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.
-$$\mathrm { C } = \left[ \begin{array} { l l l }
.2 & .1 & .1 \
.3 & .2 & .3 \
.4 & .1 & .3
\end{array} \right] , \mathrm { d } = \left[ \begin{array} { l }
213 \
323 \
298
\end{array} \right]$$
A) $\mathbf { x } = \left[ \begin{array} { r } 728 \ 978 \ - 302 \end{array} \right]$
B) $\mathbf { x } = \left[ \begin{array} { r } 108 \ 105 \ 91 \end{array} \right]$
C) $\mathbf { x } = \left[ \begin{array} { l } 105 \ 218 \ 207 \end{array} \right]$
D) $\mathbf { x } = \left[ \begin{array} { l } 482 \ 895 \ 829 \end{array} \right]$

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.
-$$\mathrm { C } = \left[ \begin{array} { l l l } 
.2 & .1 & .1 \
.3 & .2 & .3 \
.4 & .1 & .3
\end{array} \right] , \mathrm { d } = \left[ \begin{array} { l } 
213 \
323 \
298
\end{array} \right]$$
A) $\mathbf { x } = \left[ \begin{array} { r } 728 \ 978 \ - 302 \end{array} \right]$
B) $\mathbf { x } = \left[ \begin{array} { r } 108 \ 105 \ 91 \end{array} \right]$
C) $\mathbf { x } = \left[ \begin{array} { l } 105 \ 218 \ 207 \end{array} \right]$
D) $\mathbf { x } = \left[ \begin{array} { l } 482 \ 895 \ 829 \end{array} \right]$

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. After calculating, option D provides the correct production levels.

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