Price Theory Assignment 2 - Market Power Firms 1 and 2 produce horizontally differentiated products. The demand for firm 1's product is given by the...

Firms 1 and 2 produce horizontally differentiated products. The demand for firm 1’s

product is given by the equation,

Q1 = 100 − P1 + P2/2

The demand for firm 2’s product is given by the equation,

Q2 = 200 − 4P2 + 2P1 .

Firm 1’s marginal cost is MC1 = $10, while firm 2’s marginal cost is MC2 = $20. The

two firms compete in Bertrand competition, by simultaneously selecting prices.

Question 1: What is the equation of firm 1’s reaction function

Question 2: What is the equation of firm 2’s reaction function?

Question 3: Find the equilibrium prices.

Question 4: Find the equilibrium profits.

Question 5: Which firm enjoys the greater market power? Briefly explain your answer.

Now suppose that firm 2 adopts a new technology that lowers it’s marginal cost to

M C2 = 5. (Assume that demand for each firm’s product, and firm 1’s marginal cost

are unchanged.)

Question 6: Find the new equilibrium prices, quantities and profits.

Question 7: What has happened to firm 1’s Lerner Index of market power? Briefly

explain why it has changed.