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