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各位大神们，能不能帮小弟做下下面三道题目，基本的我已经做出来了，可是不知道对不对，希望能够将答案讨论一下，万分感谢啊。第一道里的MC是不是要分情况讨论的？第二道的第三小问怎么感觉跟第二小问一样的，可是老师讲不一样，所以万望解答？第三道的第三小问不懂什么意思？其他小问都还OK，只需对下答案。。。哪位好心的能够帮忙解答下，谢谢了啊。。。
1) Let the inverse demand for a product be given by the following equation: P = 10 – Q There are n firms, which set their strategic variable simultaneously. Assume firms have constant marginal costs c, and no fixed costs. What is the highest marginal cost for which production in this market is feasible?
2) Consider a duopoly where both firms have zero marginal costs of production. The inverse demand function for this market takes the following form: P = 40 – 10Q, where Q = q1 + q2. Firms play this game repeatedly forever.
a) How many equilibria exist in this game?
b) What is the minimum discount factor that supports collusion in this market?
c) Formulate the strategies which support this equilibrium.
d) How is the set of equilibria affected by an increase in the number of firms?
e) Suppose firms only set prices every 4th period. How is the set of equilibria affected?
3) Consider the game discussed in the previous question. Now the inverse demand function is given by P = a – 10Q, where Q = q1 + q2.
In each period, the state of the world is determined. The parameter a captures whether the economy is in a boom or a recession and a is stochastic. In any given period, it takes a value of 30 with probability ½ and a value of 40 with probability ½. Firms play this game infinitely many times.
a) Under what conditions can both firms charge the monopoly price in each state of the world?
b) Is collusion easier or harder to sustain than in question 2? Why?
c) Suppose the minimum discount value of one of the firms is lower than the discount factor that sustains the aforementioned equilibrium. What other sustainable collusive equilibria can there be?
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