Consider an industry which consists of 3 identical firms that are Cournot oligopolists. The inverse market demand is
P(Q)=100-Q

where 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