In: Economics

# Consider an industry which has a market demand curve given by P=260−2Q. There are two firms...

Consider an industry which has a market demand curve given by P=260−2Q. There are two firms who are Cournot competitors. Firm 1 has marginal costc1=80 and firm2 has marginal costc2=20.

(a) [10 points] Find the Nash equilibrium quantities for these two firms.

(b) [20 points] Use the quantities you found in part (a) to find the profits for each firm and the market-clearing price.

(c) [20 points] Suppose these firms decide to form a cartel and collude. The firms will split the profits generated by the cartel equally. Will firm 1, firm 2 or both firms produce output? Why? How much output will the cartel produce? How much profit will each firm receive from the cartel?

(d) [20 points] Suppose firm 1 takes as given that firm 2 will produce the agreed upon amount from the previous question. If firm 1 decides to deviate from the agreement, how much output will firm 1 produce?   How much profit will they generate? Assume that firm 1 is given half of firm 2’s profits as per the cartel agreement.

(e) [30 points] If this game is repeated indefinitely, what are the probability-adjusted discount factors that each firm must have in order to sustain the collusive agreement? Hint: these will be different for the two firms.

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