In class we kept to the basic location game.Let's extend the model to help think about fixed costs and branding.Now our locations are on a circle rather than a straight line.(A circle can be a good approximation of a city block, for example; using a circle might mean that we don't want to worry about the special characteristics of corners for the time being.)Assume firms locate on the perimeter of the circle, customers walk around that perimeter to reach the closest firm, and that the other assumptions are as in the straight line game (even distribution of customers, they don't like to walk, ...).

-Describe

how 2 competitive firms would locate.

-Describe

where a monopolist would put two locations (branches).

Now let's look at entry and

fixed costs.Introduce a cost structure: $100 fixed cost per location per

day.On the circle, total revenues minus variable costs are $350

per day.So, for example, a single firm with one location would have a net

profit of $350 - $100 = $250.

-Suppose

you are, for the moment, a monopolist and a single location maximizes your

profits.(Consumers might grumble, but they are willing to walk at least

half the circumference of the circle.) But then you face a threat of another

firm entering.How many locations should you open, and where should they

be located?Explain.

-An

important antitrust case accused the then 4 big breakfast cereal producers of

anticompetitive behavior through the profusion of individual cereal

offerings.As evidence the government showed that some of the individual

offerings appeared to lower company profits.Explain this in terms of the

circle model.

The Location Game

A municipal beach is one mile long. Each day beachgoers show up and spread out evenly. The municipality decides to allow two ice cream stands to set up later in each day (the beachgoers are already there). The two stands offer the same products at the same price, by law. Beachgoers don't like to walk and will go to the closer stand when they want an ice cream. Where would the two stands locate if they are rivals? What if they are owned by the same firm?The beach is a metaphor for consumer preferences. This has proven to be an incredibly useful model for thinking about product differentiation.