### 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:

$$HHI={\displaystyle \sum}_{i-1}^{N}{\left(100\frac{{S}_{i}}{{\displaystyle \sum _{i-1}^{N}{S}_{i}}}\right)}^{2}$$

where *S _{i}* is the total sales of firm

*i*.

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.