Salop’s circular city model is a variant of the Hotelling’s linear city model. Developed by Steven C. Salop in his article “Monopolistic Competition with Outside Goods”, 1979, this locational model is similar to its predecessor´s, but introduces two main differences: firms are located in a circle instead of a line and consumers are allowed to choose a second commodity. Consumers will have to choose between buying one or none of the differentiated goods, and spending the rest of their income in the second, non-differentiated good.
In this circular model all firms that offer the differentiated goods are located on a circle of perimeter 1, equidistant from each other, and it is an outside firm that offers the undifferentiated good. Consumers purchase goods taking into consideration several aspects such as their preferred brand specification, the distance and transportation cost and their price, and so will act accordingly in order to maximize their utility.
We will designate x’ as the consumer’s preferred good, and x will be the least valued good. Consumers enjoy a surplus S when x’ is consumed instead of x. Knowing that consumers can buy x at location xi for a price of pi, we can equate a decision formula:
Taking into consideration transportation cost,
where xi-x’ is the shortest arc length between xi and x’. If we reformulate the first equation,
This way the effective reservation price v is given by,
Changing now our attention towards the firm’s perspective, there is a total of n firms, and we know that they are at an equidistant distance of 1/n from each other, spread around in a circle. Suppose firm A charged p while the rest of firms charged p*. In the absence of competition the maximum distance consumers are willing to travel T, which is equal to:
If L is the total number of customers in the market, the catchment area of a given firm in the absence of competition is defined by,
However competition is a condition that is given in this market and consumers will consume from the firm that reports the highest surplus. The quantity sold by firm A will be equal to,
It is a logical outcome that firms that have their price set above v will not sell their goods. Only when they lower prices below v will they start attracting consumers.
There will be a point where the price is low enough to overlap with neighbouring firms. If a firm keeps lowering its price it will even capture its competition’s customers.
The choice amongst firms is indifferent to client when the price is equal to,
To sum up, the number of firms in this market will depend on the degree of differentiation between goods, as well as price. We have here similar conclusions to those seen in the linear city model: there are two opposite effects. On one hand, there is an incentive for both stands to locate at the centre of the beach in order to increase their market share by reaching out to the greatest amount of customers, in what is known as the demand effect. And, on the other hand, there is an incentive for both stands to locate at opposite extremes in what is considered to be the strategic effect. While the first effect will reduce differentiation between the stands, the second one will increase it.
This model constitutes an important development from its predecessor, since it can be used to understand contestable markets and entry and exit barriers. It is considered, along with Harold Hotelling’s model, an important part of monopolistic competition theory.