Hotelling's Model

Publication Date :

12 Jan, 2025

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Table Of Contents

Hotelling's Model Definition

The Hotelling Model is a linear city model, which states that when two symmetric firms in the city compete with themselves and consumers pay for linear transportation costs, it is likely that both firms will stall near the middle of the population of the consumers. It suggests that sellers with identical products or perfect alternatives of a product can follow this model for fruitful results.

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Following this location model ensures making the same products accessible and available to an entire population segmented within the two extremes. The transportation costs involved in buyers reaching the sellers become the primary factor determining which individual would choose which seller based on how much extra they would have to pay to reach them.

Key Takeaways

Hotelling's model is a linear city model based on location theory. It states that firms will stall in a linear arrangement to make themselves equally reachable by customers, thereby leading to an equal division of the customer demand for each of them.
Customers refrain from paying extra for transportation to buy a product, and this is what makes this model the best approach for sellers who make buying products convenient for consumers.
The model was presented in 1929 by Harold Hotelling in his paper Stability in Competition.
It is based on a few assumptions, such as the cost of travel being equal for all consumers and each of them having a unit demand. In addition to consumers being equally distributed and incurring equal or similar production costs, etc.

Hotelling's Model Explained

Hotelling's model of spatial competition presents a picture of two firms that compete, selling homogeneous goods to their customers. The firms are in a linear market and are spread evenly. The model states that the two duopolists are often located close to each other, especially at the market's center.

Harold Hotelling presented the model in 1929 in his paper Stability in Competition, elaborating on how the presence of two sellers selling identical products can improve the accessibility of the items to the entire population of an area without them having to travel much for the same. Implementing this model works in favor of all sellers located at a certain distance within a range. The customers get equally divided between them, depending on how far they are from them. The best part of this model is that it is recommended only for sellers with identical products at the same price.

The model attempts to explain commonly seen social phenomena, such as certain stores or restaurants often seen close to each other or certain towns having a majority of stores of one kind located in a linear arrangement. It also explains the reasons behind a specific part of the city having clusters of stores in a queue. Hence, his model ends up not only looking at spatial differences but also other differences.

The model illustrates how factors beyond a product's price and characteristics influence consumers' purchasing decisions. It suggests how important the location of the sellers is for customers to decide where they should buy a product from. Sellers may sell at higher prices than others in faraway areas, but they are likely to experience the same demand from consumers if their store is conveniently reachable.

Assumptions

Hotelling's model of spatial competition is based on a few assumptions, which include the following:

Cost of travel is a factor that determines equilibrium.
The formula for determining the cost of travel is the same for all consumers.
Each consumer in the market has a unit demand.
Consumers in the market are equitably distributed.
Firms either incur zero or equal production costs.
The firm's relocation cost is zero.

Examples

Let us consider the following instances to understand the concept better:

Example #1

Scenario 1

Suppose there are two lemonade stands on a road - A and B. They sell their product on the road, and they are located horizontally straight. The ideal position where both stands could benefit is illustrated below (Scenario 1).

In this case, both sides will witness an equal share of customer demand. This is because consumers who arrive on the left side will purchase from A, and those on the right side will purchase from B. This way, consumers have to travel a shorter distance.

Scenario 2

Now, suppose the lemonade stand moved right to the center of the road from its initial position to ensure more consumer inflow. This move should ideally increase B's demand as consumers from a portion of the area that previously could have been A's will now be B's, as illustrated below (Scenario 2).

In this situation, B will experience greater demand than A. This is a state of disequilibrium. Hence, the next step could be A moving to the midpoint, which becomes the third move in the spatial model competition for a better flow of customers.

Assuming they are located next to each other, it is the equilibrium point, as neither A nor B has the upper hand. Both the stands have an equal share in the market, and further relocation cannot benefit them. However, at this point, the distance for consumers increases, and their cost of travel also increases along with production costs. This point is also known as Nash equilibrium. Since the consumers can choose from either stand at this point, any changes (reductions) in price from one stand can shift the entire demand to their side. This will induce a price struggle between A and B, which may lead to undercutting each other's price until it reduces their profit. Continued price reduction will make one stand to incur a loss, and the other reach a break-even point, eventually with one exiting the market, leading to a monopoly. Hence, the initial positions are considered optimal. It allows the stands to regulate prices to attain maximum profit.

Example #2

In 2015, research was conducted to study the impact of production technology and labor inputs on the location of firms, which is an essential factor in Hotelling's model. In the process, production technology and labor input were incorporated into the Hotelling model of spatial competition. The research initiative was taken given multiple papers suggesting the production side of the items also needs significant attention.

In the study, the firms chose their locations simultaneously and, in the second stage, decided the prices of products and labor wages. However, it was found that production technology and minimum wage requirements did not influence finding socially optimal locations. This is because the production technology used by every seller in a region is almost the same, and the residents, being symmetric, hardly pay attention to how products are produced.