The following three FIs dominate a local market and their total assets are given below. $$\begin{array} { | c | r | }
\hline \text { Institution } & \text { Asset Size } \
\hline \text { Bank A } & \text { \$50 million } \
\hline \text { Bank B } & \text { \$60 million } \
\hline \text { Bank C } & \text { \$90 million } \
\hline
\end{array}$$ If Bank C splits into two separate institutions at ½ its original size each, what is the new Herfindahl-Hirschman (HHI) Index?
A)60.
B)340.
C)2,538.
D)2,847.
E)10,000.

Question

The following three FIs dominate a local market and their total assets are given below. $$\begin{array} { | c | r | } 
\hline \text { Institution } & \text { Asset Size } \
\hline \text { Bank A } & \text { \$50 million } \
\hline \text { Bank B } & \text { \$60 million } \
\hline \text { Bank C } & \text { \$90 million } \
\hline
\end{array}$$ If Bank C splits into two separate institutions at ½ its original size each, what is the new Herfindahl-Hirschman (HHI) Index?
A)60.
B)340.
C)2,538.
D)2,847.
E)10,000.

Quizplus · Accepted Answer

The Herfindahl-Hirschman Index (HHI) is calculated by squaring the market share of each firm competing in the market and then summing the resulting numbers. After Bank C splits, we have Bank A with \$50 million, Bank B with \$60 million, and two new banks each with \$45 million (half of Bank C's original \$90 million). The total market is now \$200 million. The market shares are 25% for Bank A (\$50 million / \$200 million), 30% for Bank B (\$60 million / \$200 million), and 22.5% for each of the new banks (\$45 million / \$200 million). Squaring these and summing gives: $0.25^2 + 0.30^2 + 0.225^2 + 0.225^2 = 0.0625 + 0.09 + 0.050625 + 0.050625 = 0.25375$. Multiplying by 10,000 to convert to the HHI scale gives 2,537.5, which rounds to 2,538.

The Following Three FIs Dominate a Local Market and Their