Solve for the profit maximizing level of output of each

Question

All firms operating in a competitive market have cost functions: C(Q) = 16 - 3Q+ Q², where their marginal costs are: MC(Q) = -3 + 2. The average total cost is: ATC(Q) = (16/Q)-3+Q

a) The firm is currently in the short-run, where price is:  P= $9. Solve for each firm's profit-maximizing level of output, Q^*.

b) How much profit does each firm make in the short-run? Will firms enter or exit the market in the long-run?

c) Solve for the profit maximizing level of output of each firm in the long-run. (hint: each firm earns zero profit in the long-run...)

d) What price results in the long-run?