A firm has a total cost of TC=0.5q2+15q+300 where q is its output, and faces a demand for its product given by q=100-3p where p is the price it charges.
a. Find the profit maximizing price and output for this firm.
b. Is it making a profit? If not, why does the firm keep producing in the short run?
c. If the state imposes a license fee of $100 on the firm, will it continue producing in the short run? How about the long run? Explain.
d. If the state taxes the firm at a rate of 0.2 per unit of output, so there is an additional cost of 0.2q what will happen to the firm's output and price in the short run? Explain.