If there are six firms in a market, and the following market share percentages are provided, it is very much possible to calculate and analyze the Industrial Concentration.

This note will outline how we can calculate this, with reference to the following information:

We must first notice that one value is missing, before we can continue with the calculation (using method 1 or method 2) it is recommended to determine all percentage market shares of all the given firms in the market. This can be done by simple algebra.

\( X% = 100 - (50 + 25 + 10 + 10 + 10 + 2) )

\( \therefore X% = 3% //)

We now have all the values of the table and can continue with our calculation.

Let us look at the first method,

Herfindahl Hirschman Index (HHI)

• This method involves squaring all the percentage market shares in the market, then adding them together.
• Mathematically, this may be represented as: ( HHI = \sum s^2 )

Interpretation and Analysis of the HHI Value

• If the HHI can only fall between 0 and 10 000.
• Mathematically, this may be represented as ( 0 < HHI < 10 000 ).
• Where 0 represents Perfect Competition and 10 000 represents Monopoly.
• If the HHI lies between 0 and 1 000 (0< HHI < 1 000) - the market is NOT CONCENTRATED.
• If the HHI lies between 1 000 and 1 800 (0 < HHI <1 800) - the market is MEDIUM CONCENTRATED.
• If the HHI lies over 1 800 (HHI >1 800) - the market is HIGHLY CONCENTRATED.

Now if we refer back to the table above; let us calculate the HHI of the market and hence interpret the results.

\( HHI = 50^2 + 25^2 + 10^2 + 10^2 + 3^2 + 2^2 )

( HHI = 3338 )

Let us interpret this HHI of 3338,

It falls within the range of HHI > 1 800 - therefore it is HIGHLY CONCENTRATED.

Now, let us look at the second method,

Four-Firm Concentration Ratio ( (C_4 ) )

• This method involves adding the percentage market shares of the four largest firms in the market (hence the name four-firm).
• ⚠️ Note that you are NOT squaring these values - you are simply adding the percentages. This is a common mistake made by students.

Interpretation and Analysis of the Four-Firm Concentration Ratio Value

• The four-firm value concentration value can only fall between 0%and 100%.
• Mathematically this may be represented as ( 0% < HHI < 100% ).
• Where 0% represents Perfect Competition and 100% represents Monopoly.
• If the four-firm concentration value falls between 0% and 50% - the market has a LOW CONCENTRATION.
• If the four-firm concentration value falls between 50% to 80% - the market has a MEDIUM CONCENTRATION.
• If the four-firm concentration falls between 80% and 100% - the market has a HIGH CONCENTRATION.

Now if we refer back to the table above; let us calculate the Four-Firm Concentration of the market and hence interpret the results.

\( C_4 = 50% + 25% + 10% + 10% )

\( C_4 = 95% )

Let us interpret this Four-Firm Concentration of 95%.

It falls withing the range of 80% to 100% meaning it is HIGHLY CONCENTRATED.

🚨NOTICE BOTH METHODS (HHI & FOUR-FIRM) PRODUCE THE SAME INTERPRETATION OF HIGHLY CONCENTRATED.

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More knowledge the better - for your CAPE Economics Unit 1 Syllabus, you are only required to know about the Four-Firm Concentration & HHI method. However the Firm Concentration method has some variations.

There are also Two-Firm Concentration Ratios, Three-Firm Concentration Rations - etc.

This simply means summing the percentages of the two/three highest percentage market shares in the market. Hence the name TWO-firm, THREE-firm and FOUR-firm.

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