Circular City Model with Various Mergers.

Four firms, labelled 1, 2, 3, and 4 are

located equidistant from each other around a circle of unit circumference, and each

produces a single product (labelled products 1, 2, 3, and 4 to correspond with the firm

label) at constant marginal and average cost c. L consumers are uniformly distributed

around the circle, and each is willing to pay v for one unit of the product. A purchase

requires a consumer to pay a "transport" cost equal to t per unit distance between the

consumer and the firm from which it purchases. Assume that v is large enough that every

consumer around the circle purchases the product.

a.

(10 pts) What are the pre-merger Bertrand equilibrium prices?

b.

(10 pts) Suppose firms 1 and 2 merge and continue to sell from their pre-merger

locations. Assume that all firms are able to adjust their prices in the new equilibrium.

What are the post-merger equilibrium prices for each of the four products?

c.

(10 pts) Suppose firms 1 and 4 merge and locations do not change. Assume that all

firms are able to adjust their prices in the new equilibrium. What is the effect of this

merger on the prices?

d.

(10 pts) Compare and contrast (if there is a contrast) your findings in 4.b and your

findings in 4.c.