Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.
-$$\mathrm { C } = \left[ \begin{array} { l l }
.4 & .3 \
.1 & .6
\end{array} \right] , \mathrm { d } = \left[ \begin{array} { l }
52 \
74
\end{array} \right]$$
A) $x = \left[ \begin{array} { r } 43 \ 4 \end{array} \right]$
B) $x = \left[ \begin{array} { r } 4 \ 24 \end{array} \right]$
C) $x = \left[ \begin{array} { l } 205 \ 236 \end{array} \right]$
D) $\mathbf { x } = \left[ \begin{array} { l } 43 \ 50 \end{array} \right]$

Question

Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.
-$$\mathrm { C } = \left[ \begin{array} { l l } 
.4 & .3 \
.1 & .6
\end{array} \right] , \mathrm { d } = \left[ \begin{array} { l } 
52 \
74
\end{array} \right]$$
A) $x = \left[ \begin{array} { r } 43 \ 4 \end{array} \right]$
B) $x = \left[ \begin{array} { r } 4 \ 24 \end{array} \right]$
C) $x = \left[ \begin{array} { l } 205 \ 236 \end{array} \right]$
D) $\mathbf { x } = \left[ \begin{array} { l } 43 \ 50 \end{array} \right]$

Quizplus · Accepted Answer

To find the production vector $x$ that satisfies demand, we use the formula $x = (I - C)^{-1}d$, where $I$ is the identity matrix, $C$ is the consumption matrix, and $d$ is the final demand vector. Calculating $(I - C)^{-1}d$ with the given $C$ and $d$ yields the production vector $x = \left[ \begin{array} { l } 205 \ 236 \end{array} \right]$.

Determine the Production Vector X That Will Satisfy Demand in an Economy