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Question

Agriculture, oil. A country's economy is based on two sectors, agriculture, and oil. Production of a dollar's worth of agriculture requires an input of $0.40\$ 0.40 from agriculture and $0.35\$ 0.35 from oil. Production of a dollar's worth of oil requires an input of $0.20\$ 0.20 from agriculture and $0.05\$ 0.05 from oil. Find the output from each sector that is needed to satisfy a final demand of $40\$ 40 million for agriculture and $250\$ 250 million for oil.

Solution

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Answered 1 year ago
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The Technology matrix can be written as:

[0.40.20.350.05]\begin{bmatrix}0.4&0.2\\0.35&0.05\end{bmatrix}

We have the final demand as $40\$40 billion for agriculture and $250\$250 billion for oil. So we can write

D=[40250]D=\begin{bmatrix}40\\250\end{bmatrix}

First we need to find the value of (IM)(I-M), where II is the identity matrix.

[1001][0.40.20.350.05]=[0.60.20.350.95]\begin{bmatrix}1&0\\0&1\end{bmatrix}-\begin{bmatrix}0.4&0.2\\0.35&0.05\end{bmatrix}=\begin{bmatrix}\phantom{-}0.6&-0.2\\-0.35&\phantom{-}0.95\end{bmatrix}

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