a cartel case of duopolist

Consider an industry with k + m duopolists. There are m cooperating duopolists who belong to a cartel. The cartel acts like a leader. Each cartel member (each cooperating duopolist ) has an output of qi and cost function Ci = .5q;. There are k followers (fringe duopolists), each with an output y and a cost function Ci = .5yi. The duopolists have identical products and face a market demand function: p = 1 - q -y =, where k m y yi and q = qi Show the effect of an increase in the number of i=1 i=1 followers on the output of each follower