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profit level associated with the Cournot quantity

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Suppose the market demand curve in an industry is characterized by P=1-Q, where P is the market price and Q is the total quantity supplied to the market. Suppose there are three firms in this industry. All have a zero marginal cost of production.

1. In a one-shot interaction, what is the Cournot quantity for each firm?
2. What is the profit level associated with the Cournot quantity for each firm?

Now consider an infinitely repeated version of the above game. Suppose that the firms agree to act collectively as a monopolist. All firms have the same discount factor .

3. How much will each individual firm produce under the cartel arrangement?
4. How much profit will each individual firm make under the cartel arrangement?
5. Suppose a firm decided to cheat on the cartel arrangement. How much would it produce i.e. what is the best possible deviation it could make? How much profit would it get from making this deviation?
6. How big does the discount factor have to be in order to support the cartel arrangement through the threat of playing Cournot forever as punishment for deviation?
7. Compare this with the two firm case. Is the delta that supports the two-firm case higher or lower than the three-firm case i.e. is it easier to support a cartel with two firms or with three firms? Explain.

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Solution Preview

Please see the attached file.

Suppose the market demand curve in an industry is characterized by P=1-Q, where P is the market price and Q is the total quantity supplied to the market. Suppose there are three firms in this industry. All have a zero marginal cost of production.

1. In a one-shot interaction, what is the Cournot quantity for each firm?
2. What is the profit level associated with the Cournot quantity for each firm?

Now consider an infinitely repeated version of the above game. Suppose that the firms agree to act collectively as a monopolist. All firms have the same discount factor .

3. How much will each individual firm produce under the cartel arrangement?
4. How much profit will each individual firm make under the cartel arrangement?
5. Suppose a firm decided to cheat on the cartel arrangement. How much would it produce i.e. what is the best possible deviation it could make? How much profit would it get from making this deviation?
6. How big does the discount factor have to be in order to support the cartel arrangement through the threat of playing Cournot forever as punishment for deviation?
7. Compare this with the two firm case. Is the delta that supports the two-firm case higher or lower than the three-firm case i.e. is it easier to support a cartel with two firms or with three firms? Explain.

Question 1
Let's call Q1, Q2 and Q3 to the quantities produced by each of the firms. We get that the ...

Solution Summary

The profit level associated with the Cournot quantity is determined.

$2.19