Question

Consider the following industry that has eight firms with the following market share percentages: 20, 20, 16, 16, 9, 8, 6, and 5.

a) Calculate the four-firm concentration ratio for this industry.

b) Calculate the Herfindahl-Hirschman index for this industry.

c) Calculate the “number equivalent” for the HHI you calculated in part b. Interpret what the value means.

d) Now suppose that only the market shares of the top four firms are given for this market (i.e., 20, 20, 16, 16). What would be the minimum value the HHI can take for this market? What would be the maximum value the HHI could take for this market? Explain how you know it is the minimum and maximum values.

Answer 1

Answer for a)

Total share= 20+20+16+16+9+8+6+5=100

First four highest share = 20,20,16,16 Sum of Four Firm share=72

Four Firm Concentration share=SUm of Highest share first four firm/ Total share=75/100=75%

ANswer fpr b)

HHI index is just the square of all shares=0.20^2+0.20^2+0.16^2+0.16^2+0.09^2+0.08^2+0.06^2+0.05^2=15.18%

ANswer for c)

Number equivalent for HHI in this case =1/(0.20^2+0.20^2+0.16^2+0.16^2+0.09^2+0.08^2+0.06^2+0.05^2)=1/0.1518=6.75 i,e Approximately 7 equal sized firms

Hence This industry is as equivalent as 7 equivalent firms in an industry wiht respect to share

Answer for d)

If we have an infomraion only about 4 firms out of 8 firms then minimum value for HHI can be calculated as below

HHI=Sum of Square of shares for known firms+ Unknown Parameter

This unknown parameter will provide minimum and maximum HHI

Min Unknown Parameter=(1-(0.2+0.2+0.16+0.16))^2/(8-4)=0.216/4=0.054

Max Unknown Parameter=(1-(0.2+0.2+0.16+0.16))^2=0.216

Min HHI=0.72^2+0.054=0.5184+0.054=0.5724

Max HHI=0.72^2+0.216=0.5184+0.22=0.7384