Concentration Ratio (CRn) Calculator
This tool calculates the Concentration Ratio (CRn) for a market. The CRn is the sum of the market share percentages of the top 'n' firms in the market. It's a simple measure of market concentration.
Enter the market share percentage for each relevant company, one per line or separated by commas. Then, specify the number of top companies ('n') you want to include in the ratio (e.g., 4 for CR4, 8 for CR8).
Note: Enter *market share percentages* (e.g., 15 for 15%). Ensure shares are non-negative. For simplicity, the tool calculates based on the numbers provided; their sum doesn't need to equal exactly 100, but they should represent shares.
Input Market Data
Understanding Concentration Ratio (CRn)
What is the Concentration Ratio?
The Concentration Ratio (CRn) is a measure used in economics and business to assess the level of competition within a market. It's calculated as the sum of the market shares of the largest 'n' firms in an industry. Common ratios include CR4 (sum of the top 4 firms' shares) and CR8 (sum of the top 8 firms' shares).
Concentration Ratio Formula
The formula is straightforward:
CRn = S1 + S2 + S3 + ... + Sn
Where S1 is the market share of the largest firm, S2 is the market share of the second largest firm, and so on, up to Sn for the n-th largest firm. The shares are typically expressed as percentages.
Interpreting the CRn Value
The value of the CRn ranges from 0% (a perfectly competitive market with infinite firms) to 100% (a monopoly or a market where the top 'n' firms account for the entire market). Generally:
- CR4 < 40%: Often considered a loose oligopoly or competitive market.
- CR4 ≥ 40%: Often considered a tight oligopoly.
- CR8 < 50%: Often considered a competitive market.
- CR8 ≥ 50%: Often considered an oligopoly.
- CR1 = 100%: Indicates a monopoly.
These are general guidelines; interpretation can vary by industry and regulatory body.
CRn vs. Herfindahl-Hirschman Index (HHI)
While the CRn is simple to calculate and understand, it has limitations. It doesn't capture the *distribution* of market share among the top firms (e.g., a CR4 of 60% could be one firm with 60% or four firms with 15% each). The Herfindahl-Hirschman Index (HHI), which sums the *squares* of individual market shares, is another common measure that gives more weight to firms with larger shares and provides a better indication of market power and potential anti-competitive concerns.
Concentration Ratio Examples
Click on an example to see the market data and calculated ratio:
Example 1: CR4 in a 6-Firm Market
Scenario: Calculate the CR4 for a market with 6 companies.
1. Market Shares (%): Firm A: 25, Firm B: 20, Firm C: 15, Firm D: 10, Firm E: 8, Firm F: 5.
2. Total Firms: 6. Target 'n': 4.
3. Sorted Shares (Descending): 25, 20, 15, 10, 8, 5
4. Top 4 Shares: 25, 20, 15, 10
5. Calculation: CR4 = 25 + 20 + 15 + 10 = 70
6. Result: CR4 = 70%.
Conclusion: This market is relatively concentrated, often considered a tight oligopoly.
Example 2: CR8 in a 12-Firm Market
Scenario: Calculate the CR8 for a market with 12 firms.
1. Market Shares (%): 18, 15, 12, 10, 8, 7, 6, 5, 4, 3, 2, 1.
2. Total Firms: 12. Target 'n': 8.
3. Sorted Shares: (Already sorted descending) 18, 15, 12, 10, 8, 7, 6, 5, 4, 3, 2, 1
4. Top 8 Shares: 18, 15, 12, 10, 8, 7, 6, 5
5. Calculation: CR8 = 18 + 15 + 12 + 10 + 8 + 7 + 6 + 5 = 81
6. Result: CR8 = 81%.
Conclusion: This market is highly concentrated among the top 8 firms.
Example 3: CR4 in a Fragmented Market
Scenario: Calculate CR4 for a market with many small firms.
