Principles of Microeconomics / Unit 10 MIC 0903 worked example, 60 to 90 seconds
Measuring a Merger
The idea
From a market's share table, compute the four-firm ratio and the Herfindahl-Hirschman Index before the merger. Then combine the merging firms' shares and recompute both. The increase in the index equals twice the product of the two merging shares. Report the post-merger level and the increase, and note that a merger among small firms can leave the four-firm ratio unchanged while still raising the index.
In practice
Worked example: shares are twenty-five, twenty, fifteen, twelve, ten, eight, six and four percent. The four-firm ratio is seventy-two and the index is six twenty-five plus four hundred plus two twenty-five plus one forty-four plus one hundred plus sixty-four plus thirty-six plus sixteen: one thousand six hundred ten. The third and fourth firms merge into one at twenty-seven. The ratio becomes eighty-two. The increase is two times fifteen times twelve, three hundred sixty, so the index is one thousand nine hundred seventy. If instead the two smallest merged into one at ten, the increase would be two times six times four, forty-eight, the index one thousand six hundred fifty-eight, and the ratio unchanged.
Where people slip
The twice-the-product shortcut works only for the two merging firms; every other square is unchanged. And an increase of forty-eight is small even though the merged firm doubled in size, because the index weights large shares; that is the point of squaring.
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