# Monopolies & Oligopolies

### Problems

Problem :

Two firms with identical cost structures produce a homogeneous good. Both firms choose the quantity to produce at the same time, but before then, one firm has the privilege of announcing its production quantity decision. Explain how the credibility of this announcement can change the outcome. Do we reach the Cournot equilibrium or the Stackelberg equilibrium?

Problem :

Two firms have marginal costs of 10. They face a market demand curve of P = 100 - 4Q . The government imposes a tax of 10 dollars per unit sold. Determine the Cournot equilibrium quantity.

Problem :

Assume three firms face identical marginal costs of 20 with fixed costs of 10. They face a market demand curve of P = 200 - 2Q . Find the Cournot equilibrium price and quantity.

Problem :

Assume two firms have marginal costs of 20. They face a market demand of P = 90 - 3Q . Determine the Bertrand equilibrium quantity and price. Now assume one firm moves ahead of the other. Find the Stackelberg equilibrium and price.

Problem :

A group of n identical firms face a market demand curve of P = 2000 - 3Q . MC = 100 . Show that as n approaches , the quantity approaches the perfectly competitive outcome.

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