Question: Consider a market characterized by the following demand condition:

where Q is the total industry output such that Q = q1 + q2 + …+ qn. There are n firms in the industry, each with the following cost function:

i =1, 2…„ n.

1. Derive the Cournot-Nash equilibrium quantities, price, and profits.
2. Derive the joint-profit maximizing quota output for each firm — i.e., given that all firms produce the same output, what is the individual firm's output which maximizes the joint profit?
3. Let us assume that the firms use the grim trigger strategies (as discussed in class) to support the cartel quota output: Produce the quota output as long as no one has deviated from it in the past, but immediately revert to the Cournot-Nash equilibrium quantities if a deviation is observed. What is the condition on the common discount factor that would sustain the cartel quota using these strategies?
4. Discuss how the number of firms, a, affects the sustainability of the cartel.

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