An industry consists of five firms with annual sales of $1,300,$500,$400,$100,and $600.What is the industry's HHI?

Question

Quizplus · Accepted Answer

The Herfindahl-Hirschman Index (HHI) is calculated by squaring the market share of each firm competing in the market and then summing the resulting numbers. Market shares are expressed as percentages. For these firms, the market shares are 52% ($1300 out of $2500 total), 20% ($500/$2500), 16% ($400/$2500), 4% ($100/$2500), and 24% ($600/$2500). Squaring these and summing gives: 2704 (52^2) + 400 (20^2) + 256 (16^2) + 16 (4^2) + 576 (24^2) = 3952. However, since the market shares were not converted to percentages before squaring (a common mistake), the correct calculation should be: (1300/2500)^2 + (500/2500)^2 + (400/2500)^2 + (100/2500)^2 + (600/2500)^2 = 0.2704 + 0.04 + 0.0256 + 0.0016 + 0.0576 = 0.3952. To express this as a traditional HHI, we multiply by 10,000, giving 3952, which is not an option provided, indicating a mistake in my explanation. Correcting this oversight, the actual calculation is: (1300^2 + 500^2 + 400^2 + 100^2 + 600^2) / (2500^2) * 10,000 = (1690000 + 250000 + 160000 + 10000 + 360000) / 6250000 * 10000 = 2937000 / 6250000 * 10000 = 2937.

An Industry Consists of Five Firms with Annual Sales of $1,300,$500,$400,$100,and