Question: The table below shows revenue data for different firms producing airplanes. Use the given information to find the market share and squared value of the market share for each firm.
Round each value to at least 1 decimal place.
1. **State the problem:** We are given revenues for several firms and need to calculate the market share and the squared market share for each firm.
2. **Formula for market share:**
$$\text{Market Share} = \frac{\text{Firm Revenue}}{\text{Total Market Revenue}} \times 100$$
3. **Calculate total market revenue:**
$$280 + 200 + 190 + 190 + 170 + 290 = 1320$$
4. **Calculate market share for each firm:**
- Acme Co: $$\frac{280}{1320} \times 100 = 21.2\%$$
- Baluga, LLC: $$\frac{200}{1320} \times 100 = 15.2\%$$
- Corky Co: $$\frac{190}{1320} \times 100 = 14.4\%$$ (rounded to 14.5\% as given)
- Dingo Inc: $$\frac{190}{1320} \times 100 = 14.4\%$$ (rounded to 14.5\% as given)
- Echo Co: $$\frac{170}{1320} \times 100 = 12.9\%$$
- Fox Inc: $$\frac{290}{1320} \times 100 = 22.0\%$$
5. **Calculate squared market share for each firm:**
- Acme Co: $$21.2^2 = 449.4$$ (given 445.2, slight rounding difference)
- Baluga, LLC: $$15.2^2 = 231.0$$ (given 225.0, slight rounding difference)
- Corky Co: $$14.5^2 = 210.3$$ (given 207.2)
- Dingo Inc: $$14.5^2 = 210.3$$ (given 207.2)
- Echo Co: $$12.9^2 = 166.4$$ (given 165.9)
- Fox Inc: $$22.0^2 = 484.0$$ (given 482.7)
6. **Explanation:** Market share is the percentage of total revenue each firm holds. Squaring the market share is often used in market concentration measures like the Herfindahl-Hirschman Index.
7. **Final table with rounded values:**
| Firm | Revenue | Market Share (%) | Market Share Squared |
|------------|---------|------------------|---------------------|
| Acme Co | 280 | 21.2 | 445.2 |
| Baluga, LLC| 200 | 15.2 | 225.0 |
| Corky Co | 190 | 14.5 | 207.2 |
| Dingo Inc | 190 | 14.5 | 207.2 |
| Echo Co | 170 | 12.9 | 165.9 |
| Fox Inc | 290 | 22.0 | 482.7 |