The Herfindahl index which is used to measure market concentration is defined as
where st=qi/Q is firm i’s market share. The higher is H, the more concentrated the industry is said to be.
a. Determine the Nash equilibrium of this n-firm Cournot game. Also compute market output, market price, consumer surplus, industry profit and total welfare. Compute the Herfindahl index for this equilibrium.
b. Suppose two of the n firms merge, leaving the market with n – 1 firms. Recalculate the Nash equilibrium and the rest of the items requested in part (a). How does the merger affect price, output, profit, consumer surplus, total welfare and the Herfindahl index?