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): 27%, 26%, 22%, 12%, 7%, 4%, and 2%.

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?

     

Answer 1

Market share of firms = 27%, 26%, 22%, 12%, 7%, 4%, 2%

a) Four firm concentraction ratio = (Market share of top 4 firms / Total market shares of all firms) = [(27% + 26% + 22% + 12%) / 100%] = 87%

b) Herfindahl index is the sum of square of market share of all firms which is 27^² + 26^² + 22^{^2} + 12^² + 7^² + 4^² + 2^² = 2,102

c) If top three sellers combined to form a single firm, market share of firms would be 75%, 12%, 7%, 4%, 2%

Four firm concentration ratio would be [(75% + 12% + 7% + 4%) / 100%] = 98%

HHI index would be 75^² + 12^{^2} + 7^{^2} + 4^² = 5,834