Mathematics II207910 marksNumerical: Leontief production modelThe Leontief input output model
The economy whose consumption matrix C is and the final demand is 50 units for manufacturing, 30 units for agriculture and 20 units for service. Find the production level x that will satisfy this demand.
The economy whose consumption matrix C is and the final demand is 50 units for manufacturing, 30 units for agriculture and 20 units for service. Find the production level x that will satisfy this demand.
$$C = \begin{bmatrix} 0.5 & 0.4 & 0.2 \ 0.2 & 0.3 & 0.1 \ 0.1 & 0.1 & 0.3 \end{bmatrix}$$
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- Consumption matrix: $$C = \begin{bmatrix} 0.5 & 0.4 & 0.2 \ 0.2 & 0.3 & 0.1 \ 0.1 & 0.1 & 0.3 \end{bmatrix}$$ - Final demand: $d = \begin{bmatrix} 50 \ 30 \ 20 \end{bmatrix}$ We solve $(I - C)x = d$. $$I - C = \begin{bmatrix} 0.5 & -0.4 & -0.2 \ -0.2 & 0.7 & -0.1 \ -0.1 & -0.1 & 0.7 \end{...