Suppose that a firm is the only domestic producer of a commodity and that

Question

there are no imports of the good. The firm’s total cost and demand curves are
given by the following two equations:

TC = 6Q + ·05Q2 : Q = 360 - 20P

q) The government wishes to impose a maximum price of $14 on the
commodity. Assuming that the firm is a profit maximiser, what
quantity will it produce and what will be the level of its profits.

p.s. originally, p=15 and q=60

Answer 1

Hummm.
This firm should act like a monopolist. Your P=15 and Q=60 are what the monopolist would do sans any government intervention.

With a price cap below what the monopolist would charge, simply plug 14 into the demand equation and solve for Q. Total revenue will be 14*Q. Plug the Q into the total cost equation then calculate profit.