Final answer:
The Herfindahl-Hirschman Index (HHI) computed for the industry is 317 after rounding to the nearest integer. The four-firm concentration ratio (C4) for the three firms is 100%, representing the total market share accounted for by these firms.
Step-by-step explanation:
The Herfindahl-Hirschman Index (HHI) is a measure of market concentration, and it is calculated by summing the squared market shares of all firms in an industry. To compute the HHI for the given industry, we first find the market share of each firm by dividing each firm's sales by the total sales of all firms. Then, we square these market shares and sum them up. The total sales in the industry are $225,000 + $45,000 + $315,000 = $585,000. Here are the calculations:
- Firm 1: (225,000 / 585,000)² ≈ 0.1473²
- Firm 2: (45,000 / 585,000)² ≈ 0.0769²
- Firm 3: (315,000 / 585,000)² ≈ 0.5385²
By adding these together: HHI ≈ 0.1473² + 0.0769² + 0.5385² ≈ 21.701 + 5.923 + 289.792 ≈ 317.416 (rounded to 317).
The four-firm concentration ratio (C4) is calculated by summing the market shares of the four largest firms. However, since only three firms are given, we will add the market shares of all three firms, which results in a C4 ratio of:
C4 = (225,000 + 45,000 + 315,000) / 585,000 ≈ 1.0 or 100%.