Advanced Seminar In Economics. Oligopoly

Week 8 – Oligopoly
Part a
1. What is oligopoly? What is duopoly?
2. What is game theory? What is its role in explaining the behavior of an oligopolist or a duopolist? How do we determine
the equilibrium strategies in a duopoly?
3. Cournot model: Quantity competition in simultaneous move homogeneous product duopolyó explain in words.
The market for bricks consists of two Örms that produce identical products. Competition in the market is such that
each of the Örms simultaneously and independently produces a quantity of output, and these quantities are then sold
in the market at a price that is determined by the total amount produced by the two Örms. Firm 2 has a patented
technology that provides it with a cost advantage over Örm 1. A recent study found that the market demand curve
faced by the two Örms is P = 1
1
50000 (x + y); and costs are C1(x) = 0:03x and C2(y) = 0:02y; where Örm 1 produces
x units and Örm 2 produces y units of bricks.
(a) Determine the reaction function for each Örm.
(b) How much output will each Örm produce in equilibrium? At what price? How much will be the equilibrium proÖt
for each Örm?
4. Stackelberg model: Quantity competition in sequential move homogeneous product duopolyó explain in words.
Refer to the information given before part a of Question 3. Suppose Örm 2 is a “naive” Cournot duopolist so that Örm
1 can act as a Stackelberg leader.
(a) What level of output will each one of them produce in equilibrium? At what price? How much will be the
equilibrium proÖt for each Örm?
Part b
(b) Ignoring antitrust considerations, would it be proÖtable for Örm 1 to merge with Örm 2? Explain.
5. Bertrand model: Price competition in simultaneous move homogeneous product duopolyó explain in words.
Consider the brick producers again. This time, each Örm simultaneously and independently picks the price. Since the
product is homogeneous, the consumer buys from the producer o§ering at a cheaper price. The market demand curve
faced by the two Örms is P = 1
1
50000 (x + y); and costs are C1(x) = 0:02x and C2(y) = 0:02y; where Örm 1 produces
x units and Örm 2 produces y units of bricks. What price will each one of them charge in equilibrium? Why not any
other priceó elaborate? How much will be the proÖt in equilibrium?
6. Price competition in simultaneous move di§erentiated product duopoly:
There are only two gourmet food restaurants in a town. Their menus are not identical, but not totally di§erent either.
The price for each entree in a restaurant is the same. The restaurants pick their prices and sell according to their
demand. The demand curve faced by restaurant 1 is given by: x = 100
4p1 + 2p2 and by restaurant 2 is given by:
y = 100
4p2 + 2p1: The costs are C1(x) = 5x and C2(y) = 25
2
y; where Örm 1 serves x consumers and Örm 2 serves y
consumers.
(a) Determine the reaction function for each Örm.
(b) How much output will each Örm produce in equilibrium? At what price? How much will be the equilibrium proÖt
for each