### Herfindahl - Hirschman Index (HHI)

Governments are interested in controlling market power, and to do this they need a way of measuring it. The most common tool is called the Herfindahl - Hirschman Index (HHI)

This is the sum of the squares of each firm’s market share, expressed in percentage terms:

$$HHI={\displaystyle \sum}_{i=1}^{N}{{S}_{i}}^{2}$$

where *S _{i}* is the market share of firm

*i*in percentage. Market share can be calculated as firm's sale divided by total market sale.

So, if we have one firm in an industry, the HHI will be 10,000, and if we have an infinite number of tiny firms, it will approach zero.

#### Example

Say we have an industry with four firms. They have market shares of 40%, 30%, 20% and 10% respectively. What is the HHI?

HHI = $={40}^{2}+{30}^{2}+{20}^{2}+{10}^{2}=1600+900+400+100=3000$

Now, what happens if the largest firm buys out the third largest firm?

Now, we have three firms with the following market shares: 60%, 30% and 10%.

So, the HHI $={60}^{2}+{30}^{2}+{10}^{2}=3600+900+100=4600$ . The concentration has increased by over 50%.

- If the HHI is less than 1000, a market is generally considered to be not concentrated.
- If the HHI is between 1000 and 1800, a market is thought to be “moderately concentrated.”
- If the HHI is above 1,800, the industry is considered to be highly concentrated.

In the third case, governments will often act to reduce concentration. This is called an “anti-trust” action.