15.8 herfindahl index of market concentration The Herfindahl index which is used to measure market concentration is defined as n

H = a i

=

1 s 2 i , 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-irm Cournot game. Also compute market output, market price, consumer surplus, industry proit and total welfare. Compute the Herindahl index for this equilibrium.

b.

Suppose two of the n irms merge, leaving the market with n – 1 irms. Recalculate the Nash equilibrium and the rest of the items requested in part (a). How does the merger affect price, output, proit, consumer surplus, total welfare and the Herindahl index?