In economics, a location model or spatial model refers to any monopolistic competition model 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. 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. An example of fixed firms 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 and , which is divided in the center by point . Consumers face a transportation/time cost for reaching a firm, denoted by ; they have no preferences for the firms. There are two firms in this scenario, Firm x and Firm y; each one is located at a