3. The Herfindahl index Suppose that three firms make up the entire bicycle manufacturing industry. One has a 50% market share, and the other two have a 25% market share each. The Herfindahl index of this industry is . A new firm, Abe's Bikes, enters the bicycle manufacturing industry and immediately captures a 15% share of the market. This would cause the Herfindahl index for the industry to . The largest possible value of the Herfindahl index is 10,000 because: An index of 10,000 corresponds to a monopoly firm with 100% market share An industry with an index higher than 10,000 is automatically regulated by the Justice Department An index of 10,000 corresponds to 100 firms with a 1% market share each

Please refer to Explanation.

Explanation:

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I) The way to find the herfindahi index is to take the sum of squares of market shares of all firms in the market

In this scenario therefore we can work it out like this,

Herfindahi index = (50)^2 +(25)^2 + (25)^2

= 3750

The Herfindahi Index is 3750

ii) When there is a new entry into the market, it signifies a rise in competition. This will cause the Herfindahi Index to FALL. Using Abe's bike as an example. Let's say they captured 5% from each firm.

That would mean then that the index is,

Herfindahi index = (45)^2 +(20)^2 + (20)^2 + (15)^2

= 3,050

III) The largest possible value of the Herfindahl index is 10,000 because:

An index of 10,000 corresponds to a monopoly firm with 100% market share

A monopoly would have a 100% market share. This would mean then that of the Herfindahi Index was calculated for it, it would come to 10,000. A Monopoly with 100% signifies the highest amount of the market that can be taken. Anything above 10,000 is implausible.

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