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Question

# Boran Stockbrokers, Inc., selects four stocks for the purpose of developing its own index of stock market behavior. Prices per share for a 2007 base period, January 2009, and March 2009 follow. Base-year quantities are set on the basis of historical volumes for the four stocks.$\begin{matrix} \text{ } & \text{ } & \text{ } & \text{ } & \text{Price per Share (\)}\\ \text{ } & \text{ } & \text{2007} & \text{2007} & \text{January} & \text{March}\\ \text{Stock} & \text{Industry} & \text{Quantity} & \text{Base} & \text{2009} & \text{2009}\\ \hline \text{A} & \text{Oil} & \text{100} & \text{31.50} & \text{22.75} & \text{22.50}\\ \text{B} & \text{Computer} & \text{150} & \text{65.00} & \text{49.00} & \text{47.50}\\ \text{C} & \text{Steel} & \text{75} & \text{40.00} & \text{32.00} & \text{29.50}\\ \text{D} & \text{Real Estate} & \text{50} & \text{18.00} & \text{6.50} & \text{3.75}\\ \end{matrix}$Use the 2007 base period to compute the Boran index for January 2009 and March 2009. Comment on what the index tells you about what is happening in the stock market.

Solution

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$\boxed{\text{Weighted Aggregate Price Index in Period t : }\color{#4257b2}{I_t=\dfrac{\sum{P_{it}Q_i}}{\sum{P_{i0}Q_i}}(100)}}$

where

$P_{it}$ - unit price for item $i$ in period $t$

$P_{i0}$ - unit price for item $i$ in the base period

$Q_i$ - quantity of usage for item $i$

• {Boran index for January 2009}

\begin{align*} I_t &=\dfrac{\sum{P_{it}Q_i}}{\sum{P_{i0}Q_i}}(100)\\ &=\dfrac{22.75(100)+49.00(150)+32.00(75)+6.50(50)}{31.50(100)+65.00(150)+40.00(75)+18.00(50)}(100)\\ &\approx\boxed{73.5} \end{align*}

• {Boran index for March 2009}

\begin{align*} I_t &=\dfrac{\sum{P_{it}Q_i}}{\sum{P_{i0}Q_i}}(100)\\ &=\dfrac{22.50(100)+47.50(150)+29.50(75)+3.75(50)}{31.50(100)+65.00(150)+40.00(75)+18.00(50)}(100)\\ &\approx\boxed{70.1} \end{align*}

Thus, the stock market price decreases from January to March in 2009.

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