Consider the market for a (fictional) brand of car, Carro. (We will analyse this market

in isolation.) Carros are produced by a single producer, Carro Motors. The production

technology exhibits constant returns to scale, at a marginal cost of cM = 2. There are

no fixed costs.

Carro Motors sells all the cars it produces to two dealers, Carro East and Carro West,

who then sell the cars to consumers. The price that Carro Motors charges the dealers

is pM. Both dealers pay the same price. Each dealer, however, is allowed to charge a

different price to consumers.

Both dealers sell only Carros, and neither has any costs other than the cost of buying

the cars. Because Carro East and Carro West sell the same physical product, customers

regard buying from the dealers as substitute. However, because the dealers

are located in different areas, the substitutes are imperfect. Therefore, the dealers face

the following demand functions:

qE=8-3pE+pW;

qW=8-3pW+pE;

where pE and pW are the prices of Carros at Carro East and Carro West, respectively,

and qE and qW are the quantities sold at the two dealerships.

The dealers compete by simultaneously setting prices.

Please answer the following questions. Make sure that you explain all the steps of your

analysis and that you define any new notation that you use. You may assume that cars

are infinitely divisible (this can be justified by interpreting the quantities as shipments

containing many cars).

(a)Compute the equilibrium prices, quantities, and profits when all three firms are

independent.

(b) Suppose all three firms merge, forming a single entity, Carro Cars, which manufactures

the cars and sells them in both geographical areas (let qE and qW now

be the quantities sold in the areas formerly served by Carro East and Carro West,

respectively). Compute the new equilibrium prices, quantities, and profits.

(c) Did the merger increase or decrease total surplus? (Note: you do not need to

compute total surplus explicitly)

(d) Now suppose that the final retail market becomes perfectly competitive. Would

there still be a benefit to vertical integration?