A dominant firm operates in various markets. In one of these markets, it is a monopolist and produces with the following cost function: C(q1) = 5q1. The market demand is P = 1005 - Q.
(a) Find the profit maximizing P and q1 and profit.
(b) A new fringe firm with C = 28,900 + (qf^2)/4 enters the market. The fringe firm acts as a price taker and maximizes its profits. The dominant firm, after the entry , subtracts the fringe firm's supply and behaves as a monopolist for the residual demand. Find the new profit maximizing P, q1, qf and profits as well.
My attempt for (a):
P = 1005 - Q.
MR = 1005 - 2Q.
MR = MC.
1005 - 2Q = 5
Q = 500
P = 505
Profit = 505 x 500 - 5 x 505 = 249975
Hopefully I'm right.
My real problem is I'm stuck on (b). I'm not familiar with price taker. I did read my course book but it wasn't that helpful. I'd appreciate if anyone can help me, thank you. Please let me know if (a) was right as well