Competition and Unit Cost
Seminar 4 - Industrial Economics
Week 16: beginning November 14th 2011
Price Competition and Bertrand Model
Discussion Questions
1. Suppose firm 1 and firm 2 each produce the same product and face a market demand curve described by:
Q = 5000 - 200P Firm 1 has a unit cost of production c1 equal to 6 whereas firm 2 has a higher unit cost of production c2 equal to 10. a. What is the Bertrand-Nash equilibrium outcome? b. What are the profits for each firm? c. Is this outcome efficient?
Answer:
(a) At equilibrium, assuming that if both firms charge the same price, then the firms split the market evenly.
(b) The higher cost firm makes zero profit, whereas the lower cost firm’s profit is
(c) No, this outcome is not efficient as we have a monopolistic situation (the most efficient market structure from the consumers' point of view is perfect competition where the most output is produced at the lowest price).
2. Suppose that market demand for golf balls is described by:
Q = 90 - 3P where Q is measured in kilos of balls. There are two firms that supply the market. Firm 1 can produce a kilo of balls at a constant unit cost of £15, whereas firm 2 has a constant unit cost equal to £10. a. Suppose firms compete in quantities. How much does each firm sell in a Cournot equilibrium? What is the market price and what are firms' profits? b. Suppose firms compete in price. How much does each firm sell in a Bertrand equilibrium? What is market price and what are firms' profits? c. Would your answer in b. change if there were three firms, one with unit cost = £20 and two with unit cost = £10? Explain why or why not.
d. Would your answer in b. change if firm 1's golf balls where green and endorsed by Tiger Woods, whereas firm 2's are plain and white? Explain why or why not.
Answer:
(a) Note that the inverse demand function is . Then the Cournot quantities are:
The market price is
Profit of Firm 1 =
Week 16: beginning November 14th 2011
Price Competition and Bertrand Model
Discussion Questions
1. Suppose firm 1 and firm 2 each produce the same product and face a market demand curve described by:
Q = 5000 - 200P Firm 1 has a unit cost of production c1 equal to 6 whereas firm 2 has a higher unit cost of production c2 equal to 10. a. What is the Bertrand-Nash equilibrium outcome? b. What are the profits for each firm? c. Is this outcome efficient?
Answer:
(a) At equilibrium, assuming that if both firms charge the same price, then the firms split the market evenly.
(b) The higher cost firm makes zero profit, whereas the lower cost firm’s profit is
(c) No, this outcome is not efficient as we have a monopolistic situation (the most efficient market structure from the consumers' point of view is perfect competition where the most output is produced at the lowest price).
2. Suppose that market demand for golf balls is described by:
Q = 90 - 3P where Q is measured in kilos of balls. There are two firms that supply the market. Firm 1 can produce a kilo of balls at a constant unit cost of £15, whereas firm 2 has a constant unit cost equal to £10. a. Suppose firms compete in quantities. How much does each firm sell in a Cournot equilibrium? What is the market price and what are firms' profits? b. Suppose firms compete in price. How much does each firm sell in a Bertrand equilibrium? What is market price and what are firms' profits? c. Would your answer in b. change if there were three firms, one with unit cost = £20 and two with unit cost = £10? Explain why or why not.
d. Would your answer in b. change if firm 1's golf balls where green and endorsed by Tiger Woods, whereas firm 2's are plain and white? Explain why or why not.
Answer:
(a) Note that the inverse demand function is . Then the Cournot quantities are:
The market price is
Profit of Firm 1 =