Consider an industry which consists of 3 identical firms that are Cournot oligopolists. The inverse

Consider an industry which consists of 3 identical firms that are Cournot oligopolists. The inverse market demand isP(Q)=100-Qwhere Q=q1+q2+q3 & qi is output of firm i, i E {1,2,3} . Each firm has a constant average cost of $20.1. Derive the cournot equilibrium output & profit for a firm as well as the market price. What is the H-index for this market?2. Suppose two of these firms contemplate merging with one another. Assume that the merger has no impact on the average cost and, thus, it remains at $20 for all firms. The merger only changes the market concentration. Derive the post-merger Cournot equilibrium output and profit for a firm as well as the market price.3. Since the merger has no impact on the production efficiency, any incentive for merger must come from a potential increase in market power. Is there an incentive to merge in this case?4. Show that a merger to monopoly (all 3 firms merging together) is profitable