Given the technology matrix A, and an external demand vector D, find the production vector X.
$A = \left[ \begin{array} { c c }
0.2 & 0.3 \
0 & 0.4
\end{array} \right]$ , $D = \left[ \begin{array} { l }
14,000 \
15,000
\end{array} \right]$
A) $X = \left[ \begin{array} { l }
26,875 \
25,000
\end{array} \right]$
B) $X = \left[ \begin{array} { l }
25,000 \
26,875
\end{array} \right]$
C) $X = \left[ \begin{array} { l }
53,750 \
26,875
\end{array} \right]$
D) $X = \left[ \begin{array} { l }
25,000 \
53,750
\end{array} \right]$
E) $X = \left[ \begin{array} { l }
53,750 \
53,750
\end{array} \right]$

Question

Given the technology matrix A, and an external demand vector D, find the production vector X.  
  $A = \left[ \begin{array} { c c } 
0.2 & 0.3 \
0 & 0.4
\end{array} \right]$ , $D = \left[ \begin{array} { l } 
14,000 \
15,000
\end{array} \right]$  
A) $X = \left[ \begin{array} { l } 
26,875 \
25,000
\end{array} \right]$
B)   $X = \left[ \begin{array} { l } 
25,000 \
26,875
\end{array} \right]$
C)   $X = \left[ \begin{array} { l } 
53,750 \
26,875
\end{array} \right]$
D)   $X = \left[ \begin{array} { l } 
25,000 \
53,750
\end{array} \right]$
E)   $X = \left[ \begin{array} { l } 
53,750 \
53,750
\end{array} \right]$

Quizplus · Accepted Answer

The production vector $X$ can be found using the formula $X = (I - A)^{-1}D$, where $I$ is the identity matrix. Calculating $(I - A)^{-1}D$ with the given $A$ and $D$ results in $X = \left[ \begin{array} { l } 26,875 \ 25,000 \end{array} \right]$.

Given the Technology Matrix A, and an External Demand Vector A=[0.20.300.4]A = \left[ \begin{array} { c c } 0.2 & 0.3 \\0 & 0.4\end{array} \right]A=[0.20​0.30.4​]

Given the Technology Matrix A, and an External Demand Vector $A = \left[ \begin{array} { c c } 0.2 & 0.3 \\0 & 0.4\end{array} \right]$