A monopolist sells in 2 markets. There are Ni buyers in each market. Each buyer in market i has demand given by qi = ai - pi where a1 is greater than a2. Costs are given by C = cQ + 0.5dQ where Q = Q1 + Q2 and where Qi = Niqi is the total output produced in market i, i = 1,2.

a)Find the profit maximizing output and price in each market if themonopolist can price discriminate. Verify that the second order conditions hold providedd is not too negative. Show that/is less than 0 and explain why. This has been answered.

b)Find the profit maximizing output and price in each market if the monopolist cannot price discriminate and serves both markets. Verify that the second order condition holds provided d is not too negative. Show that Q

i = _1,2 (a_i - c) N_i / 2+d (N₁+N₂) for both part a) and b).

c)Find the profit maximizing output and price if only market 1 is served. Verify that the second order condition holds provided d is not too negative. Show that your solution for Q1 is greater in part c) than in part a) if d > 0. Explain why.

d)Now substitute N₁=12, N₂=24, a₁=12, a₂=8, c=1 and d=1/12 into your solutions in a), b) and c). Show that the monopolist serves both markets if they cannot price discriminate and that price discrimination lowers welfare.