Help with microeconomics question

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

there still be a benefit to vertical integration?

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, cus- tomers regard buying from the dealers as substitute. However, because the dealers are located in different areas, the substitutes are imperfect. Therefore, the dealers tace the following demand functions: its :8_3PE+PWi 9w =33Pw +PE-. where pg and W are the prices of Carros at Carro East and Carro West, respectively, and {IE 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. {14 Marks} {b} Suppose all three firms merge, forming a single entity, Carro Cars, which manu- factures the cars and sells them in both geographical areas {let 9;; and cm; 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. (10 Marks} {c} Did the merger increase or decrease total surplus? (Note: you do not need to compute total surplus explicitly) {5 Marks}