1. Market Shares (%): 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, ... (Assume 20 firms total)
2. Total Firms: 20. Target 'n': 4.
3. Sorted Shares (Top portion): 5, 4, 4, 3, ...
4. Top 4 Shares: 5, 4, 4, 3
5. Calculation: CR4 = 5 + 4 + 4 + 3 = 16
6. Result: CR4 = 16%.
Conclusion: A CR4 of 16% suggests a relatively fragmented and competitive market.
Example 4: CR1 (Monopoly Case)
Scenario: Calculate CR1 for a market dominated by one firm.
1. Market Shares (%): Firm A: 95, Firm B: 2, Firm C: 1, Firm D: 1, Firm E: 1.
2. Total Firms: 5. Target 'n': 1.
3. Sorted Shares: 95, 2, 1, 1, 1
4. Top 1 Share: 95
5. Calculation: CR1 = 95
6. Result: CR1 = 95%.
Conclusion: A CR1 close to 100% indicates the market is effectively a monopoly for practical purposes.
Example 5: CR4 vs CR8 in the Same Market
Scenario: Compare CR4 and CR8 in a 10-firm market.
1. Market Shares (%): 30, 25, 15, 10, 5, 4, 3, 2, 1, 5 (Note: shares don't sum to 100, which is common with estimates).
2. Total Firms: 10.
3. Sorted Shares: 30, 25, 15, 10, 5, 5, 4, 3, 2, 1
4. Top 4 Shares: 30, 25, 15, 10. CR4 = 30 + 25 + 15 + 10 = 80%.
5. Top 8 Shares: 30, 25, 15, 10, 5, 5, 4, 3. CR8 = 30 + 25 + 15 + 10 + 5 + 5 + 4 + 3 = 97%.
6. Results: CR4 = 80%, CR8 = 97%.
Conclusion: Both ratios show high concentration, but CR8 captures more of the market if the firms outside the top 4 still hold significant combined share.
Example 6: Market with Equal Top Shares
Scenario: Calculate CR4 for a market where the top firms have equal shares.
1. Market Shares (%): 20, 20, 20, 20, 5, 5, 5, 5.
2. Total Firms: 8. Target 'n': 4.
3. Sorted Shares: 20, 20, 20, 20, 5, 5, 5, 5
4. Top 4 Shares: 20, 20, 20, 20
5. Calculation: CR4 = 20 + 20 + 20 + 20 = 80
6. Result: CR4 = 80%.
Conclusion: This indicates four equally dominant firms in a tight oligopoly.
Example 7: CR3 in a 5-Firm Market
Scenario: Calculate the Concentration Ratio for the top 3 firms in a 5-firm market.
1. Market Shares (%): 40, 30, 15, 10, 5.
2. Total Firms: 5. Target 'n': 3.
3. Sorted Shares: 40, 30, 15, 10, 5
4. Top 3 Shares: 40, 30, 15
5. Calculation: CR3 = 40 + 30 + 15 = 85
6. Result: CR3 = 85%.
Conclusion: The top 3 firms hold a very large share of this market.
Example 8: Market with Only 2 Firms (Calculate CR4)
Scenario: Calculate CR4 in a market with only two firms.
1. Market Shares (%): Firm X: 60, Firm Y: 40.
2. Total Firms: 2. Target 'n': 4.
3. Sorted Shares: 60, 40
4. Top 4 Shares: The tool will correctly identify there are only 2 firms and sum those available: 60, 40.
5. Calculation: CR4 (effectively CR2) = 60 + 40 = 100
6. Result: CR4 = 100%.
Conclusion: In a market with fewer firms than 'n', the CRn is the sum of *all* firms' shares. A CR4 of 100% with only two firms indicates a duopoly accounting for the entire market.
Example 9: Low Concentration Example
Scenario: Calculate CR4 for a market with many small competitors.
1. Market Shares (%): 2.1, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1.0, 0.9, ... (many small shares)
2. Total Firms: Many. Target 'n': 4.
3. Sorted Shares (Top 4): 2.1, 1.9, 1.8, 1.7, ...
4. Top 4 Shares: 2.1, 1.9, 1.8, 1.7
5. Calculation: CR4 = 2.1 + 1.9 + 1.8 + 1.7 = 7.5
6. Result: CR4 = 7.5%.
Conclusion: A CR4 below 10% strongly indicates a highly competitive and fragmented market.
