just part (4) the game; questions 4. and 5.

Problem4(Oligopoly.PriceWar) In the US, Barnes and Nobel (B\&N) and Amazon are the two largest online retailers of printed books. The two companies compete in the online markets for Hary Potter and the Sonenr's Stone, a famous children book by J. K. Rawling. Amazon and B\&N can buy copies of the book from Scholastic, its US publisher, for $8 per copy. Re-selling the book costs $1 per copy so that both companies have a constant average cost and marginal cost of selling one copy of Harr Potter and the Soncer's Stone equal to AC=MC=$9. Suppose that the demand for Harry Potter and the Sonenr's Stone is Q=15P where Q is measured in millions of copies and P is measured in dollars per copy. Part 1. Collusion Amazon and B\&N wish to collude and fix prices. If they collude, they sell books and fix the market price as if they were one monopolist charging a uniform price. 1. Using the MR = MC condition for a monopolist charging a uniform price, find the number of copies that the two firms combined would sell and the fixed market price. 2. Keeping in mind that in this case the firms split the market, compute cach firm's profit. Part 2. Unilateral defection. 3. However, Amazon could lower its price to $10 and if B&N does not change its price, Amazon steals all customers. Compute the two firms profit in this case. Part 3. Mutual defection. 4. If both firms lower their price to $10, they again split the market. In this case, how many copies of the book does each firm sell? What is profit at each firm? Part 4. The Game. 5. Describe the interaction between Amazon and B&N as a game of strategy in matrix form where each firm chooses to charge either the price from Part 1 . or a price of $10. 6. What is the Nash equilibrium of this game? Problem4(Oligopoly.PriceWar) In the US, Barnes and Nobel (B\&N) and Amazon are the two largest online retailers of printed books. The two companies compete in the online markets for Hary Potter and the Sonenr's Stone, a famous children book by J. K. Rawling. Amazon and B\&N can buy copies of the book from Scholastic, its US publisher, for $8 per copy. Re-selling the book costs $1 per copy so that both companies have a constant average cost and marginal cost of selling one copy of Harr Potter and the Soncer's Stone equal to AC=MC=$9. Suppose that the demand for Harry Potter and the Sonenr's Stone is Q=15P where Q is measured in millions of copies and P is measured in dollars per copy. Part 1. Collusion Amazon and B\&N wish to collude and fix prices. If they collude, they sell books and fix the market price as if they were one monopolist charging a uniform price. 1. Using the MR = MC condition for a monopolist charging a uniform price, find the number of copies that the two firms combined would sell and the fixed market price. 2. Keeping in mind that in this case the firms split the market, compute cach firm's profit. Part 2. Unilateral defection. 3. However, Amazon could lower its price to $10 and if B&N does not change its price, Amazon steals all customers. Compute the two firms profit in this case. Part 3. Mutual defection. 4. If both firms lower their price to $10, they again split the market. In this case, how many copies of the book does each firm sell? What is profit at each firm? Part 4. The Game. 5. Describe the interaction between Amazon and B&N as a game of strategy in matrix form where each firm chooses to charge either the price from Part 1 . or a price of $10. 6. What is the Nash equilibrium of this game