2). Drug Monopoly with Math!

A recent discovery by Chemonomics, a pharmaceutical company in College Park, has resulted in the production of Relaxam, a drug that prevents test anxiety. Chemonomics has a patent on Relaxam, and the FDA has approved its sale.

a). According to Chemonomics' chief economist, the demand curve for Relaxam is described by the equation:

P = 100-2Q

where Q is in thousands of exam doses. Chemonomics can produce Relaxam at a marginal cost of:

MC = 40 + 2Q

and an average cost of:

AC = (100/Q) + 40 +Q

How much Relaxam will Chemonomics produce? At what price will it be sold?

b). What will the total revenue, total cost and profits be?

c). With its patent, Chemonomics clearly has a monopoly on Relaxam. Because of Relaxam's obvious social importance, the market for Relaxam has come under intense scrutiny by the Department of Justice's (DOJ) Anti-Trust Division, the Food and Drug Administration and the public. Given the situation described in part (a), if you were a regulator with the DOJ, would you prefer some other quantity and price outcome? If so, what would that outcome be? What would be the equilibirum price and quantity in the case of this competitive outcome. (assume that the MC effectively will be the same as the supply curve once the market is competitive)