1. **State the problem:** We need to calculate the Herfindahl-Hirschman Index (HHI) for three markets (A, B, and C) using the sales data provided. The HHI measures market concentration by summing the squares of the market shares of each firm. 2. **Formula for HHI:** $$\text{HHI} = \sum \left(\frac{\text{Firm Sales}}{\text{Total Market Sales}} \times 100\right)^2$$ This means we calculate each firm's market share as a percentage, square it, and then sum these squares. 3. **Calculate market shares for each firm:** - Market A total sales = 1570 - Largest firm share = $\frac{523}{1570} \times 100 \approx 33.31$% - 2nd largest = $\frac{447}{1570} \times 100 \approx 28.47$% - 3rd largest = $\frac{343}{1570} \times 100 \approx 21.85$% - 4th largest = $\frac{257}{1570} \times 100 \approx 16.37$% - Market B total sales = 11086 - Largest firm share = $\frac{10946}{11086} \times 100 \approx 98.74$% - 2nd largest = $\frac{97}{11086} \times 100 \approx 0.87$% - 3rd largest = $\frac{43}{11086} \times 100 \approx 0.39$% - 4th largest = $\frac{0}{11086} \times 100 = 0$% - Market C total sales = 1947 - Largest firm share = $\frac{1046}{1947} \times 100 \approx 53.70$% - 2nd largest = $\frac{901}{1947} \times 100 \approx 46.27$% - 3rd largest = $\frac{0}{1947} \times 100 = 0$% - 4th largest = $0$% 4. **Calculate HHI for each market:** - Market A: $$33.31^2 + 28.47^2 + 21.85^2 + 16.37^2 = 1109.3 + 810.3 + 477.5 + 268.0 = 2665.1$$ - Market B: $$98.74^2 + 0.87^2 + 0.39^2 + 0^2 = 9749.5 + 0.76 + 0.15 + 0 = 9750.4$$ - Market C: $$53.70^2 + 46.27^2 + 0 + 0 = 2883.7 + 2141.0 = 5024.7$$ 5. **Interpretation:** - Market B has the highest HHI (9750.4), indicating very high concentration (almost monopoly). - Market C has a medium HHI (5024.7), indicating moderate concentration. - Market A has the lowest HHI (2665.1), indicating lower concentration among the three. **Final answer:** - Highest HHI: Market B - Medium HHI: Market C - Lowest HHI: Market A This shows Market B is the most concentrated, Market A the least, and Market C in between.