CrystalWater Pty Ltd and ClearWater Pty Ltd are the only producers of spring water in the local market. The market demand for spring water is given by P = 70 - Q1 - Q2. CrystalWater and ClearWater compete by choosing quantities Q1 and Q2 respectively. Each firm has a marginal cost of $10 and no fixed cost.

a. Find Crystalwater's and ClearWater's reaction functions.

b. Suppose that the two firms choose their quantities supplied to the market simultaneously. What are the equilibrium price, quantities, and profits of the two firms in this market?

c. Now suppose that only CrystalWater has a chance to bribe the government and get the right to choose first the quantity it supplies. What is the maximum amount of money that CrystalWater is willing to pay as a bribe? Assuming Crystalwater does choose first the quantity its supplies, what are the equilibrium quantities and profits of CrsytalWater and ClearWater?

d. Assume that both firms are at the position described in part (b). Suppose that the firms decide to collude and share any profit equally. Both firms value their reputation and will conform to their agreement. What are the quantities supplied and profit achieved by each firm?

e. Continuing from part (d), both firms are now less tolerant of each other and willing to take advantage of the other. Foreseeing this change, they make a legally enforceable contract stating that if a firm does not produce the quantity agreed, it must pay some penalty to the other firm. What is the minimum amount of penalty that ensures each firm produces the quantity agreed in part (d)?