Assume an industry contains four firms and has a Herfindahl-Hirschman Index equal to 3,450. If three of the firms have market share of 50%, 25%, and 10%, what is the market share of the remaining firm?

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. For the given firms with market shares of 50%, 25%, and 10%, their contributions to the HHI are 2500 (50^2), 625 (25^2), and 100 (10^2) respectively. Subtracting these from the total HHI of 3450 gives the contribution of the fourth firm's market share squared. 3450 - (2500 + 625 + 100) = 225. Taking the square root of 225 gives 15, which means the fourth firm has a market share of 15%.

Assume an Industry Contains Four Firms and Has a Herfindahl-Hirschman