Explaining the behavior of an oligopolist or a duopolist

Question

Assignment:

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 duopoly explain in words.

The market for bricks consists of two forms that produce identical products. Competition in the market is such that each of the forms 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 forms. Firm 2 has a patented technology that provides it with a cost advantage over form 1. A recent study found that the market demand curve faced by the two forms is P = 1- 1/50000 (x + y); and costs are C₁(x) = 0:03x and C₂(y) = 0:02y; where form 1 produces x units and form 2 produces y units of bricks.

(a) Determine the reaction function for each form.

(b) How much output will each form produce in equilibrium? At what price? How much will be the equilibrium profit for each form?

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 form 2 is a "naive" Cournot duopolist so that form 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 profit for each form?

Part b

(b) Ignoring antitrust considerations, would it be profitable for form 1 to merge with form 2? Explain.

5. Bertrand model: Price competition in simultaneous move homogeneous product duopoly-explain in words. Consider the brick producers again. This time, each form simultaneously and independently picks the price. Since the product is homogeneous, the consumer buys from the producer offering at a cheaper price. The market demand curve faced by the two forms is P = 1 -1/50000 (x + y); and costs are C₁(x) = 0:02x and C₂(y) = 0:02y; where form 1 produces x units and form 2 produces y units of bricks. What price will each one of them charge in equilibrium? Why not any other price elaborate? How much will be the proÖt in equilibrium?

6. Price competition in simultaneous move differentiated product duopoly:

There are only two gourmet food restaurants in a town. Their menus are not identical, but not totally different 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 form 1 serves x consumers and form 2 serves y consumers.

(a) Determine the reaction function for each form.

(b) How much output will each form produce in equilibrium? At what price? How much will be the equilibrium profit for each.