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): 19 percent, 22 percent, 18 percent, 12 percent, 11 percent, 10 percent, and 8 percent. percent. (Enter your response as a The four-firm concentration ratio for the hamburger industry in this town is whole number.) The Herfindahl index for the hamburger industry in this town is 1. (Enter your response as a whole number.) Suppose the top three sellers combined to form a single firm. The four-firm concentration ratio would be percent. (Enter your response as a whole number.) Suppose the top three sellers combined to form a single firm. The Herfindahl index would be (Enter your response as a whole number.)

Answer 1

a.

Before merging
S.No	Market share	Square of market share
1	22	484
2	19	361
3	18	324
4	12	144
5	11	121
6	10	100
7	8	64
-	Sum of squares of market shares	1598

1. Four-firm concentration ratio for the hamburger industry = Sum of the market shares of the four largest firms = 22% + 19% + 18% + 12% = 71%

Ans: 71

2. Herfindahl index for the hamburger industry = Sum of the squares of the market shares of all the firms = 1598

Ans: 1598

Top three sellers combine to form a single seller.

Therefore, the market share of the combined firm = 22% + 19% + 18% = 59%

After merging
S.No	Market share	Square of market share
1	59	3481
2	12	144
3	11	121
4	10	100
5	8	64
-	Sum of squares of market shares	3910

3. Four-firm concentration ratio for the hamburger industry = Sum of the market shares of the four largest firms = 59% + 12% + 11% + 10% = 92%

Ans: 92%

4. Herfindahl index for the hamburger industry = Sum of the squares of the market shares of all the firms = 3910

Ans: 3910