Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percentages of all hamburgers sold): 23%, 22%, 18%, 12%, 11%, 8%, and 6%. instructions: enter your answers as whole numbers.
a. what is the four-firm concentration ratio of the hamburger industry in this town?
b. what is the herfindahl index for the hamburger industry in this town?
c. 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?

a. 75%

b. 1,702

c. 94%; 4,334

Explanation:

a. A town has seven burger shops. The market share of these burger shops are 23%, 22%, 18%, 12%, 11%, 8%, and 6%.  

The four-firm concentration of the hamburger industry can be found by calculating the market share of the top four firms.  

Four firm concentration ratio

= 23% + 22% + 18% + 12%

= 75%  

b. The Herfindahl index can be found by squaring the market share of each firm and then summing them up.  

Herfindahl index

= 529 + 484 + 324 + 144 + 121 + 64 + 36  

= 1,702

c. If the top three sellers are combined to form a single firm, there market share will be

= 23% + 22% + 18%

= 63%

The new four firm concentration will be

= 63% + 12% + 11% + 8%

= 94%

The herfindahl index will be

= 3,969 + 144 + 121 + 64 + 36  

= 4,334

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