Profit Maximization for Oligopoly

Question

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?

Answer 1

Quick question re: the supply curve of the following firms. If the aggregate total costs of the following firms TCF = 1,000Q + 20Q^2, then wouldn’t you find the supply curve of the following firms by horizontally adding their individual supply curves instead of taking the derivative of the aggregate TC?  If TCF = 1,000Q + 20Q^2 then the TC for an individual following firm = 100Q + 2q^2 and their MC = 100 + 4q.  Rearranging P = 100 + 4q, or q = 0.25P - 25.  Since there are 10 firms, then the supply Q = 10q = 2.5P - 250, or P = 100 + 0.4Q.  This yields a very different supply curve and answer. I think they meant for the supply curve to equal 1,000 + 40Q in order for the question to work mathematically, but since they gave TC I think you need to dis-aggregate then sum individual MCs horizontally. Thoughts?

Answer 2