Question

2. This question is adapted from our textbook. A monopolist has two segmented markets with demand curves given by P1 = 160 – 91 P2 = 130 – 592 where pı and p2 are the prices charged in each market segment, and qı and q2 are the quantities sold. Its cost function is given by c(q) = 2q2, where q = (1 + 02. Find the monopolist's profit maximising prices p*, pand outputs q*, q* sold in each market.

Answer 1

Case I - Market I Pi = 160-94 Total Revenue (TR) = Piq - TRA= (160-9,99 Marginal Revenue (MRI) - d try differentiation du Warret qe → MR, 2 |(160–71) 9,] [MR = 160-29, C(q) = 2q? (19)= 2 (2,+9) 2 Marginal tast (MG) = (69) - MC, = 4 (q + 22 ) mc, = 49, +492) The optimal condition for the monopoly be (P > MR = MC) . MREMC 160-291 = 491 +492

[160= 64, +422 - 0 Case II - Market 2 B = 130 - 92 Total Revenue (TR2) = P2q2 1 = (130-22) 92 Marginal Revenue - 130 - 92 I MR marginal Lost = dc (9) MG da =/MG = 4 (917 22) The condition be /p> MR=MC A MR=MC » 130-92 = 491 +492 s/130 = 592 +41) - ① solving eqw ☺ and ③ we het 592 +421 = 130 +91=20 49 +691 = 160 22=10 -

- Pi = 160-91 sipi = 160-20 P=140) B = 130 - 22 a l2 = 130 - 10 B = 125 Hence p² = 140 q* = 20 p*= 125 9 * = 20 to maxe profit in Each markets