Question

Suppose that the top six firms in an industry have total annual sales of $200 billion, $100 billion, $50 billion, $60 billion, $20 billion, and $10 bilion, respectively. Instructions: Round your answers to the nearest whole number.

a. What is the four-firm concentration ratio for this industry? percent
b. Whot is the Herfindahl index for this industry?
c. Suppose another industry has a Herfindaht index of 3,000. Firms in this industry are likely to have market power.

Answer 1

The four-firm concentration ratio for this industry is 57%. The Herfindahl index for this industry is 56,500. A Herfindahl index of 3,000 indicates that firms in an industry are likely to have market power.

Step-by-step explanation:

a. To calculate the four-firm concentration ratio, we add the market shares of the four largest firms. In this case, the total market shares of the top four firms are: 200 + 100 + 50 + 60 = 410 billion. The four-firm concentration ratio is then calculated by dividing the market share of the four largest firms by the total market share of all firms in the industry and multiplying by 100. So, the answer is (410 / (200 + 100 + 50 + 60 + 20 + 10)) x 100 = 57%.

b. The Herfindahl index (HHI) is calculated by taking the squared market shares of all firms in the market and summing them. In this case, we have 6 firms, so we square their market shares and sum them: 200² + 100² + 50² + 60² + 20² + 10² = 56,500. Therefore, the Herfindahl index for this industry is 56,500.

c. A Herfindahl index of 3,000 indicates a high concentration in the market and suggests that there are few competitors. It is likely that firms in this industry have market power.

Answer 2

The four-firm concentration ratio of the given industry is 93%, and its Herfindahl-Hirschman Index (HHI) is 2923. Firms in another industry with an HHI of 3000 are likely to have significant market power.

Step-by-step explanation:

To calculate the four-firm concentration ratio for this industry, you add the market shares of the four largest firms. In this case, the top four firms have sales of $200 billion, $100 billion, $50 billion, and $60 billion. Assuming these are the market shares, the four-firm concentration ratio is calculated as follows: ((200+100+50+60) / Total Sales) × 100 = (410 / Total Sales) × 100. Given that we don't have the total sales for the industry, we'll assume the total sales are the sum of the six firms provided, which is $440 billion. Thus, the ratio is (410 / 440) × 100 = 93.18%, rounding to the nearest whole number gives us 93%.

The Herfindahl-Hirschman Index (HHI) is calculated by squaring the market share of each firm and then summing these squares. For the provided sales figures, you first need to convert the sales into market share percentages, then square these percentages and add them up:

• Market share of the first firm: (200 / 440) × 100 = 45.45%
• Market share of the second firm: (100 / 440) × 100 = 22.73%
• Market share of the third firm: (50 / 440) × 100 = 11.36%
• Market share of the fourth firm: (60 / 440) × 100 = 13.64%
• Market share of the fifth firm: (20 / 440) × 100 = 4.55%
• Market share of the sixth firm: (10 / 440) × 100 = 2.27%

Next, square each of these market share percentages and sum them:

`\[ (45.45\%)^2 + (22.73\%)^2 + (11.36\%)^2 + (13.64\%)^2 + (4.55\%)^2 + (2.27\%)^2 \]`

= 2065.20 + 516.53 + 129.13 + 186.05 + 20.70 + 5.15 = 2922.76

The HHI for this industry is 2922.76, which we can round to 2923.

When compared to another industry with an HHI of 3000, it typically indicates a higher level of concentration and suggests that firms in that industry are likelier to have market power. An HHI over 2500 is often regarded as an indicator of high market concentration, potentially leading to less competition.