Problem 2 (Third-degree price discrimination). Suppose a monopolist sells its product to two groups of buyers: teenagers (T) and adults (A). The inverse demand functions of these two groups are given by PT(QT) : 3 QT and PA(QA) : 5 QA, respectively. Note that in this question, the monopolist is able to distinguish between two groups, and can possibly charge different prices. (a) Let MC : 1 be the marginal cost of production. If this monopolist charges a single price, what is the optimal price P*? (b) Still assume M C : 1. Now the monopolist charges two different prices to the groups. Find the optimal prices Pf: and P2. ((3) Instead of constant marginal cost, now suppose the cost function is C(Q) : %(QT+QA)2- Is this problem still separable into two independent optimizations? What prices should the monopolist Charge to these two groups