Question

3. A monopolist sells in two markets and can price discriminate between them The demand curves for the two markets are: Pl 8-1 and P2 10-92 The firm's total cost is tc = 5-41 + g2). The firm has a production capacity constraint of qi +q2 S 3. The firm's objective is to maximise profit subject to the capacity constraint and the requirement that qı, q2 2 0. (i) Write the firm's profit as a function of qı and q2. (ii) Write the Lagrangean (either the standard Simon & Blume version or the Kuhn-Tucker version) for the firm's maximisation problem and the associated first order conditions. iii) Solve the first order conditions.

Answer 1

戛_f's P111 t,Rg2..te 12 231 512

11-349-5 41-92 t 1:0 1% %2 2 13 了2 1yA2

%2 011 42 -92-32