Question

1. Market concentration
   1. Suppose that there are 10 firms in a market, and each of them has an equal market share. What is the value of the Herfindahl-Hirschman Index (HHI) in this market?  
   2. Suppose instead that in this market one firm dominates such that it has a 90% market share, while the remaining nine firms each have an equal share of the remainder.  What is the value of HHI in this case?  (Hint!  10% of the market is divided among 9 firms, so each firm’s share is ?)
   3. What is the largest value HHI can take?  What market structure does this describe?
   4. What is the smallest value HHI can take?  What market structure does this describe?

Answer 1

a) The market share of 10 firm is 10% each

HHI = 10² + 10² + 10² + 10² + 10² + 10² + 10² + 10² + 10² + 10²

         = 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100

        = 1,000

b) HHI = 90² + 1.11² + 1.11² + 1.11² + 1.11² + 1.11² + 1.11² + 111² + 1.11² + 1.11²

            = 8,100 + 1.2321 + 1.2321 + 1.2321 + 1.2321 + 1.2321 + 1.2321 + 1.2321 + 1.2321 + 1.2321

            = 8,111.09

c) The largest value HHI can be 10,000. Because if there is only one firm in the market and it has 100% market share, the HHI = 100² = 10,000. This market structure is describe as monopoly.

d) The smallest value HHI can be 0. Because if there is thousands firm in the market and each have nearly 0% market share, the HHI = 0² = 0. This market structure is describe as Perfect Competition.