Barts (firm 1) and carts (firm 2) are two firms which one day discovered a steam that flows wine instead of water (lucky!).

Q4 (7 marks). Barts (Firm 1) and Carts (Firm 2) are two firms which one day discovered a stream that flows wine instead of water (lucky!). They decide to bottle wine and sell it. The marginal cost and fixed cost of bottling wine are zero. The market demand for wine is given as p = 120 - 9/4 where O is the total quantity of bottled wine and p is the market price of a bottled wine. a (1 mark). If both firms were to collude and produce the wine as a monopoly, what is the profit- maximizing price and quantity of the monopoly? What is the deadweight loss? b (2 marks). If both firms compete as Cournot duopoly, what is the Cournot-Nash equilibrium price, quantity and profit of each firm? c (2 mark). If the marginal cost of Carts increases to $30, while Barts has a zero marginal cost, what is the equilibrium price, quantity and profit of each firm under Cournot duopoly? d (2 marks). Suppose another firm, Darts (Firm 3), also discovered the stream and starts to sell wine. If three Cournot firms compete, what will be the output and profit for Barts, assuming the marginal cost is zero for all three firms