Consider a monopolist which faces the following demand curves for its product in the export market A and the domestic market B. Inverse demand curve in the export market: QA = 360 – 2pA Inverse demand curve in the domestic market: QB = 200 – pB where pi and Qi denote price and quantity sold in market i where i = A, B. The monopolist’s cost function is given by: c(Q) = 0.25Q^2 where Q = QA + QB. Assume that resale between the two markets is not possible and the monopolist maximizes profits. (a) (3 marks) Find pA and pB that maximize the monopolist’s profits. (b) Suppose the home government in country B imposes a restriction that the monopolist cannot sell more in the export market. That is: QA ≤ QB must hold. However, the monopolist can charge two different prices in countries A and B. Find the amount of output that the monopolist sells in each country and the resulting price levels (which will be different for A and B) that maximize the monopolist’s joint profits (i.e., the sum of profits in the two countries). (c) Suppose that the WTO prohibits price discrimination. That is, the monopolist cannot charge two different prices in A and B. Find the unique price that maximizes the monopolist’s joint profits (i.e., the sum of profits in the two markets).