Price Theory

Assignment 2 { Market Power

Firms 1 and 2 produce horizontally dierentiated products. The demand for rm 1’s
product is given by the equation,
Q1 = 100 ?? P1 +
P2
2
:
The demand for rm 2’s product is given by the equation,
Q2 = 200 ?? 4P2 + 2P1:
Firm 1’s marginal cost is MC1 = $10, while rm 2’s marginal cost is MC2 = $20. The
two rms compete in Bertrand competition, by simultaneously selecting prices.
Question 1: What is the equation of rm 1’s reaction function? (3 Marks)
Question 2: What is the equation of rm 2’s reaction function? (3 Marks)
Question 3: Find the equilibrium prices. (2 Marks)
Question 4: Find the equilibrium prots. (2 Marks)
Question 5: Which rm enjoys the greater market power? Brie
y explain your answer.
(2 Marks)
Now suppose that rm 2 adopts a new technology that lowers it’s marginal cost to
MC2 = 5. (Assume that demand for each rm’s product, and rm 1’s marginal cost
are unchanged.)
Question 6: Find the new equilibrium prices, quantities and prots. (4 Marks)
Question 7: What has happened to rm 1’s Lerner Index of market power? Brie
y
explain why it has changed. (4 Marks)
1

Price Theory

Assignment 2 { Market Power

Firms 1 and 2 produce horizontally dierentiated products. The demand for rm 1’s
product is given by the equation,
Q1 = 100 ?? P1 +
P2
2
:
The demand for rm 2’s product is given by the equation,
Q2 = 200 ?? 4P2 + 2P1:
Firm 1’s marginal cost is MC1 = $10, while rm 2’s marginal cost is MC2 = $20. The
two rms compete in Bertrand competition, by simultaneously selecting prices.
Question 1: What is the equation of rm 1’s reaction function? (3 Marks)
Question 2: What is the equation of rm 2’s reaction function? (3 Marks)
Question 3: Find the equilibrium prices. (2 Marks)
Question 4: Find the equilibrium prots. (2 Marks)
Question 5: Which rm enjoys the greater market power? Brie
y explain your answer.
(2 Marks)
Now suppose that rm 2 adopts a new technology that lowers it’s marginal cost to
MC2 = 5. (Assume that demand for each rm’s product, and rm 1’s marginal cost
are unchanged.)
Question 6: Find the new equilibrium prices, quantities and prots. (4 Marks)
Question 7: What has happened to rm 1’s Lerner Index of market power? Brie
y
explain why it has changed. (4 Marks)
1