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 > a2. Costs are given by C cQ 0.5dQ2

where Q = Q1 + Q2 and where Qi = Niqi is the total output produced in market i, i = 1,2.

a) (10 marks). Find the profit maximizing output and price in each market if the

monopolist can price discriminate. Verify that the second order conditions hold provided

d is not too negative. Show that

< 0 and explain why.