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Razi's Mathsoul Poster

Razi is a competition (or antitrust) lawyer. He is advising beverage manufacturer Alitani on any competition law constraints to them acquiring Hydrator, a small competitor.

Background
Razi will investigate this by using market shares (see table alongside) to calculate the industry concentration HHI (Herfindahl-Hirschman Index) using the expression below:

HHI Razi Mathsoul Posters Index formula

- n is the number of competitors, and si the market share of each.

Razi's Poster Questions
Q1.
What is the HHI index value before and after the acquisition?
Q2. How much is the HHI expected to change? Changes of 100 or more are of interest to regulators in the United States in industries with existing HHI over 1800. In Europe, they are of interest if changing by 250 points from an existing level of over 1000.

Q3. What is the maximum possible value of the HHI index, and its minimum possible value? What industry structures apply for each of these cases?

Razi Mathsoul Posters Worksheet Market Share Table

Q4. The HHI index is claimed to increase both as the number of firms in the market decreases, and as the disparity in size between those firms increases? Is this correct? Can you construct counterexamples? Would the HHI formula still do this if the exponent was other than 2 e.g. 1 or 3 or 0.5 for instance?
Q5. Sometimes the HHI is calculated using decimal market shares, with 40% share being 0.4 etc. What are the mamimum and minimum HHI decimal values?

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Worksheet last updated on 7 August 2008  

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