to each other? Or why are there so many beauty salons on the same street? Why do fast food outlets, petrol pumps, restaurants seem to gather around in the same area instead of spreading around evenly in a particular locality? In fact, we see competitors clustering a lot. While there are several factors that might affect the decision of where to place your business, clusters and grouping of similar companies can be explained by a very simple story.

Imagine that Andy sells ice cream at the beach, which is one kilometer long and Andy has no competition. Andy decides to place his ice-cream cart right in the middle of the beach so that tourists from all directions can walk up to his cart for an ice-cream and this way his cart serves as many people as possible on the beach. A few days later, his cousin Teddy shows up on the beach with his own ice cream cart, selling exactly the same type of ice cream as Andy and at the same price. So, both Andy and Teddy come to an agreement to split the beach in half. In order to ensure that customers don’t have to walk too far, Andy sets up his cart 250 meters south of the beach center, right in the middle of his territory while Teddy sets up his cart 250 meters North of the beach center. With this arrangement, both of them equally divide the share of customers on the beach as customers closest to each cart buy from the respective owners. Game Theorists consider this a socially optimal solution. It minimizes the maximum number of steps a customer must take, in order to reach an ice cream cart.

The next day when Andy arrives at work he sees that Teddy has set up his cart in the middle of the beach. But Andy continues to remain located 250 meters South of the beach center and he gets only 25% customers to the south, while Teddy gets his original 50% customers and an additional 25% from the south.

On day 3, Andy gets to the beach early and sets up his cart right in the center of Teddy’s territory, assuming he will serve 75% of customers to his south leaving Teddy with only 25% customers to the north. But when Teddy arrives, he sets up just south of Andy’s cart, stealing all of the customers from South and leaving Andy with only a small group of people to the north.

Source: Hotelling’s Game – Mind your Decisions

In retaliation, Andy moves 10 paces south of Teddy to regain his customers and then later, Teddy shuffles another 10 paces south of Andy again. Throughout the day, both Andy and Teddy continue to periodically move south towards the larger bulk of customers, until both of them eventually end up at the center of the beach, back to back, each serving 50% of the customers. At this point, Andy and his competitor Teddy, have reached Nash Equilibrium, the point where neither of them can improve their position by deviating from their current strategy. 

The original strategy where both Andy and Teddy were both 250 meters from the middle of the beach didn’t last, because it was not Nash Equilibrium. Either of them could move their cart towards the other to sell more ice cream. With both of them now in the center of the beach, one can’t reposition their cart closer to the furthest customers without making their current customers worse off. However, now they no longer have a socially optimal solution, since the customers at either end of the beach have to walk further than necessary to get an ice cream. 

Customers maybe better served by distributing services throughout a community, but this leaves businesses vulnerable to aggressive competition. In the real world, customers come from more than one direction, and businesses are free to compete with marketing strategies, by differentiating their product line, and with price cuts, but at the core of their locational placement strategy, companies like to keep their competition as close as possible.

This example of the ice cream carts at the beach clearly explains Hotelling’s Model of Spatial Competition, that represents the relationship between location and pricing behavior of firms. One of the pioneers in introducing the concept of spatial market competition was Hotelling (1929), who looked at how sellers would pick sites in a linear market. He made the assumptions that the product was uniform, buyers would purchase it from the vendor who was closest to them, and that the friction caused by distance was linear and isotropic. Thus, the market price plus the transportation cost equals the final price for the buyer (time or effort spent to go to the market). Two rivals will decide on locations A and B for the best market coverage in such a scenario. If P1 were the market price, the market border would be F1 (point of cost indifference), since consumers who were right of F1 would pay less at site B than they would have paid at location A, and customers who were left of F1 would pay less at location A. Location A’s market area would increase from F1 to F2 at the expense of location B if for any reason the market price could be reduced from P1 to P2.

Source: The geography of transport systems: Hotelling’s Principle for Market Competition

According to Hotelling’s Location Model, businesses solely compete and set prices for their products based on their geographic location, not on variances in their product’s features. Therefore, consumers who believe items are perfect alternatives, should employ this model according to tradition, or it can serve as the basis for more contemporary location models. The idea was initially created as a game in which businesses first selected a location before deciding on a selling price for their goods. The enterprises will have to assess three crucial factors: the location of competitors, consumer distribution, and transportation costs, in order to position their business in the ideal area to maximize earnings. 

When considering the Hotelling framework, the implications of the monopolistic competition theory in the location theory becomes clearer: Location can be seen as a differentiating characteristic that enables businesses to market their differentiated product to their particular demand. By selecting a location site that is more or less similar to the other competing firms, a company can establish different pricing for the same good, balancing the quantity of people interested in the product with the dominant position that allows for a higher price.

This model has an enormous scope of practical implications that have been studied and incorporated in the model by economists and game theorists of the 20th century with respect to the changes occurring in the market structures of modern economies and holds a great value in the study of factors affecting Spatial and Locational Market Competition in today’s era too. 



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