# Herfindahl-Hirschman index

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An industry consists of 5 firms, with sales of $100,000, $500,000, $400,000, $300,000, and $200,000. Now, suppose the largest and smallest firms merge.

-Calculate the four-firm concentration ratio (C4) before the merger.

-Calculate the Herfindahl-Hirschman index (HHI) before the merger.

-Calculate the four-firm concentration ratio (C4) after the merger.

-Calculate the Herfindahl-Hirschman index (HHI) after the merger.

https://brainmass.com/economics/principles-of-mathematical-economics/herfindahl-hirschman-index-55432

#### Solution Preview

Hello!

Here are your answers:

-Calculate the four-firm concentration ratio (C4) before the merger

The four-firm concentration ratio of an industry is the sum of the market shares of the 4 largest firms in that industry. In this question, there are 5 firms. The four largest ones have sales of $500, $400, $300 and $200 (in thousands).

The market share is easy to compute. The size of this market is:

500 + 400 + 300 + 200 + 100 = $1,500

The market share of each firm is (Sales of the firm/Market size)*100. Ordered by size, here are the market shares of these firms:

Firm 1: ...

#### Solution Summary

Herfindahl-Hirschman index and other items are calculated.