Dorchester County has the following five banks in its market area:
$\begin{array} { l c }
\text { Bank } & \text { Total Assets } \
\text { First National Bank, NA } & \$ 1,500 \text { million } \
\text { Dorehester County Bank } & \$ 750 \text { million } \
\text { First State Bank } & \$ 500 \text { million } \
\text { Summerfield Bank } & \$ 250 \text { million } \
\text { Charlestown Bank } & \$ 250 \text { million } \
\text { All Banks } & \$ 3,250 \text { million }
\end{array}$
-There are 10 banks in a particular market area all with a market share of 10 percent.Two of the banks plan to merge.What would the Herfindahl-Hirschman Index be after the merger?

Question

Dorchester County has the following five banks in its market area:
$\begin{array} { l c } 
\text { Bank } & \text { Total Assets } \
\text { First National Bank, NA } & \$ 1,500 \text { million } \
\text { Dorehester County Bank } & \$ 750 \text { million } \
\text { First State Bank } & \$ 500 \text { million } \
\text { Summerfield Bank } & \$ 250 \text { million } \
\text { Charlestown Bank } & \$ 250 \text { million } \
\text { All Banks } & \$ 3,250 \text { million }
\end{array}$
-There are 10 banks in a particular market area all with a market share of 10 percent.Two of the banks plan to merge.What would the Herfindahl-Hirschman Index be after the merger?

Quizplus · Accepted Answer

HHI is calculated by summing the squared market shares of all firms in the market. Before the merger, each of the 10 banks had a 10% market share, leading to an HHI of 10^2 * 10 = 1,000. After the merger, there will be 9 banks, with 2 banks having a combined market share of 20%, and the other 7 banks each having a market share of 10%. The HHI can be calculated as follows:

(0.1)^2 * 7 + (0.2)^2 * 2 + (0.1)^2 * 7 = 0.014 + 0.04 + 0.014 = 0.068
HHI = 68 * 100 = 1,200

Therefore, the HHI after the merger would be 1,200.

Dorchester County Has the Following Five Banks in Its Market