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# 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 $\ 0.40$ from agriculture and $\ 0.35$ from oil. Production of a dollar's worth of oil requires an input of $\ 0.20$ from agriculture and $\ 0.05$ from oil. Find the output from each sector that is needed to satisfy a final demand of $\ 40$ million for agriculture and $\ 250$ million for oil.

Solution

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The Technology matrix can be written as:

$\begin{bmatrix}0.4&0.2\\0.35&0.05\end{bmatrix}$

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

$D=\begin{bmatrix}40\\250\end{bmatrix}$

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

$\begin{bmatrix}1&0\\0&1\end{bmatrix}-\begin{bmatrix}0.4&0.2\\0.35&0.05\end{bmatrix}=\begin{bmatrix}\phantom{-}0.6&-0.2\\-0.35&\phantom{-}0.95\end{bmatrix}$

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