Please answer the 4 questions below Suppose an industry that

Please answer the 4 questions below.

Suppose an industry that has 10 firms. Below are the market shares for 2008 and 2013 of the 10 firms.

Market Share

Firms

2008

2013

A

B

C

D

E

F

G

H

I

G

26%

21%

16%

10%

9%

7%

4%

3%

2%

2%

22%

23%

19%

9%

8%

7%

6%

4%

1%

1%

1. Calculate the concentration ratio CR4 and the concentration ratio CR8 for 2008 and 2013

2. Calculate the Herfindahl-Hirschmann Index (HHI) for 2008 and 2013

3. Using the CR4, CR8, and HHI, analyze the evolution of the seller concentration in the industry. Has the industry become more or less concentrated?

4. Using the CR4, CR8, and HHI, analyze the evolution of the potential market power of firms in the industry.

Solution

A common type of concentration index is the concentration ratio. Two examples of concentration ratios are the four-firm concentration ratio and the eight-firm concentration ratio. The four-firm concentration ratio is an indicator of the size (as measured by output or sales) of the four largest firms within an industry, compared to the output of the entire industry. It is determined as follows:

CR4 = (X1 + X2 + X3 + X4) / T

where Xn is the output of the nth largest firm and T is the total output of the industry. Likewise, the eight-firm concentration ratio is:

CR8 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8) / T

CR4 for 2008 = (26+21+16+10)/100 = 73/100 = 73%

CR4 for 2013 = (22+23+19+9)/100 = 73/100 = 73%

CR8 for 2008 = (26+21+16+10+9+7+4+3)/100 = 96%

CR8 for 2013 =  (22+23+19+9+8+7+6+4)/100 = 98%

The Herfindahl-Hirschman Index (HHI) is a market concentration index determined as follows:

HHI is 10,000 x [Summation from i 1 to n, of S sub-i squared)

where S is the proportion of market share for the ith firm.

HHI for 2008 = 10,000 x [.26² + .21² + .16² + .10² +.09² + .07² + .04² + .03² + .02² + .02² ] = 1636

HHI for 2010 = 10,000 x [ .22² + .23² + .19² + .09² +.08² +.07² + .06² +.04² + .01²+.01²] = 1622

So the economy has become less concentrated.

answer.