Need help answering this.

8. (15 points) The inverse market demand curve for a certain commodity is p=100 -10q, and costs to a single firm of producing it are C(q) = 120 +40q. (i) What is the socially desirable quantity? To do this you will need to verify that TS=CS+Prots>0 at this output level. Otherwise, the socially optimal level is zero. (ii) Show that even a rm with monopoly power would not be willing to produce this good. (iii) How might the government ensure that the socially optimal level of output? Specically, would regulation of price and a subsidy be required? If so, what should price and the subsidy be