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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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