A location (spatial) model refers to any monopolistic competition model in economics that demonstrates consumer preference for particular brands of goods and their locations. Examples of location models include Hotelling’s Location Model, Salop’s Circle Model, and hybrid variations.
Contents
Traditional vs. location models
In traditional economic models, consumers display preference given the constraints of a product characteristic space. Consumers perceive certain brands with common characteristics to be close substitutes, and differentiate these products from their unique characteristics. For example, there are many brands of chocolate with nuts and others without them. Hence, the chocolate with nuts is a constraint of its product characteristic space.
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”. Consumers are now willing to sacrifice pleasure from products for a closer geographic location, and vice versa. For example, consumers realize high costs for products that are located far from their spatial point (e.g. transportation costs, time, etc.) and also for products that deviate from their ideal features. Firms have greater market power when they satisfy the consumer’s demand for products at closer distance or preferred products.
Hotelling's Location Model
In 1929, Hotelling developed a location model that demonstrates the relationship between location and pricing behavior of firms. He represented this notion through a line of fixed length. 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.
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. 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.
Assumptions
Assume that the line in Hotelling’s location model is actually a street with fixed length.
All consumers are identical, except they are uniformly located at two equal quadrants
There are two firms in this scenario, Firm x and Firm y; each one is located at a different end of the street, is fixed in location and sells an identical product.
Advanced Analysis
Given the assumptions of the Hotelling model, consumers will choose either firm as long as the combined price
For example, if both firms sell the product at the same price
As long as
Assumptions
Assume that the line in Hotelling’s location model is actually a street with fixed length.
All consumers are identical, except they are uniformly located in four quadrants
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.
Analysis
In this example, Firm x and Firm y will maximize their profit by increasing their consumer pool. Firm x will move slightly toward Firm y, in order to gain Firm y’s customers. In response, Firm y will move slightly toward Firm x to re-establish its loss, and increase the pool from its competitor. The cycle repeats until both firms are at point
If only Firm x can relocate without costs and Firm y is fixed, Firm x will move to the side of Firm y where the consumer pool is maximized. Consequently, the profits gained from Firm X significantly increase, while Firm Y incurs a significant loss.
Salop’s Circle Model
One of the most famous variations of Hotelling’s location model is Salop’s circle model. Similar to the previous spatial representations, the circle model examines consumer preference with regards to geographic location. However, Salop introduces two significant factors: 1) firms are located around a circle with no end-points, equivalent to a line with infinite distance, and 2) it allows the consumer to choose a second, heterogeneous good.
Assumptions
Assume that the consumers are equidistant from one another around the circle. The model will occur for one time period, in which only one product is purchased. The consumer will have a choice of purchasing variations of Product A (a differentiated product) or Product B (an outside good; undifferentiated product).
There are three firms also located equidistant around the circle. Each firm offers a variation of Product A, and an outside firm offers a good, Product B.
Analysis
In this example, the consumer wants to purchase their ideal variation of Product A. They are willing to purchase the product, given that it is within the constraint of their utility, transportation/distance costs, and price.
The utility
Where
The consumer’s primary goal is to maximize consumer surplus, i.e. purchase the product that best satisfies any combination of price and quality. Although the consumer may receive more pleasure from their superior brand, the inferior brand may maximize the surplus
Now suppose the consumer also has the option to purchase an outside, undifferentiated Product B. The utility gained from a consumer’s consumption of Product B is denoted by
Therefore, for a given amount of money, the consumer will purchase the superior variation of Product A over Product B as long as
Alternatively, the consumer only purchases the superior variation of product A as long as