$~~~~~{ \text { Industry } \mathbf { X } } ~~~~~~~~~~~~~ { \text { Industry } \mathbf { Y } } \
\begin{array} { c c c c }
& \text { Market }& & { \text { Market } } \
\text { Firm } &\text { Share } & \text { Firm } & \text { Share } \
1 & .40 & 1 & .30 \
2 & .20 & 2 & .30 \
3 & .10 & 3 & .30 \
4 & .10 & 4 & .05 \
5 & .10 & 5 & .03 \
6 & .10 & 6 & .02
\end{array}$
-According to the Herfindahl-Hirschman Index,which is the more concentrated industry?

Question

$~~~~~{ \text { Industry } \mathbf { X } } ~~~~~~~~~~~~~ { \text { Industry } \mathbf { Y } } \
\begin{array} { c c c c } 
& \text { Market }& & { \text { Market } } \
\text { Firm } &\text { Share } & \text { Firm } & \text { Share } \
1 & .40 & 1 & .30 \
2 & .20 & 2 & .30 \
3 & .10 & 3 & .30 \
4 & .10 & 4 & .05 \
5 & .10 & 5 & .03 \
6 & .10 & 6 & .02
\end{array}$
-According to the Herfindahl-Hirschman Index,which is the more concentrated industry?

Quizplus · Accepted Answer

The Herfindahl-Hirschman Index (HHI) is calculated by squaring the market share of each firm and then summing the squares. For Industry X, HHI = $0.4^2 + 0.2^2 + 0.1^2 + 0.1^2 + 0.1^2 + 0.1^2 = 0.16 + 0.04 + 0.01 + 0.01 + 0.01 + 0.01 = 0.24$, or 2,400 when multiplied by 10,000. For Industry Y, HHI = $0.3^2 + 0.3^2 + 0.3^2 + 0.05^2 + 0.03^2 + 0.02^2 = 0.09 + 0.09 + 0.09 + 0.0025 + 0.0009 + 0.0004 = 0.2738$, or 2,738 when multiplied by 10,000. Therefore, Industry Y is more concentrated.

-According to the Herfindahl-Hirschman Index,which Is the More Concentrated Industry