Question

{0.2 0.3 0.2

0.4 0.1 0.2

0.1 0.3 0.2}

 Give three industries having input coefficient matrix as above. Find the production of output of X1 X2 X3 IF THE final demand 10 5 6. Provide economic meaning of 0.1 and 0.4 if any

Answer 1

$$solution$$

given the input as :

$\begin{bmatrix} 0.2& 0.3 & 0.2 \\0.4& 0.1& 0.2\\ 0.1& 0.3& 0.2 \end{bmatrix}$

production of output$\ X1,X2,X3.$ is:

$\begin{bmatrix} 0.2& 0.3 & 0.2 \\0.4& 0.1& 0.2\\ 0.1& 0.3& 0.2 \end{bmatrix} \begin{bmatrix} X_1 \\ X_2\\ X_3 \end{bmatrix}=\begin{bmatrix} 10 \\5\\ 6 \end{bmatrix}$

$X_1=40\\ X_2=65\\ X_3=87.5$

$0.1$ or $\frac{1}{10}$ , $0.4$ or $\frac{4}{10}$ are used to show a fraction of a part/ production line used in obtaining the final product / output in this case.