Question

Consider a market of pens where there are 15 firms: one fimm sells 870 pens, 4 firms sell 250 pens each, and 10 firms sell 120 pens each. a. Determine the market shares for each firm. b. Calculate the four-firm concentration ratio for this industry. c. Calculate the eight-firm concentration ratio for this industry. d. Calculate the Herfindahl-Hirshman index for this industry. e. What are the measures above used for?

Answer 1

a)

Total number of pens sold in the market = 870 + 4 $\times$ 250 + 10 $\times$ 120

Total number of pens sold in the market = 3070 pens

Market share of the firm that sells 870 pens = 870 $\div$ 3070 = 28.34%

Market share of the firm that sells 250 pens = 250 $\div$ 3070 = 8.14 %

As there are 4 firms that sell 250 pens each, the market share of 4 firms = 32.57 %

Market share of the firm that sell 120 pens each = 120 $\div$ 3070 = 3.91%

As there are 10 firms that sell 120 pens eacgh, the market share of 10 firms = 39.09%

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b)

Four firm concentration ratio = Sales accounted by four largest firms 870 + 250 x 3 Total industry sales 3070

Four firm concentration ratio = 52.77%

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c)

Eight firm concentration ratio= Sales accounted by eight largest firms 870 + 250 x 4 + 120 x 3 Total industry sales 3070

Eight firm concentration ratio = 72.64 %

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d)

The sum of the squares of the market share of each firm is known as Herfindahl-Hirschman index.

HHI index = 28.34² + 8.14 ² +  8.14 ² + 8.14 ² ​​​​​​​+ 8.14 ² ​​​​​​​+ 3.91² + 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​+ 3.91² ​​​​​​​

HHI index = 1221.1

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e)

The HHI index gives a measure of market concentration and a HHI index below 1000 suggests that the market is not concentrated and HHI index above 1800 is considered to be highly concentrated. A HHI index between 1000 and 1800 suggests that the market is moderately concentrated.

In the market for pens, the HHI index of 1221.1 suggests that the market is moderatly concentrated.

The measures of concetration ratio gives the market share of the four or eight largest firms in the market. A high concetration ratio suggests that the market is dominated by a few large firms.