Question

5) A firm’s market share is the quantity the firm sells, divided by the total market quantity. In an industry there are 11 firms with market shares: 10%, 20%, 15%, 5%, 30%, 10%, and five additional firms with 2% each.

a) The I4 index is defined as the sum of shares of the largest 4 firms in the market. What is the I4 index of market concentration for this market? The I8 index is the sum of the shares of the largest 8 firms in the market. What is the I8 index of market concentration for this market?

c) The HHI (Herfindhal- Hirshman Index) is the sum of squared market shares. What is the HHI of market concentration for this market?

d) Provide an example of an industry that also has 11 firms but is more concentrated than this one according to both the I4 and the HHI index.

e) Provide an example of an industry that also has 11 firms, that is more concentrated than this one according to the I4 index by less concentrated according to the HHI index.

Answer 1

S.No	Market Shares in Descending Order
1	30%
2	20%
3	15%
4	10%
5	10%
6	5%
7	2%
8	2%
9	2%
10	2%
11	2%

a. I4 Index = Sum of market shares of the top 4 firms = 30 + 20 + 15 + 10 =  75

I8 Index = Sum of the market shares of the top 8 firms = 30+20+15+10+10+5+2+2 = 94

c. HHI Index = Sum of squares of market shares of all the firms = 30²+20²+15²+10²+10²+5²+2²+2²+2²+2²+2² = 900+400+225+100+100+25+4+4+4+4+4= 1770

d. Increase the market share of top 4 firms while decreasing the market share of the remaining firms to obtain more concentrated markets according to both I4 and HHI Indices

Let the market shares be 30%, 25%, 15%, 10%, 5%, 5%, 2%, 2%, 2%, 2%, 2% respectively for the 11 firms

I4 Index = 30+25+15+10 = 80

HHI Index = 30²+25²+15²+10²+5²+5²+2²+2²+2²+2²+2² = 900+625+225+100+25+25+4+4+4+4+4 = 1920

e. In order to increase I4 index but reduce HHI index, the market shares of the top 4 firms must be increased while the differences between the market shares are smoothened

Let the market shares be 20%, 20%, 20%, 20%, 5%, 5%, 2%, 2%, 2%, 2%, 2%, 2% respectively for the 11 firms

I4 Index = 20+20+20+20 = 80

HHI Index = 20²+20²+20²+20²+5²+5²+2²+2²+2²+2²+2² = 400+400+400+400+25+25+4+4+4+4+4 = 1670