Concentration Ratios

N-firm concentration ratio is sum of the market shares of the N largest firms.

Herfindahl index (N-firm or industry) is sum of the squared market shares. Herfindahl < 0.1 is competitive industry, >0.18 is concentrated. 1/ Herfindahl is equivalent number of equal-size firms.

Question:
The three largest firms in a $200bn industry have revenues of$50bn, $30bn &$20bn. Assuming that there are 10 other equal-size firms in the industry, calculate the 3-firm concentration ratio & the Herfindahl index for the entire industry.

Ans:
Three-firm concentration ratio = (50+30+20)/200 = 0.50

Herfindahl = (50/200)2 + (30/200)2 + (20/200)2 + 10(10/200)2

= 0.12