Question

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are​ (as percentages of all hamburgers​ sold): 22 ​percent, 22 ​percent, 18 ​percent, 11 percent, 10 ​percent, 9 percent, and 8 percent.

The​ four-firm concentration ratio for the hamburger industry in this town is (?) percent. ​(Enter your response as a whole​ number.)

What is the Herfindahl index for the hamburger industry in this town?

If the top three sellers combined to form a single firm, what would happen to the four-firm concentration ratio and to the Herfindahl index?

Answer 1

✓ Four firm concentration ratio is calculated by total market share of largest 4 firms out of total market share.

Here market share of 7 burger shops on hamburger market are : 22% , 22% , 18% , 11% , 10% , 9% , 8%. Total = 100%

Largest 4 share is = 22% , 22% , 18% , 11%

Total share of these largest 4 shops is = (22+22+18+11)% = 73%

So, four firm's concentration ratio = 73% . (Answer).

✓ Herfindahl Index is calculated as square of market share of all firms in the hamburger industry.

Herfindahl Index = 22^2 + 22^2 + 18^2 + 11^2 + 10^2 + 9^2 + 8^2

Herfindahl Index = 484 + 484 + 324 + 121 + 100 + 81 + 64

Herfindahl Index = 1658.

✓ If top three sellers combined to form a single firm then market share of that single firm which will be formed by taking 3 largest firm will be = (22+22+18)% = 62%

The remaining share of other shops or firms are - 11% , 10% , 9% and 8% .

So, now four firm's concentration ratio will be = 62% + 11% + 10% + 9% = 92%.

Before Merger of three largest firm the four firm's concentration ratio was 73% but after the merger the concentration ratio becomes 92%. The concentration ratio has increased. It is not good for industry because as concentration ratio will increase monopolised situation will arise.

After the merger of largest 3 firms the share of merger firm is = 62%.

The other four firm's share are - 11% , 10% , 9% , 8%

Herfindahl Index is square of market share of all firms in the hamburger industry.

Herfindahl Index = 62^2 + 11^2 + 10^2 + 9^2 + 8^2

Herfindahl Index = 3,844 + 121 + 100 + 81 + 64

Herfindahl Index = 4,210

Herfindahl Index after top three sellers combined form a single firm is 4,210.

The maximum value of Herfindahl Index is 10,000 and it is possible when there is single firm this single firm has all 100% share in the market.

Here after merger of three largest firms the Herfindahl Index has increased to 4,210 from before merger situation where Herfindahl Index was 1658. As Herfindahl Index has increased after merger of 3 largest firms it is not good for hamburger industry.