Principles of Microeconomics / Unit 9 MIC 0819 worked example, 60 to 90 seconds
Computing Both Measures
The idea
From a table of market shares, compute the four-firm ratio by adding the largest four. Compute the Herfindahl-Hirschman Index by squaring each share and adding all the squares, including the small firms. Then test a proposed merger: combine the merging firms' shares into one, recompute both measures, and report the index's new level and the increase the merger caused. Two industries with the same four-firm ratio can have very different indexes, which is why regulators use the index.
In practice
Worked example: a market's shares are thirty, twenty-five, twenty, ten, ten and five percent. The four-firm ratio is eighty-five. The index is nine hundred plus six twenty-five plus four hundred plus one hundred plus one hundred plus twenty-five, two thousand one hundred fifty. Now the two ten-percent firms merge into one at twenty. The ratio is still eighty-five, since the fourth firm is now twenty rather than ten plus something below. The index becomes nine hundred plus six twenty-five plus four hundred plus four hundred plus twenty-five, two thousand three hundred fifty: an increase of two hundred.
Where people slip
Square the percentages as whole numbers, thirty as thirty, not as a fraction; the scale from zero to ten thousand depends on it. And include every firm in the index; leaving out the small ones understates it, though usually by little.
Your place on the trail
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