A monopolist sells its product in two markets, North (N) and South (S). Demand in the North is PN = 100 - QN. Demand in the South is PS = 220 - 5 QS. The firm's cost function is C(Q) = Q^2 , where Q is the total production (i.e., Q = QN + QS).

a. What is the aggregate demand curve facing the monopolist? Hint: at what prices does it sell only to the South, and at what prices does it sell to both North and South?

b. If the monopolist must charge the same price in the North and South, what price does it charge? How many units does it sell in each region? What is its profit?

c. Suppose the monopolist can charge different prices in the North and South. What price should it charge? How many units does it sell in each region? What is its profit?

d. Repeat parts (a) - (c) assuming that demand in the North remains the same but demand in the South is PS = 165 - QS