Question

Consider two symmetric Cournot duopolists who face inverse market demand of

p = 140−Q.

Suppose that they each have long-run cost functions Ci(qi) = 20qi for i = 1, 2.

1. (a) Draw a graph containing the demand and marginal cost curves.

2. (b) What are the efficient quantity and price, QC and pC? How much total surplus is generated at this quantity and price?

3. (c) What are the monopoly quantity and price, QM and pM ? How much profit would a monopolist earn in this market? How much consumer surplus would be generated under monopoly? Indicate the point on the demand curve where a monopolist would operate in your diagram.

4. (d) Derive the best-response function for firm 1, q1∗(q2), that gives 1’s optimal output as a function of what it thinks 2 will do.

5. (e) Suppose that the firms make an informal agreement to each produce half the monopoly output. If 1 believes that 2 will abide by this agreement, how much should 1 actually produce if it wants to maximize its profit? How much profit would it make and how much would 2 make in this case?

6. (f) What are the Cournot-Nash equilibrium quantities (q1∗,q2∗). What is the market price in the Cournot-Nash equilibrium. How much profit does each firm make and how much surplus is received by consumers? Indicate the relevant point on the demand curve in your diagram.

7. (g) Briefly discuss why these firms would or would not like to merge. Briefly discuss why or why not the Department of Justice or the Federal Trade Commission is or is not likely to allow such a merger.

Answer 1