(25points) Firm1 and firm2 are the only producers of spring water in the market.The market demand for spring water is given by P = 70 ? Q1 ? Q2. Firm1and firm 2 compete by choosing quantities Q1and Q2 respectively. Each firm has a marginal cost of 10 and no fixed cost. (5points) Find out firm1â€™s and firm2â€™s reaction functions. (5 points) Suppose the two firms choose quantities simultaneously. What are the equilibrium price, quantities, and profits of the two firms in this market? (5points) 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 offirm1 and firm2? [Hint: if firm1 does not bribe the government, the two firms will choose quantities simultaneously as in (b).] (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?(5 points) Suppose the two firms decide to collude and share the profit equally, but both firms do not care about their reputation and might try to take advantage of the other. Fore seeing this, they make a legally enforceable contract saying that if a firm does not produce the quantity agreed, it has to pay some penalty to the other firm. What is the minimum amount of penalty that ensures each firm producing the right quantity agreed in part (d).
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