Question

Your job is to calculate concentration ratios for different industries. Based on this information, answer the following three questions. Where necessary, please ensure that you show FULL calculations, and keep your answers to 2 decimal points. (a) What is the difference between the Herfindahl Hirschman Index (the HHI) and the n-firm Concentration Ratio? (b) Suppose that there are a total of 6 firms in an industry. You find out that the sales are as follows: Firm 1 has annual sales of $2000; Firm 2 has annual sales of $1800; Firm 3 has annual sales of $1500; Firm 4 has annual sales of $700; Firm 5 has annual sales of $600 and Firm 6 has annual sales of $250. Calculate the HHI for this industry. (c) Now suppose that in a different industry, which is called Industry JKL, and which has 5 firms, you find that the sales of four of the firms are $650,000, $250,000, $150,000, and $145,000. If the C4 ratio is 95 percent, then what is the HHI?

Answer 1

A) HHI: it is the sum of squares of market share of each firm in industry

n-firm concentration ratio: it's also a measure of market concentration & market power & is obtained as the sum of the market share of top n firms

As HHI takes in to account all of the firm's market shares, while N-C measure only incorporates market share of top n firms, so HHI is more appropriate measure

B)

Firm	sales	% of market share = (sales/total sale size)*100
1	2000	29.2%
2	1800	26.27%
3	1500	21.9%
4	700	10.22%
5	600	8.8%
6	250	3.65%

Total sale size = 6850

HHI = Summation of squares of market share

= (29.2)² + (26.27)² + (21.9)² + (10.22)² + (8.8)² + (3.65)²

= 2217.5738

= 2217.58

C) C4 is sum of market share of top 4 firms

= ((650+250+150+145)*1000)/x = 95

1195,000/x = .95

So , x = 1195,000/.95 = 1258,000

So sale of 5th firm= 1258,000-1195,000 = 63,000

So HHI=

((650,000)² + (250,000)² + (150,000)² + (145,000)²+ (63,000)²)/(1258,000)²

= 3364.75