If a firm with a 20 percent market share merges with a firm with a 5 percent market share and the other firms have market shares of 40 percent,15 percent,10 percent,and 10 percent,respectively,the Herfindahl-Hirschman Index will _____

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The Herfindahl-Hirschman Index (HHI) is calculated by summing the squares of the market shares of all firms in the market. Before the merger, the HHI is $20^2 + 5^2 + 40^2 + 15^2 + 10^2 + 10^2 = 400 + 25 + 1600 + 225 + 100 + 100 = 2450$. After the merger, the market shares are 25%, 40%, 15%, 10%, and 10%, so the HHI is $25^2 + 40^2 + 15^2 + 10^2 + 10^2 = 625 + 1600 + 225 + 100 + 100 = 2650$. The difference is $2650 - 2450 = 200$, indicating the HHI rises by 200.

If a Firm with a 20 Percent Market Share Merges