Profit Maximization for Oligopoly
2. You are the dominant firm in an oligopoly, with ten follower firms who take price as given from you. The market demand for your product is Q = 2,000 - 0.1P. Your total cost are TC = 10,000 + 2,000Q. Aggregate total costs for the follower firms are TCF = 1,000Q + 20Q2.
a. Solve for your profit-maximizing price and quantity, and resulting profits.
b. Solve for the optimal production for the follower firms.
c. Verify that the market is in short-run equilibrium. Is the market also in long-run equilibrium? How can we tell? If not, what do you expect will happen as a result?