Question

 

Consider an industry with 21 producers that has the following market share:

one producer: 18%

two producers: 12% each

six producers: 5% each

eight producers: 3% each

four producers: 1% each

The second and third largest producers are wanting to merge.

Calculate the four-firm concentration ratio and the Herfindahl-Hirshman Index for this industry, both before and after the proposed merger.

Answer 1

Before the merger:

The table below shows the market shares of 21 firms in the given industry arranged in descending order and the squares of the market shares before the merger

Before the Merger
S.No	Market Share (%)	Square of market share
1	18	324
2	12	144
3	12	144
4	5	25
5	5	25
6	5	25
7	5	25
8	5	25
9	5	25
10	3	9
11	3	9
12	3	9
13	3	9
14	3	9
15	3	9
16	3	9
17	3	9
18	1	1
19	1	1
20	1	1
21	1	1
Sum of the squares of market shares	838

Four-firm concentration ratio, CR4 = Sum of the market shares of the 4 largest firms = 18% + 12% + 12% + 5% = 47%

Herfindahl-Hirshman Index, HHI = Sum of the squares of the market shares of all the firms = 838

After the merger:

The market shares of the second and third largest producers are 12% and 12% respectively. After their merger, the market share of the new firm becomes 12% + 12% = 24%

After the merger
S.No	Market Share (%)	Square of market share
1	24	576
2	18	324
3	5	25
4	5	25
5	5	25
6	5	25
7	5	25
8	5	25
9	3	9
10	3	9
11	3	9
12	3	9
13	3	9
14	3	9
15	3	9
16	3	9
17	1	1
18	1	1
19	1	1
20	1	1
Sum of the squares of market shares	1126

Four-firm concentration ratio, CR4 = Sum of the market shares of the 4 largest firms = 24% + 18% + 5% + 5% = 52%

Herfindahl-Hirshman Index, HHI = Sum of the squares of the market shares of all the firms = 1126