Price Theory

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