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Two firms produce a homogenous product. Let p denote the products

price. The output level of firm 1 is denoted q1, and the output of firm 2 is denoted q2. Total quantity supplied is given by Q = q1 + q2. The industry (inverse) demand curve is given by p = α − Q.
The cost of firm 1 is given by C1(q1) = c1q1 and the cost of firm 2 is given by C2(q2) = c2q2. Note that, α>c2 >c1 >0.

-Solve for the competitive equilibrium. What is the price? What is the output level of each firm?
-Solve for the cournot equilibrium. What is the price? What is the output level for each firm?
-Compare the cournot outcome to the competitive outcome using a diagram and accompanying words.
-Quantify the total loss in economic welfare loss arising in the cournot outcome. Decomposethis into allocative and productive inefficiency. Use a diagram as appropriate.
-Now consider what happens when these firms enter into a cartel agreement to split the market 50/50. What price and quantity should they select to maximize the returns to cartelization? What is the welfare cost, relative to the cournot outcome, from this new market structure? What is the change in consumer surplus?
-Describe how a game is structured in which this cartel agreement is enforced through repeated interaction.
-Assume that firms play trigger strategies. What are these strategies in this instance? What is the stage game when the two firms cooperate? What is the stage game when they defect? What are profits for each firm?
-What is the minimum discount factor δ required to support the cartel agreement (i.e. to make the firms want to cooperate?) 

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Two firms produce a homogenous product. Let p denote the products price. The output level of firm 1 is denoted q1, and the output of firm 2 is
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