4. Vertical Relations (43 points) Suppose that a car dealer has a local monopoly in selling Volvo cars. It pays the wholesale price w to the monopolist Volvo for each car that it sells, and charges each consumer the retail price p. The demand function in the retail market is given by p-600-q. The marginal cost of Volvo is 200. A. (12 points) Suppose that the car dealer and Volvo work separately. What will be the Nash equilibrium? B. (6 points) Find the equilibrium profits for the dealer and Volvo. Find the equilibrium consumer surplus in this separation case. C. (5 points) Now suppose that Volvo bought the ownership of the car dealer. For the integrated firm, what will be the equilibrium quantity q and retail price p? What will be the total profit for the integrated firm? What will be the consumer surplus? D. (7 points) Provide detailed economic reasons why for both the consumers and the firms the integration case is better than the separation case? (Rather than compare the numbers, you have to show the economic reasons here.) E. (13 points) Retailers' Competition El. (6 points) Now suppose that Volvo has two dealers who compete in the one-period Bertrand competition (short term) in the retail market. All the other conditions remain the same as before. Findthe new Nash equilibrium in this game. E2. (7 points) If these two dealers compete with each other in the long run, i.e.., an infinitely repeated Bertrand competition, with a discount rate of 0.8. All the other conditions remain the same as before. What is the new Nash equilibrium? (You don't have to provide a rigorous answer in every step, and an intuitive explanantion will be fine)