How the herfindahl-hirschman index is affected


Question:

Based only on the knowledge that the premerger market share of two firms proposing to merge was 20 percent each, an economist working for the justice department was able to determine that, if approved, the post merge HHI would increase by 800. How was the economist able to draw this conclusion without knowledge of the other firms' market shares? From this information can you devise a general rule explaining how the Herfindahl-Hirschman index is affected when exactly two firms in the market merge?

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Macroeconomics: How the herfindahl-hirschman index is affected
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