Example 10: Using Sales Data (Concept)
Scenario: Calculate CR4 using company sales figures.
1. Annual Sales ($ million): Firm P: 500, Firm Q: 300, Firm R: 150, Firm S: 50, Firm T: 25.
2. Calculate Total Market Sales: 500 + 300 + 150 + 50 + 25 = 1025 million.
3. Calculate Market Share %:
- P: (500 / 1025) * 100 ≈ 48.78%
- Q: (300 / 1025) * 100 ≈ 29.27%
- R: (150 / 1025) * 100 ≈ 14.63%
- S: (50 / 1025) * 100 ≈ 4.88%
- T: (25 / 1025) * 100 ≈ 2.44%
4. Enter Market Share % into the Calculator: 48.78, 29.27, 14.63, 4.88, 2.44. Target 'n': 4.
5. Sorted Shares: 48.78, 29.27, 14.63, 4.88, 2.44
6. Top 4 Shares: 48.78, 29.27, 14.63, 4.88
7. Calculation: CR4 ≈ 48.78 + 29.27 + 14.63 + 4.88 = 97.56
8. Result: CR4 ≈ 97.6%.
Conclusion: This example shows how to derive market shares from sales before using the calculator. The CR4 indicates a very high concentration.
How to Use the Calculator
- Enter the market share percentage for each company in the large text box. Put each share on a new line or separate them with commas. Decimals are allowed.
- Enter the number 'n' for the top companies you want the ratio for (e.g., 4 for CR4) in the 'Number of Top Companies (n)' box. This must be a whole number, 1 or greater.
- Click the "Calculate Concentration Ratio" button.
- The tool will sort the shares, select the top 'n', sum them, and display the result as a percentage. It will also show which top shares were included.
- Error messages will appear if inputs are invalid (e.g., non-numeric entries, n is not a positive integer, or n is greater than the number of valid shares entered).
Frequently Asked Questions about Concentration Ratio
1. What is the Concentration Ratio (CRn)?
It's the sum of the market share percentages of the largest 'n' firms in a market. It's used to gauge market concentration.
2. What does a high CRn indicate?
A high CRn (closer to 100%) indicates a more concentrated market, suggesting less competition among the top firms.
3. What does a low CRn indicate?
A low CRn (closer to 0%) indicates a more fragmented and potentially more competitive market with many small players.
4. What is the difference between CR4 and CR8?
CR4 sums the market shares of the top 4 firms, while CR8 sums the market shares of the top 8 firms. CR8 will always be equal to or higher than CR4 for the same market data.
5. Do the market shares I enter need to sum to exactly 100%?
Ideally, if you had data for *all* firms, the total would be 100%. However, in practice, you often only have data for the significant players. The calculator works with the shares you provide, sorts them, and sums the top 'n'. It does not require the total to be 100%.
6. Can I use sales figures instead of market share percentages?
Yes, but you must first calculate the market share percentage for each company from the sales figures. To do this, divide each company's sales by the *total market sales* and multiply by 100. Then, enter these calculated percentages into the tool.
7. What is a typical range for CRn?
The CRn always falls between 0% and 100%. Markets with CR4 below 40% are often seen as less concentrated, while those above 40% are more concentrated. This is just a general guideline.
8. How is CRn different from the Herfindahl-Hirschman Index (HHI)?
The CRn is a simple sum of the top 'n' shares. HHI is the sum of the *squares* of *all* firms' shares. HHI gives more weight to larger firms and provides a more nuanced view of concentration than CRn.
9. What if I enter negative numbers for market share?
The calculator is designed to ignore negative numbers as market share cannot be negative. It will only process valid, non-negative numerical inputs.
10. What if the number 'n' I specify is greater than the total number of firms entered?
If 'n' is greater than the count of valid market shares you entered, the calculator will sum all the valid shares you provided. For example, if you enter 5 shares and ask for CR8, it will calculate CR5 (the sum of all 5 shares).
