4. (25 points) Firm 1 and firm 2 are the only producers of spring water in the market. The market demand for spring water is given by P = 70 -91 -Q2 . Firm 1 and firm 2 compete by choosing quantities 9, and O, respectively. Each firm has a marginal cost of 10 and no fixed cost. (a) (5 points) Find out firm 1's and firm 2's reaction functions. Solution: 91 60 -92 02 60 - 21 2 2 (b) (5 points) Suppose the two firms choose quantities simultaneously. What are the equilibrium price, quantities, and profits of the two firms in this market? Solution: 91 = 02 = 20, P = 30 (c) (5 points) Suppose only firm 1 has a chance to bribe the government and get the right to choose the quantity first, what is the maximum amount of money that firm 1 is willing to pay? If firm 1 gets to move first, what are the equilibrium quantities and profits of firm 1 and firm 2? [Hint: if firm 1 does not bribe the government, the two firms will choose quantities simultaneously as in (b). ] Solution: The quantity of the first mover is 30 and the profit is 450. The quantity of the second mover is 15 and the profit is 225. If firm I does not get the right, its profit is 400. Therefore, firm 1 is willing to pay is 450-400=50. (d) (5 points) Now back to the situation that the two firms choose quantities simultaneously. Suppose the two firms decide to collude and share the profit equally. Assume that both firms value their reputation and will behave according to their agreement. What are the quantities they will choose for each firm? What is the profit of each firm? Solution: Each firm produces 15 units and gets profit 450